Merge branch 'norvig:main' into master
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Vladimir Lojanica
GitHub
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README.md
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<div align="right" style="text-align:right"><i>Peter Norvig<br><a href="https://github.com/norvig/pytudes/blob/master/LICENSE">MIT License</a><br>2015-2020</i></div>
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<div align="right" style="text-align:right"><i>Peter Norvig
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<br><a href="https://github.com/norvig/pytudes/blob/main/LICENSE">MIT License</a><br>2015-2020</i></div>
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# pytudes
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"An *étude* (a French word meaning *study*) is an instrumental musical composition, usually short, of considerable difficulty, and designed to provide practice material for perfecting a particular musical skill." — [Wikipedia](https://en.wikipedia.org/wiki/%C3%89tude)
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"An *étude* (a French word meaning *study*) is an instrumental musical composition, usually short, of considerable difficulty,
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and designed to provide practice material for perfecting a particular musical skill." — [*Wikipedia*](https://en.wikipedia.org/wiki/%C3%89tude)
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This project contains **pytudes**—Python programs, usually short, for perfecting particular programming skills.
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Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each notebook you can:
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This project contains **pytudes**—Python programs, usually short, for perfecting particular programming skills.
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# Who is this for?
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To continue the musical analogy, some people think of programming like [Spotify](http://spotify.com): they want to know how to install the app, find a good playlist, and hit the "play" button; after that they don't want to think about it. There are plenty of other tutorials that will tell you how to do the equivalent of that for various programming tasks—this one won't help. But if you think of programming like playing the piano—a craft that can take [years](https://norvig.com/21-days.html) to perfect—then I hope this collection can help.
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# Index of Jupyter (IPython) Notebooks
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For each notebook you can:
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- Click on [c](https://colab.research.google.com) to **run** the notebook on Colab
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- Click on [d](https://deepnote.com) to **run** the notebook on DeepNote
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- Click on [m](https://mybinder.org) to **run** the notebook on MyBinder
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@@ -16,115 +26,117 @@ Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each
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- Hover over the title to **view** a description.
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# Index of Jupyter (IPython) Notebooks
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|Run|Year|Programming Examples|
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|---|----|---|
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Advent-2020.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FAdvent-2020.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FAdvent-2020.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Advent-2020.ipynb) | <u>2020</u> | <b><a href="ipynb/Advent-2020.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2018 ">Advent of Code 2020</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Advent-2018.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FAdvent-2018.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FAdvent-2018.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Advent-2018.ipynb) | 2018 | <b><a href="ipynb/Advent-2018.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2018 ">Advent of Code 2018</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Advent%202017.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FAdvent%202017.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FAdvent%202017.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Advent%202017.ipynb) | 2017 | <b><a href="ipynb/Advent%202017.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2017">Advent of Code 2017</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Advent%20of%20Code.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FAdvent%20of%20Code.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FAdvent%20of%20Code.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Advent%20of%20Code.ipynb) | 2016 | <b><a href="ipynb/Advent%20of%20Code.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2016*">Advent of Code 2016</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Beal.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FBeal.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FBeal.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Beal.ipynb) | 2018 | <b><a href="ipynb/Beal.ipynb" title="A search for counterexamples to Beal's Conjecture">Beal's Conjecture Revisited</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Bike%20Speed%20versus%20Grade.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FBike%20Speed%20versus%20Grade.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FBike%20Speed%20versus%20Grade.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Bike%20Speed%20versus%20Grade.ipynb) | <u>2020</u> | <b><a href="ipynb/Bike%20Speed%20versus%20Grade.ipynb" title="Visualizing statistics about bike routes.">Bicycling Statistics</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Cant-Stop.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCant-Stop.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCant-Stop.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Cant-Stop.ipynb) | 2018 | <b><a href="ipynb/Cant-Stop.ipynb" title="Optimal play in a dice board game">Can't Stop</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Sierpinski.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FSierpinski.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FSierpinski.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Sierpinski.ipynb) | 2019 | <b><a href="ipynb/Sierpinski.ipynb" title="A surprising appearance of the Sierpinski triangle in a random walk between vertexes">Chaos with Triangles</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Life.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FLife.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FLife.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Life.ipynb) | 2017 | <b><a href="ipynb/Life.ipynb" title="The cellular automata zero-player game">Conway's Game of Life</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Maze.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FMaze.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FMaze.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Maze.ipynb) | <u>2020</u> | <b><a href="ipynb/Maze.ipynb" title="Make a maze by generating a random tree superimposed on a grid and solve it.">Generating and Solving Mazes</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/PhotoFocalLengths.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FPhotoFocalLengths.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FPhotoFocalLengths.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/PhotoFocalLengths.ipynb) | <u>2020</u> | <b><a href="ipynb/PhotoFocalLengths.ipynb" title="Generate charts of what focal lengths were used on a photo trip.">Photo Focal Lengths</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Pickleball.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FPickleball.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FPickleball.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Pickleball.ipynb) | 2018 | <b><a href="ipynb/Pickleball.ipynb" title="Scheduling a doubles tournament fairly and efficiently">Pickleball Tournament</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Project%20Euler%20Utils.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FProject%20Euler%20Utils.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FProject%20Euler%20Utils.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Project%20Euler%20Utils.ipynb) | 2017 | <b><a href="ipynb/Project%20Euler%20Utils.ipynb" title="My utility functions for the Project Euler problems, including `Primes` and `Factors`">Project Euler Utilities</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Electoral%20Votes.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FElectoral%20Votes.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FElectoral%20Votes.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Electoral%20Votes.ipynb) | <u>2020</u> | <b><a href="ipynb/Electoral%20Votes.ipynb" title="How many electoral votes would Trump get if he wins the state where he has positive net approval?">Tracking Trump: Electoral Votes</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2020.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2020.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2020.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2020.ipynb) | <u>2020</u> | <b><a href="ipynb/Advent-2020.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2020 ">Advent of Code 2020</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent-2018.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent-2018.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent-2018.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent-2018.ipynb) | 2018 | <b><a href="ipynb/Advent-2018.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2018 ">Advent of Code 2018</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent%202017.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent%202017.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent%202017.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent%202017.ipynb) | 2017 | <b><a href="ipynb/Advent%202017.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2017">Advent of Code 2017</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Advent%20of%20Code.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FAdvent%20of%20Code.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FAdvent%20of%20Code.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Advent%20of%20Code.ipynb) | 2016 | <b><a href="ipynb/Advent%20of%20Code.ipynb" title="Puzzle site with a coding puzzle each day for Advent 2016*">Advent of Code 2016</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Beal.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FBeal.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FBeal.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Beal.ipynb) | 2018 | <b><a href="ipynb/Beal.ipynb" title="A search for counterexamples to Beal's Conjecture">Beal's Conjecture Revisited</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Bike%20Speed%20versus%20Grade.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FBike%20Speed%20versus%20Grade.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FBike%20Speed%20versus%20Grade.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Bike%20Speed%20versus%20Grade.ipynb) | <u>2020</u> | <b><a href="ipynb/Bike%20Speed%20versus%20Grade.ipynb" title="Visualizing statistics about bike routes">Bicycling Statistics</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cant-Stop.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCant-Stop.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCant-Stop.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cant-Stop.ipynb) | 2018 | <b><a href="ipynb/Cant-Stop.ipynb" title="Optimal play in a dice board game">Can't Stop</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Sierpinski.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSierpinski.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSierpinski.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Sierpinski.ipynb) | 2019 | <b><a href="ipynb/Sierpinski.ipynb" title="A surprising appearance of the Sierpinski triangle in a random walk">Chaos with Triangles</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Life.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FLife.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FLife.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Life.ipynb) | 2017 | <b><a href="ipynb/Life.ipynb" title="The cellular automata zero-player game">Conway's Game of Life</a></b> |
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Maze.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FMaze.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FMaze.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Maze.ipynb) | <u>2020</u> | <b><a href="ipynb/Maze.ipynb" title="Make a maze by generating a random tree superimposed on a grid and solve it">Generating and Solving Mazes</a></b> |
|
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/PhotoFocalLengths.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPhotoFocalLengths.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPhotoFocalLengths.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/PhotoFocalLengths.ipynb) | <u>2020</u> | <b><a href="ipynb/PhotoFocalLengths.ipynb" title="Generate charts of what focal lengths were used on a photo trip">Photo Focal Lengths</a></b> |
|
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| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Pickleball.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPickleball.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPickleball.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Pickleball.ipynb) | 2018 | <b><a href="ipynb/Pickleball.ipynb" title="Scheduling a doubles tournament fairly and efficiently">Pickleball Tournament</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Project%20Euler%20Utils.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FProject%20Euler%20Utils.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FProject%20Euler%20Utils.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Project%20Euler%20Utils.ipynb) | 2017 | <b><a href="ipynb/Project%20Euler%20Utils.ipynb" title="My utility functions for the Project Euler problems, including `Primes` and `Factors`">Project Euler Utilities</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Electoral%20Votes.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FElectoral%20Votes.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FElectoral%20Votes.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Electoral%20Votes.ipynb) | <u>2020</u> | <b><a href="ipynb/Electoral%20Votes.ipynb" title="How many electoral votes would Trump get if he wins the state where he has positive net approval?">Tracking Trump: Electoral Votes</a></b> |
|
||||
|
||||
|Run|Year|Logic and Number Puzzles|
|
||||
|---|----|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Cryptarithmetic.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCryptarithmetic.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCryptarithmetic.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Cryptarithmetic.ipynb) | 2014 | <b><a href="ipynb/Cryptarithmetic.ipynb" title="Substitute digits for letters and make NUM + BER = PLAY">Cryptarithmetic</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Euler's%20Conjecture.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FEuler's%20Conjecture.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FEuler's%20Conjecture.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Euler's%20Conjecture.ipynb) | 2018 | <b><a href="ipynb/Euler's%20Conjecture.ipynb" title="Solving a 200-year-old puzzle by finding integers that satisfy a<sup>5</sup> + b<sup>5</sup> + c<sup>5</sup> + d<sup>5</sup> = e<sup>5</sup>">Euler's Sum of Powers Conjecture</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Countdown.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCountdown.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCountdown.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Countdown.ipynb) | <u>2020</u> | <b><a href="ipynb/Countdown.ipynb" title="Solving the equation 10 _ 9 _ 8 _ 7 _ 6 _ 5 _ 4 _ 3 _ 2 _ 1 = 2016. From an Alex Bellos puzzle">Four 4s, Five 5s, and Countdowns</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Socks.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FSocks.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FSocks.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Socks.ipynb) | 2019 | <b><a href="ipynb/Socks.ipynb" title="What is the probability that you will be able to pair up socks as you randomly pull them out of the dryer?">Pairing Socks</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Sicherman%20Dice.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FSicherman%20Dice.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FSicherman%20Dice.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Sicherman%20Dice.ipynb) | 2018 | <b><a href="ipynb/Sicherman%20Dice.ipynb" title="Find a pair of dice that is like a regular pair of dice, only different">Sicherman Dice</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Golomb-Puzzle.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FGolomb-Puzzle.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FGolomb-Puzzle.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Golomb-Puzzle.ipynb) | 2014 | <b><a href="ipynb/Golomb-Puzzle.ipynb" title="A Puzzle involving placing rectangles of different sizes inside a square">Sol Golomb's Rectangle Puzzle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/SquareSum.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FSquareSum.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FSquareSum.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/SquareSum.ipynb) | <u>2020</u> | <b><a href="ipynb/SquareSum.ipynb" title="Place the numbers from 1 to n in a chain such that adjacent pairs sum to a perfect square.">Square Sum Puzzle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Cheryl.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCheryl.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCheryl.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Cheryl.ipynb) | <u>2020</u> | <b><a href="ipynb/Cheryl.ipynb" title="Solving the *Cheryl's Birthday* logic puzzle">When is Cheryl's Birthday? (new: Mad Cheryl)</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Cheryl-and-Eve.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCheryl-and-Eve.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCheryl-and-Eve.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Cheryl-and-Eve.ipynb) | 2015 | <b><a href="ipynb/Cheryl-and-Eve.ipynb" title="Inventing new puzzles in the Style of Cheryl's Birthday">When Cheryl Met Eve: A Birthday Story</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/xkcd1313.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fxkcd1313.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fxkcd1313.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/xkcd1313.ipynb) | 2015 | <b><a href="ipynb/xkcd1313.ipynb" title="Find the smallest regular expression; inspired by Randall Munroe">xkcd 1313: Regex Golf</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/xkcd1313-part2.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fxkcd1313-part2.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fxkcd1313-part2.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/xkcd1313-part2.ipynb) | 2015 | <b><a href="ipynb/xkcd1313-part2.ipynb" title="Regex Golf: better, faster, funner. With Stefan Pochmann.">xkcd 1313: Regex Golf (Part 2: Infinite Problems)</a></b> |
|
||||
|---|---|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cryptarithmetic.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCryptarithmetic.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCryptarithmetic.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cryptarithmetic.ipynb) | 2014 | <b><a href="ipynb/Cryptarithmetic.ipynb" title="Substitute digits for letters and make NUM + BER = PLAY">Cryptarithmetic</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Euler's%20Conjecture.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FEuler's%20Conjecture.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FEuler's%20Conjecture.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Euler's%20Conjecture.ipynb) | 2018 | <b><a href="ipynb/Euler's%20Conjecture.ipynb" title="Solving a 200-year-old puzzle by finding integers that satisfy a<sup>5</sup> + b<sup>5</sup> + c<sup>5</sup> + d<sup>5</sup> = e<sup>5</sup>">Euler's Sum of Powers Conjecture</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Countdown.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCountdown.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCountdown.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Countdown.ipynb) | <u>2020</u> | <b><a href="ipynb/Countdown.ipynb" title="Solving the equation 10 _ 9 _ 8 _ 7 _ 6 _ 5 _ 4 _ 3 _ 2 _ 1 = 2016. From an Alex Bellos puzzle">Four 4s, Five 5s, and Countdowns</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/KenKen.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FKenKen.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FKenKen.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/KenKen.ipynb) | 2021 | <b><a href="ipynb/KenKen.ipynb" title="A Sudoku-like puzzle, but with arithmetic.">KenKen (Sudoku-like Puzzle)</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Socks.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSocks.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSocks.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Socks.ipynb) | 2019 | <b><a href="ipynb/Socks.ipynb" title="What is the probability that you will be able to pair up socks as you randomly pull them out of the dryer?">Pairing Socks</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Sicherman%20Dice.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSicherman%20Dice.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSicherman%20Dice.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Sicherman%20Dice.ipynb) | 2018 | <b><a href="ipynb/Sicherman%20Dice.ipynb" title="Find a pair of dice that is like a regular pair of dice, only different">Sicherman Dice</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Golomb-Puzzle.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FGolomb-Puzzle.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FGolomb-Puzzle.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Golomb-Puzzle.ipynb) | 2014 | <b><a href="ipynb/Golomb-Puzzle.ipynb" title="A Puzzle involving placing rectangles of different sizes inside a square">Sol Golomb's Rectangle Puzzle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/StarBattle.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStarBattle.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStarBattle.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/StarBattle.ipynb) | 2021 | <b><a href="ipynb/StarBattle.ipynb" title="Fill-in-the-grid puzzle similar to Sudoku">Star Battle (Sudoku-like Puzzle)</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Sudoku.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSudoku.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSudoku.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Sudoku.ipynb) | 2006 | <b><a href="ipynb/Sudoku.ipynb" title="Classic fill-in-the-grid puzzle">Sudoku</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SudokuJava.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSudokuJava.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSudokuJava.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SudokuJava.ipynb) | 2021 | <b><a href="ipynb/SudokuJava.ipynb" title="A version of the Sudoku solver using parallel threads and other optimizations">Sudoku: 100,000 puzzles/second in Java</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SquareSum.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSquareSum.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSquareSum.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SquareSum.ipynb) | <u>2020</u> | <b><a href="ipynb/SquareSum.ipynb" title="Place the numbers from 1 to n in a chain (or a circle) such that adjacent pairs sum to a perfect square">Square Sum Puzzle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCheryl.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCheryl.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cheryl.ipynb) | <u>2020</u> | <b><a href="ipynb/Cheryl.ipynb" title="Solving the *Cheryl's Birthday* logic puzzle">When is Cheryl's Birthday?</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCheryl-and-Eve.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCheryl-and-Eve.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Cheryl-and-Eve.ipynb) | 2015 | <b><a href="ipynb/Cheryl-and-Eve.ipynb" title="Inventing new puzzles in the Style of Cheryl's Birthday">When Cheryl Met Eve: A Birthday Story</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd1313.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fxkcd1313.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fxkcd1313.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/xkcd1313.ipynb) | 2015 | <b><a href="ipynb/xkcd1313.ipynb" title="Find the smallest regular expression; inspired by Randall Munroe">xkcd 1313: Regex Golf</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd1313-part2.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fxkcd1313-part2.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fxkcd1313-part2.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/xkcd1313-part2.ipynb) | 2015 | <b><a href="ipynb/xkcd1313-part2.ipynb" title="Regex Golf: better, faster, funner (with Stefan Pochmann)">xkcd 1313: Regex Golf (Part 2: Infinite Problems)</a></b> |
|
||||
|
||||
|Run|Year|The Riddler (from 538)|
|
||||
|---|----|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Riddler%20Battle%20Royale.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FRiddler%20Battle%20Royale.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FRiddler%20Battle%20Royale.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Riddler%20Battle%20Royale.ipynb) | 2017 | <b><a href="ipynb/Riddler%20Battle%20Royale.ipynb" title="A puzzle involving allocating your troops and going up against an opponent">Battle Royale</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/CrossProduct.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCrossProduct.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCrossProduct.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/CrossProduct.ipynb) | 2021 | <b><a href="ipynb/CrossProduct.ipynb" title="A puzzle where digits fill a table, subject to constraints on their products">CrossProduct</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/flipping.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fflipping.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fflipping.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/flipping.ipynb) | <u>2020</u> | <b><a href="ipynb/flipping.ipynb" title="Can you go through a deck of cards, guessing higher or lower correctly for each card?">Flipping Cards; A Guessing Game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/RiddlerLottery.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FRiddlerLottery.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FRiddlerLottery.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/RiddlerLottery.ipynb) | 2019 | <b><a href="ipynb/RiddlerLottery.ipynb" title="Can you find what lottery number tickets these five friends picked?">Lottery</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/NightKing.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FNightKing.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FNightKing.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/NightKing.ipynb) | 2019 | <b><a href="ipynb/NightKing.ipynb" title="A battle between the army of the dead and the army of the living">How Many Soldiers to Beat the Night King?</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Mean%20Misanthrope%20Density.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FMean%20Misanthrope%20Density.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FMean%20Misanthrope%20Density.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Mean%20Misanthrope%20Density.ipynb) | 2017 | <b><a href="ipynb/Mean%20Misanthrope%20Density.ipynb" title="How crowded will this neighborhood be, if nobody wants to live next door to anyone else?">Misanthropic Neighbors</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Orderable%20Cards.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FOrderable%20Cards.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FOrderable%20Cards.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Orderable%20Cards.ipynb) | 2018 | <b><a href="ipynb/Orderable%20Cards.ipynb" title="Can you get your hand of cards into a nice order with just one move?">Properly Ordered Card Hands</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/TourDe538.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FTourDe538.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FTourDe538.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/TourDe538.ipynb) | <u>2020</u> | <b><a href="ipynb/TourDe538.ipynb" title="Solve a puzzle involving the best pace for a bicycle race.">Tour de 538</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/TwelveBalls.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FTwelveBalls.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FTwelveBalls.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/TwelveBalls.ipynb) | <u>2020</u> | <b><a href="ipynb/TwelveBalls.ipynb" title="A puzzle where you are given some billiard balls and a balance scale, and asked to find the one ball that is heavier or lighter, in a limited number of weighings">Weighing Twelve Balls</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/war.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fwar.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fwar.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/war.ipynb) | <u>2020</u> | <b><a href="ipynb/war.ipynb" title="How likely is it to win a game of war in 26 turns?">War. What is it Good For?</a></b> |
|
||||
|---|---|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Riddler%20Battle%20Royale.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FRiddler%20Battle%20Royale.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FRiddler%20Battle%20Royale.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Riddler%20Battle%20Royale.ipynb) | 2017 | <b><a href="ipynb/Riddler%20Battle%20Royale.ipynb" title="A puzzle involving allocating your troops and going up against an opponent">Battle Royale</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/CrossProduct.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCrossProduct.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCrossProduct.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/CrossProduct.ipynb) | 2021 | <b><a href="ipynb/CrossProduct.ipynb" title="A puzzle where digits fill a table, subject to constraints on their products">CrossProduct</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/flipping.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fflipping.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fflipping.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/flipping.ipynb) | <u>2020</u> | <b><a href="ipynb/flipping.ipynb" title="Can you go through a deck of cards, guessing higher or lower correctly for each card?">Flipping Cards; A Guessing Game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/RiddlerLottery.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FRiddlerLottery.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FRiddlerLottery.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/RiddlerLottery.ipynb) | 2019 | <b><a href="ipynb/RiddlerLottery.ipynb" title="Can you find what lottery number tickets these five friends picked?">Lottery</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/NightKing.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FNightKing.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FNightKing.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/NightKing.ipynb) | 2019 | <b><a href="ipynb/NightKing.ipynb" title="A battle between the army of the dead and the army of the living">How Many Soldiers to Beat the Night King?</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Mean%20Misanthrope%20Density.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FMean%20Misanthrope%20Density.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FMean%20Misanthrope%20Density.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Mean%20Misanthrope%20Density.ipynb) | 2017 | <b><a href="ipynb/Mean%20Misanthrope%20Density.ipynb" title="How crowded will this neighborhood be, if nobody wants to live next door to anyone else?">Misanthropic Neighbors</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FOrderable%20Cards.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FOrderable%20Cards.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Orderable%20Cards.ipynb) | 2018 | <b><a href="ipynb/Orderable%20Cards.ipynb" title="Can you get your hand of cards into a nice order with just one move?">Properly Ordered Card Hands</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SplitStates.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSplitStates.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSplitStates.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SplitStates.ipynb) | 2021 | <b><a href="ipynb/SplitStates.ipynb" title="Split the US states into two near-halves by area.">Split the States</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TourDe538.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTourDe538.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTourDe538.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TourDe538.ipynb) | <u>2020</u> | <b><a href="ipynb/TourDe538.ipynb" title="Solve a puzzle involving the best pace for a bicycle race.">Tour de 538</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TwelveBalls.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTwelveBalls.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTwelveBalls.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TwelveBalls.ipynb) | <u>2020</u> | <b><a href="ipynb/TwelveBalls.ipynb" title="A puzzle where you are given some billiard balls and a balance scale, and asked to find the one ball that is heavier or lighter, in a limited number of weighings">Weighing Twelve Balls</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/war.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fwar.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fwar.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/war.ipynb) | <u>2020</u> | <b><a href="ipynb/war.ipynb" title="How likely is it to win a game of war in 26 turns?">War. What is it Good For?</a></b> |
|
||||
|
||||
|Run|Year|Word Puzzles|
|
||||
|---|----|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Boggle.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FBoggle.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FBoggle.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Boggle.ipynb) | <u>2020</u> | <b><a href="ipynb/Boggle.ipynb" title="Find all the words on a Boggle board; then find a board with a lot of words">Boggle / Inverse Boggle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/ElementSpelling.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FElementSpelling.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FElementSpelling.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/ElementSpelling.ipynb) | <u>2020</u> | <b><a href="ipynb/ElementSpelling.ipynb" title="Spelling words using the chemical element symbols, like CoIn">Chemical Element Spelling</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/equilength-numbers.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fequilength-numbers.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fequilength-numbers.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/equilength-numbers.ipynb) | <u>2020</u> | <b><a href="ipynb/equilength-numbers.ipynb" title="What number names have the same letter count as the number they name (such as FOUR)?">Equilength Numbers: FOUR = 4</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Gesture%20Typing.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FGesture%20Typing.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FGesture%20Typing.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Gesture%20Typing.ipynb) | 2017 | <b><a href="ipynb/Gesture%20Typing.ipynb" title="What word has the longest path on a gesture-typing smartphone keyboard?">Gesture Typing</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Ghost.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FGhost.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FGhost.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Ghost.ipynb) | 2017 | <b><a href="ipynb/Ghost.ipynb" title="The word game Ghost (add letters, try to avoid making a word)">Ghost: A Word game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/How%20to%20Do%20Things%20with%20Words.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FHow%20to%20Do%20Things%20with%20Words.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FHow%20to%20Do%20Things%20with%20Words.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/How%20to%20Do%20Things%20with%20Words.ipynb) | 2018 | <b><a href="ipynb/How%20to%20Do%20Things%20with%20Words.ipynb" title="Spelling Correction, Secret Codes, Word Segmentation, and more">How to Do Things with Words: NLP in Python</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/jotto.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fjotto.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fjotto.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/jotto.ipynb) | <u>2020</u> | <b><a href="ipynb/jotto.ipynb" title="The word guessing game Jotto">Jotto: A Word Guessing Game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Fred%20Buns.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FFred%20Buns.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FFred%20Buns.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Fred%20Buns.ipynb) | 2015 | <b><a href="ipynb/Fred%20Buns.ipynb" title="A tale of a bicycle combination lock that uses letters instead of digits. Inspired by Bike Snob NYC">Let's Code About Bike Locks</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Scrabble.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FScrabble.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FScrabble.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Scrabble.ipynb) | 2017 | <b><a href="ipynb/Scrabble.ipynb" title="Refactoring the Scrabble / Word with Friends game from Udacity 212">Scrabble: Refactoring a Crossword Game Program</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/SpellingBee.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FSpellingBee.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FSpellingBee.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/SpellingBee.ipynb) | <u>2020</u> | <b><a href="ipynb/SpellingBee.ipynb" title="Find the highest-scoring board for the NY Times Spelling Bee puzzle">Spelling Bee</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/PropositionalLogic.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FPropositionalLogic.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FPropositionalLogic.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/PropositionalLogic.ipynb) | 2017 | <b><a href="ipynb/PropositionalLogic.ipynb" title="Automatically convert informal English sentences into formal Propositional Logic">Translating English into Propositional Logic</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/pal3.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fpal3.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fpal3.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/pal3.ipynb) | 2017 | <b><a href="ipynb/pal3.ipynb" title="Searching for a long Panama-style palindrome, this time letter-by-letter">World's Longest Palindrome</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Portmantout.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FPortmantout.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FPortmantout.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Portmantout.ipynb) | <u>2020</u> | <b><a href="ipynb/Portmantout.ipynb" title="Find a word that squishes together a bunch of words">World's Shortest Portmantout Word</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/xkcd-Name-Dominoes.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fxkcd-Name-Dominoes.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fxkcd-Name-Dominoes.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/xkcd-Name-Dominoes.ipynb) | 2018 | <b><a href="ipynb/xkcd-Name-Dominoes.ipynb" title="Lay out dominoes legally; the dominoes have people names, not numbers">xkcd 1970: Name Dominoes</a></b> |
|
||||
|---|---|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Boggle.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FBoggle.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FBoggle.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Boggle.ipynb) | <u>2020</u> | <b><a href="ipynb/Boggle.ipynb" title="Find all the words on a Boggle board; then find a board with a lot of words">Boggle / Inverse Boggle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/ElementSpelling.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FElementSpelling.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FElementSpelling.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/ElementSpelling.ipynb) | <u>2020</u> | <b><a href="ipynb/ElementSpelling.ipynb" title="Spelling words using the chemical element symbols, like CoIn">Chemical Element Spelling</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/equilength-numbers.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fequilength-numbers.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fequilength-numbers.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/equilength-numbers.ipynb) | <u>2020</u> | <b><a href="ipynb/equilength-numbers.ipynb" title="What number names have the same letter count as the number they name (such as FOUR)?">Equilength Numbers: FOUR = 4</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Gesture%20Typing.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FGesture%20Typing.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FGesture%20Typing.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Gesture%20Typing.ipynb) | 2017 | <b><a href="ipynb/Gesture%20Typing.ipynb" title="What word has the longest path on a gesture-typing smartphone keyboard?">Gesture Typing</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Ghost.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FGhost.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FGhost.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Ghost.ipynb) | 2017 | <b><a href="ipynb/Ghost.ipynb" title="The word game Ghost (add letters, try to avoid making a word)">Ghost: A Word game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/How%20to%20Do%20Things%20with%20Words.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FHow%20to%20Do%20Things%20with%20Words.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FHow%20to%20Do%20Things%20with%20Words.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/How%20to%20Do%20Things%20with%20Words.ipynb) | 2018 | <b><a href="ipynb/How%20to%20Do%20Things%20with%20Words.ipynb" title="Spelling Correction, Secret Codes, Word Segmentation, and more">How to Do Things with Words: NLP in Python</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/jotto.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fjotto.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fjotto.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/jotto.ipynb) | <u>2020</u> | <b><a href="ipynb/jotto.ipynb" title="The word guessing game Jotto">Jotto: A Word Guessing Game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Fred%20Buns.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FFred%20Buns.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FFred%20Buns.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Fred%20Buns.ipynb) | 2015 | <b><a href="ipynb/Fred%20Buns.ipynb" title="A tale of a bicycle combination lock that uses letters instead of digits. Inspired by Bike Snob NYC">Let's Code About Bike Locks</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Scrabble.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FScrabble.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FScrabble.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Scrabble.ipynb) | 2017 | <b><a href="ipynb/Scrabble.ipynb" title="Refactoring the Scrabble / Word with Friends game from Udacity 212">Scrabble: Refactoring a Crossword Game Program</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/SpellingBee.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSpellingBee.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSpellingBee.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/SpellingBee.ipynb) | <u>2020</u> | <b><a href="ipynb/SpellingBee.ipynb" title="Find the highest-scoring board for the NY Times Spelling Bee puzzle">Spelling Bee</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/PropositionalLogic.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPropositionalLogic.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPropositionalLogic.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/PropositionalLogic.ipynb) | 2017 | <b><a href="ipynb/PropositionalLogic.ipynb" title="Automatically convert informal English sentences into formal Propositional Logic">Translating English into Propositional Logic</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/pal3.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fpal3.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fpal3.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/pal3.ipynb) | 2017 | <b><a href="ipynb/pal3.ipynb" title="Searching for a long Panama-style palindrome, this time letter-by-letter">World's Longest Palindrome</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Portmantout.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FPortmantout.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FPortmantout.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Portmantout.ipynb) | <u>2020</u> | <b><a href="ipynb/Portmantout.ipynb" title="Find a word that squishes together a bunch of words">World's Shortest Portmantout Word</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/xkcd-Name-Dominoes.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fxkcd-Name-Dominoes.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fxkcd-Name-Dominoes.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/xkcd-Name-Dominoes.ipynb) | 2018 | <b><a href="ipynb/xkcd-Name-Dominoes.ipynb" title="Lay out dominoes legally; the dominoes have people names, not numbers">xkcd 1970: Name Dominoes</a></b> |
|
||||
|
||||
|Run|Year|Probability and Uncertainty|
|
||||
|---|----|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Probability.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FProbability.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FProbability.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Probability.ipynb) | 2018 | <b><a href="ipynb/Probability.ipynb" title="Code and examples of the basic principles of Probability Theory">A Concrete Introduction to Probability</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/ProbabilityParadox.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FProbabilityParadox.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FProbabilityParadox.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/ProbabilityParadox.ipynb) | 2016 | <b><a href="ipynb/ProbabilityParadox.ipynb" title="Some classic paradoxes in Probability Theory, and how to think about disagreements">Probability, Paradox, and the Reasonable Person Principle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/ProbabilitySimulation.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FProbabilitySimulation.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FProbabilitySimulation.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/ProbabilitySimulation.ipynb) | <u>2020</u> | <b><a href="ipynb/ProbabilitySimulation.ipynb" title="When the sample space is too complex, simulations can estimate probabilities">Estimating Probabilities with Simulations</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Coin%20Flip.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FCoin%20Flip.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FCoin%20Flip.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Coin%20Flip.ipynb) | 2019 | <b><a href="ipynb/Coin%20Flip.ipynb" title="How to beat the Devil at his own game">The Devil and the Coin Flip Game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Dice%20Baseball.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FDice%20Baseball.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FDice%20Baseball.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Dice%20Baseball.ipynb) | <u>2020</u> | <b><a href="ipynb/Dice%20Baseball.ipynb" title="Simulating baseball games">Dice Baseball</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Economics.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FEconomics.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FEconomics.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Economics.ipynb) | 2018 | <b><a href="ipynb/Economics.ipynb" title="A simulation of a simple economic game">Economics Simulation</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/poker.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Fpoker.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Fpoker.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/poker.ipynb) | 2012 | <b><a href="ipynb/poker.ipynb" title="How do we decide which poker hand wins? Several variants of poker are considered.">Poker Hand Ranking</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/risk.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2Frisk.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2Frisk.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/risk.ipynb) | <u>2020</u> | <b><a href="ipynb/risk.ipynb" title="Determining who is likely to win an interminably long game of Risk">The Unfinished Game .... of Risk</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/WWW.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FWWW.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FWWW.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/WWW.ipynb) | 2019 | <b><a href="ipynb/WWW.ipynb" title="Computing the probability of winning the NBA title, for my home town Warriors, or any other team">WWW: Who Will Win (NBA Title)?</a></b> |
|
||||
|---|---|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Probability.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FProbability.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FProbability.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Probability.ipynb) | 2018 | <b><a href="ipynb/Probability.ipynb" title="Code and examples of the basic principles of Probability Theory">A Concrete Introduction to Probability</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/ProbabilityParadox.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FProbabilityParadox.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FProbabilityParadox.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/ProbabilityParadox.ipynb) | 2016 | <b><a href="ipynb/ProbabilityParadox.ipynb" title="Some classic paradoxes in Probability Theory, and how to think about disagreements">Probability, Paradox, and the Reasonable Person Principle</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/ProbabilitySimulation.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FProbabilitySimulation.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FProbabilitySimulation.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/ProbabilitySimulation.ipynb) | <u>2020</u> | <b><a href="ipynb/ProbabilitySimulation.ipynb" title="When the sample space is too complex, simulations can estimate probabilities">Estimating Probabilities with Simulations</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Coin%20Flip.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FCoin%20Flip.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FCoin%20Flip.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Coin%20Flip.ipynb) | 2019 | <b><a href="ipynb/Coin%20Flip.ipynb" title="How to beat the Devil at his own game">The Devil and the Coin Flip Game</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Dice%20Baseball.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDice%20Baseball.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDice%20Baseball.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Dice%20Baseball.ipynb) | <u>2020</u> | <b><a href="ipynb/Dice%20Baseball.ipynb" title="Simulating baseball games">Dice Baseball</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Economics.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FEconomics.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FEconomics.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Economics.ipynb) | 2018 | <b><a href="ipynb/Economics.ipynb" title="A simulation of a simple economic game">Economics Simulation</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/poker.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Fpoker.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Fpoker.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/poker.ipynb) | 2012 | <b><a href="ipynb/poker.ipynb" title="How do we decide which poker hand wins? Several variants of poker are considered">Poker Hand Ranking</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/risk.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2Frisk.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2Frisk.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/risk.ipynb) | <u>2020</u> | <b><a href="ipynb/risk.ipynb" title="Determining who is likely to win an interminably long game of Risk">The Unfinished Game .... of Risk</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/WWW.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FWWW.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FWWW.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/WWW.ipynb) | 2019 | <b><a href="ipynb/WWW.ipynb" title="Computing the probability of winning the NBA title, for my home town Warriors, or any other team">WWW: Who Will Win (NBA Title)?</a></b> |
|
||||
|
||||
|
||||
|Run|Year|Computer Science Algorithms and Concepts|
|
||||
|---|----|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Snobol.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FSnobol.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FSnobol.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Snobol.ipynb) | 2017 | <b><a href="ipynb/Snobol.ipynb" title="As a student, did you ever get a bad grade on a programming assignment? (Snobol, Concordance)">Bad Grade, Good Experience</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/BASIC.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FBASIC.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FBASIC.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/BASIC.ipynb) | 2017 | <b><a href="ipynb/BASIC.ipynb" title="How to write an interpreter for the BASIC programming language">BASIC Interpreter</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Convex%20Hull.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FConvex%20Hull.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FConvex%20Hull.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Convex%20Hull.ipynb) | 2017 | <b><a href="ipynb/Convex%20Hull.ipynb" title="A classic Computer Science Algorithm">Convex Hull Problem</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/How%20To%20Count%20Things.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FHow%20To%20Count%20Things.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FHow%20To%20Count%20Things.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/How%20To%20Count%20Things.ipynb) | <u>2020</u> | <b><a href="ipynb/How%20To%20Count%20Things.ipynb" title="Combinatorial math: how to count how many things there are, when there are a lot of them">How to Count Things</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/StableMatching.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FStableMatching.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FStableMatching.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/StableMatching.ipynb) | <u>2020</u> | <b><a href="ipynb/StableMatching.ipynb" title="What is the best way to pair up two groups with each other, obeying preferences?">Stable Matching Problem</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/Differentiation.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FDifferentiation.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FDifferentiation.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/Differentiation.ipynb) | 2017 | <b><a href="ipynb/Differentiation.ipynb" title="A computer algebra system that manipulates expressions, including symbolic differentiation">Symbolic Algebra, Simplification, and Differentiation</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/master/ipynb/TSP.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2FTSP.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2FTSP.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/master/ipynb/TSP.ipynb) | 2018 | <b><a href="ipynb/TSP.ipynb" title="Another of the classics">Traveling Salesperson Problem</a></b> |
|
||||
|---|---|---|
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Snobol.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FSnobol.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FSnobol.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Snobol.ipynb) | 2017 | <b><a href="ipynb/Snobol.ipynb" title="As a student, did you ever get a bad grade on a programming assignment? (Snobol, Concordance)">Bad Grade, Good Experience</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/BASIC.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FBASIC.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FBASIC.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/BASIC.ipynb) | 2017 | <b><a href="ipynb/BASIC.ipynb" title="How to write an interpreter for the BASIC programming language">BASIC Interpreter</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FConvex%20Hull.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FConvex%20Hull.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb) | 2017 | <b><a href="ipynb/Convex%20Hull.ipynb" title="A classic Computer Science Algorithm">Convex Hull Problem</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/How%20To%20Count%20Things.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FHow%20To%20Count%20Things.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FHow%20To%20Count%20Things.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/How%20To%20Count%20Things.ipynb) | <u>2020</u> | <b><a href="ipynb/How%20To%20Count%20Things.ipynb" title="Combinatorial math: how to count how many things there are, when there are a lot of them">How to Count Things</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/StableMatching.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FStableMatching.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FStableMatching.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/StableMatching.ipynb) | <u>2020</u> | <b><a href="ipynb/StableMatching.ipynb" title="What is the best way to pair up two groups with each other, obeying preferences?">Stable Matching Problem</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FDifferentiation.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FDifferentiation.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/Differentiation.ipynb) | 2017 | <b><a href="ipynb/Differentiation.ipynb" title="A computer algebra system that, including symbolic differentiation">Symbolic Algebra, Simplification, and Differentiation</a></b> |
|
||||
| [c](https://colab.research.google.com/github/norvig/pytudes/blob/main/ipynb/TSP.ipynb) [d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2FTSP.ipynb) [m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2FTSP.ipynb) [n](https://nbviewer.jupyter.org/github/norvig/pytudes/blob/main/ipynb/TSP.ipynb) | 2018 | <b><a href="ipynb/TSP.ipynb" title="Another of the classics">Traveling Salesperson Problem</a></b> |
|
||||
|
||||
|
||||
# Index of Python Files
|
||||
|
||||
| File | Description | Documentation |
|
||||
|:--|:----|----|
|
||||
|[beal.py](/blob/master/py/beal.py)|*Search for counterexamples to Beal's Conjecture*|[documentation](http://norvig.com/beal.html)|
|
||||
|[docex.py](/blob/master/py/docex.py)|*An obsolete framework for running unit tests, similar to `doctest`*||
|
||||
|[ibol.py](/blob/master/py/ibol.py)|*An Exercise in Species Barcoding*|[documentation](http://norvig.com/ibol.html)|
|
||||
|[lettercount.py](/blob/master/py/lettercount.py)|*Convert Google Ngram Counts to Letter Counts*|[documentation](http://norvig.com/mayzner.html)|
|
||||
|[lis.py](/blob/master/py/lis.py)|*Lisp Interpreter written in Python*|[documentation](http://norvig.com/lispy.html)|
|
||||
|[lispy.py](/blob/master/py/lispy.py)|*Even Better Lisp Interpreter written in Python*|[documentation](http://norvig.com/lispy2.html)|
|
||||
|[lispytest.py](/blob/master/py/lispytest.py)|*Tests for Lisp Interpreters*||
|
||||
|[pal.py](/blob/master/py/pal.py)|*Find long palindromes*|[documentation](http://norvig.com/palindrome.html)|
|
||||
|[pal2.py](/blob/master/py/pal2.py)|*Find longer palindromes*|[documentation](http://norvig.com/palindrome.html)|
|
||||
|[pal3.py](/blob/master/py/pal3.py)|*Find even longer palindromes*|[documentation](http://norvig.com/palindrome.html)|
|
||||
|[pytudes.py](/blob/master/py/pytudes.py)|*Pre-process text to generate this README.md file.*||
|
||||
|[py2html.py](/blob/master/py/py2html.py)|*Pretty-printer to format Python files as html*||
|
||||
|[SET.py](/blob/master/py/SET.py)|*Analyze the card game SET*|[documentation](http://norvig.com/SET.html)|
|
||||
|[spell.py](/blob/master/py/spell.py)|*Spelling corrector*|[documentation](http://norvig.com/spell-correct.html)|
|
||||
|[sudoku.py](/blob/master/py/sudoku.py)|*Program to solve sudoku puzzles*|[documentation](http://norvig.com/sudoku.html)|
|
||||
|[testaccum.py](/blob/master/py/testaccum.py)|*Tests for my failed Python `accumulation display` proposal*|[documentation](http://norvig.com/pyacc.html)|
|
||||
|[yaptu.py](/blob/master/py/yaptu.py)|*Yet Another Python Templating Utility*||
|
||||
|File|Description|Documentation|
|
||||
|---|---|---|
|
||||
|[beal.py](/py/beal.py)|*Search for counterexamples to Beal's Conjecture*|[documentation](http://norvig.com/beal.html)|
|
||||
|[docex.py](/py/docex.py)|*An obsolete framework for running unit tests, similar to `doctest`*||
|
||||
|[ibol.py](/py/ibol.py)|*An Exercise in Species Barcoding*|[documentation](http://norvig.com/ibol.html)|
|
||||
|[lettercount.py](/py/lettercount.py)|*Convert Google Ngram Counts to Letter Counts*|[documentation](http://norvig.com/mayzner.html)|
|
||||
|[lis.py](/py/lis.py)|*Lisp Interpreter written in Python*|[documentation](http://norvig.com/lispy.html)|
|
||||
|[lispy.py](/py/lispy.py)|*Even Better Lisp Interpreter written in Python*|[documentation](http://norvig.com/lispy2.html)|
|
||||
|[lispytest.py](/py/lispytest.py)|*Tests for Lisp Interpreters*||
|
||||
|[pal.py](/py/pal.py)|*Find long palindromes*|[documentation](http://norvig.com/palindrome.html)|
|
||||
|[pal2.py](/py/pal2.py)|*Find longer palindromes*|[documentation](http://norvig.com/palindrome.html)|
|
||||
|[pal3.py](/py/pal3.py)|*Find even longer palindromes*|[documentation](http://norvig.com/palindrome.html)|
|
||||
|[pytudes.py](/py/pytudes.py)|*Pre-process text to generate this README.md file.*||
|
||||
|[py2html.py](/py/py2html.py)|*Pretty-printer to format Python files as html*||
|
||||
|[SET.py](/py/SET.py)|*Analyze the card game SET*|[documentation](http://norvig.com/SET.html)|
|
||||
|[spell.py](/py/spell.py)|*Spelling corrector*|[documentation](http://norvig.com/spell-correct.html)|
|
||||
|[sudoku.py](/py/sudoku.py)|*Program to solve sudoku puzzles*|[documentation](http://norvig.com/sudoku.html)|
|
||||
|[testaccum.py](/py/testaccum.py)|*Tests for my failed Python `accumulation display` proposal*|[documentation](http://norvig.com/pyacc.html)|
|
||||
|[yaptu.py](/py/yaptu.py)|*Yet Another Python Templating Utility*||
|
||||
|
||||
# Etudes for Programmers
|
||||
I got the idea for the *"etudes"* part of the name from
|
||||
|
||||
713
ipynb/ClimbingWall.ipynb
Normal file
713
ipynb/ClimbingWall.ipynb
Normal file
File diff suppressed because one or more lines are too long
File diff suppressed because it is too large
Load Diff
@@ -1122,7 +1122,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"It is still surprising that we still have no efect from restricting trade."
|
||||
"It is still surprising that we still have no effect from restricting trade."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
993
ipynb/KenKen.ipynb
Normal file
993
ipynb/KenKen.ipynb
Normal file
File diff suppressed because one or more lines are too long
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -36,7 +36,7 @@
|
||||
" The set of all possible outcomes for the trial. \n",
|
||||
" <br>*For example,* `{1, 2, 3, 4, 5, 6}`.\n",
|
||||
"- **[Event](https://en.wikipedia.org/wiki/Event_(probability_theory%29):**\n",
|
||||
" A subset of outcomes that together have some property we are interested in.\n",
|
||||
" A subset of the sample space, a set of outcomes that together have some property we are interested in.\n",
|
||||
" <br>*For example, the event \"even die roll\" is the set of outcomes* `{2, 4, 6}`. \n",
|
||||
"- **[Probability](https://en.wikipedia.org/wiki/Probability_theory):**\n",
|
||||
" As Laplace said, the probability of an event with respect to a sample space is the \"number of favorable cases\" (outcomes from the sample space that are in the event) divided by the \"number of all the cases\" in the sample space (assuming \"nothing leads us to expect that any one of these cases should occur more than any other\"). Since this is a proper fraction, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n",
|
||||
@@ -2339,7 +2339,7 @@
|
||||
"def repeated_hist(dist, n=10**6, bins=100):\n",
|
||||
" \"Sample the distribution n times and make a histogram of the results.\"\n",
|
||||
" samples = [dist() for _ in range(n)]\n",
|
||||
" plt.hist(samples, bins=bins, normed=True)\n",
|
||||
" plt.hist(samples, bins=bins, density=True)\n",
|
||||
" plt.title('{} (μ = {:.1f})'.format(dist.__name__, mean(samples)))\n",
|
||||
" plt.grid(axis='x')\n",
|
||||
" plt.yticks([], '')\n",
|
||||
|
||||
860
ipynb/RaceTrack.ipynb
Normal file
860
ipynb/RaceTrack.ipynb
Normal file
File diff suppressed because one or more lines are too long
File diff suppressed because one or more lines are too long
719
ipynb/SplitStates.ipynb
Normal file
719
ipynb/SplitStates.ipynb
Normal file
@@ -0,0 +1,719 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div style=\"text-align:right\"><i>Peter Norvig<br>June 2021</i></div>\n",
|
||||
"\n",
|
||||
"# Split the States\n",
|
||||
"\n",
|
||||
"The [538 Riddler for 11 June 2021](https://fivethirtyeight.com/features/can-you-split-the-states/) poses this problem (paraphrased):\n",
|
||||
"\n",
|
||||
"> Given a map of the lower 48 states of the USA, remove a subset of the states so that the map is cut into two disjoint contiguous regions that are near-halves by area. Call the regions *A* and *B*, where *A* has the larger area. You can treat Michigan’s upper and lower peninsulas as two non-adjacent \"states,\" for a total of 49. \n",
|
||||
">\n",
|
||||
"> To be precise, 538's question is: \n",
|
||||
">\n",
|
||||
"> **1.** What states should you remove to maximize the area of *B*? What is *B*'s area and percent of the country's area?\n",
|
||||
">\n",
|
||||
"> There is some ambiguity in the phrase \"near-halves by area\" and [Philip Bump](https://twitter.com/pbump/status/1400185939629117442) is interested in a second question:\n",
|
||||
">\n",
|
||||
"> **2.** What states should you remove to minimize the difference of the area of *A* and the area of *B*? \n",
|
||||
">\n",
|
||||
"> Philip Bump hypothesized that {IL, MO, OK, NM} is the best subset to remove. Is he right?\n",
|
||||
"\n",
|
||||
"# Vocabulary terms \n",
|
||||
"\n",
|
||||
"Let's start by clarifying some concepts:\n",
|
||||
"- **State**: denoted by the standard 2-letter abbreviations like `'CA'` (plus `'UP'` and `'LP'` for the Michigan peninsulas). \n",
|
||||
"- **States**: a set of states; implemented as a (hashable) `frozenset`. I'll use `states('OR CA')` for `frozenset({'OR', 'CA'})`.\n",
|
||||
"- **Region**: a set of states that are **contiguous**—they are all connected by a single tree of **neighbor** relations.\n",
|
||||
"- **Neighbor**: a relation saying two states share a border. Implemented as [adjacency sets](https://en.wikipedia.org/wiki/Adjacency_list) in the dict `neighbors`.\n",
|
||||
"- **Cut**: a set of states that, when removed from the map, cuts the map into disjoint regions. \n",
|
||||
"- **Split**: a tuple `(A, B, C)`, where `A` and `B` are the two regions made by the cut `C`, with `A` larger than `B`.\n",
|
||||
"- **Border**: the states on the edge of the map (neighbors of Canada, Mexico, Atlantic, or Pacific).\n",
|
||||
"- **Area**: Each state has an area in square miles, given by the `areas` dict, and a region has a total area, given by the function `area`.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Code to implement the concepts: "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from typing import *\n",
|
||||
"from collections import defaultdict\n",
|
||||
"\n",
|
||||
"State = str # Two-letter abbrerviation\n",
|
||||
"States = frozenset # Any set of states\n",
|
||||
"Region = frozenset # A contiguous set of states\n",
|
||||
"Split = Tuple[Region, Region, Region] # (A, B, C) = (large region, small region, cut)\n",
|
||||
"\n",
|
||||
"def states(string) -> States: \"Set of states\"; return States(string.split())\n",
|
||||
"def statedict(**dic) -> dict: \"{State:States}\"; return {ST: states(dic[ST]) for ST in dic}\n",
|
||||
"\n",
|
||||
"neighbors = statedict( # https://theincidentaleconomist.com/wordpress/list-of-neighboring-states-with-stata-code/\n",
|
||||
" AK='', AL='FL GA MS TN', AR='LA MO MS OK TN TX', AZ='CA CO NM NV UT', CA='AZ NV OR', \n",
|
||||
" CO='AZ KS NE NM OK UT WY', CT='MA NY RI', DC='MD VA', DE='MD NJ PA', FL='AL GA', \n",
|
||||
" GA='AL FL NC SC TN', HI='', IA='IL MN MO NE SD WI', ID='MT NV OR UT WA WY', IL='IA IN KY MO WI', \n",
|
||||
" IN='IL KY LP MI OH', KS='CO MO NE OK', KY='IL IN MO OH TN VA WV', LA='AR MS TX', \n",
|
||||
" MA='CT NH NY RI VT', MD='DC DE PA VA WV', ME='NH', MI='IN OH WI', MN='IA ND SD WI', \n",
|
||||
" MO='AR IA IL KS KY NE OK TN', MS='AL AR LA TN', MT='ID ND SD WY', NC='GA SC TN VA', \n",
|
||||
" ND='MN MT SD', NE='CO IA KS MO SD WY', NH='MA ME VT', NJ='DE NY PA', NM='AZ CO OK TX UT', \n",
|
||||
" NV='AZ CA ID OR UT', NY='CT MA NJ PA VT', OH='IN KY LP MI PA WV', OK='AR CO KS MO NM TX', \n",
|
||||
" OR='CA ID NV WA', PA='DE MD NJ NY OH WV', RI='CT MA', SC='GA NC', SD='IA MN MT ND NE WY', \n",
|
||||
" TN='AL AR GA KY MO MS NC VA', TX='AR LA NM OK', UT='AZ CO ID NM NV WY', VA='DC KY MD NC TN WV', \n",
|
||||
" VT='MA NH NY', WA='ID OR', WI='IA IL MI MN UP', WV='KY MD OH PA VA', WY='CO ID MT NE SD UT', \n",
|
||||
" UP='WI', LP='IN OH')\n",
|
||||
"\n",
|
||||
"def area(states) -> int: \"Total area\"; return sum(areas[s] for s in states)\n",
|
||||
"\n",
|
||||
"areas = dict( # https://www.census.gov/geographies/reference-files/2010/geo/state-area.html\n",
|
||||
" AK=665384, AL=52420, AZ=113990, AR=53179, CA=163695, CO=104094, CT=5543, DE=2489, DC=68, \n",
|
||||
" FL=65758, GA=59425, HI=10932, ID=83569, IL=57914, IN=36420, IA=56273, KS=82278, KY=40408, \n",
|
||||
" LA=52378, ME=35380, MD=12406, MA=10554, MI=96714, MN=86936, MS=48432, MO=69707, MT=147040, \n",
|
||||
" NE=77348, NV=110572, NH=9349, NJ=8723, NM=121590, NY=54555, NC=53819, ND=70698, OH=44826, \n",
|
||||
" OK=69899, OR=98379, PA=46054, RI=1545, SC=32020, SD=77116, TN=42144, TX=268596, UT=84897, \n",
|
||||
" VT=9616, VA=42775, WA=71298, WV=24230, WI=65496, WY=97813, UP=16377, LP=80337) \n",
|
||||
"\n",
|
||||
"# Borders:\n",
|
||||
"north = states('WA ID MT ND MN WI MI UP IL IN LP OH PA NY VT NH ME') \n",
|
||||
"south = states('CA AZ NM TX LA MS AL FL') \n",
|
||||
"west = states('WA OR CA')\n",
|
||||
"east = states('ME NH MA RI CT NY NJ DE MD VA NC SC GA FL')\n",
|
||||
"border = north | south | west | east\n",
|
||||
"\n",
|
||||
"# \"Countries\":\n",
|
||||
"usa50 = States(areas) - states('DC UP LP') # 50 actual US states\n",
|
||||
"usa49 = States(areas) - states('AK HI DC MI') # lower 49 \"states\": MI split into UP, LP\n",
|
||||
"usa48 = States(areas) - states('AK HI DC UP LP') # lower 48 states\n",
|
||||
"four = states('UT CO AZ NM') # The \"four corners\" states\n",
|
||||
"western = states('WA OR CA ID NV UT AZ MT WY CO NM') # The 11 states west of the Rockies"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Strategy for answering the two questions\n",
|
||||
"\n",
|
||||
"My overall strategy:\n",
|
||||
"- Generate a large number of **cuts**. \n",
|
||||
"- For each cut *C*, determine the **split** into regions *A* and *B*. Discard cuts that don't produce exactly two regions.\n",
|
||||
"- Find the split that **maximizes** the area of *B*, and the split that **minimizes** the difference in area of *A* and *B*.\n",
|
||||
"\n",
|
||||
"# Making cuts\n",
|
||||
"\n",
|
||||
"Is it feasible to consider all possible cuts? A cut is a subset of the 49 states, so there are 2<sup>49</sup> or 500 trillion possible cuts, so **no**, we can't look at them all. I have four ideas to reduce the number of cuts considered:\n",
|
||||
"- **Limit the total area in a cut.** A large area in the cut means there won't be much area left to make *B* big. \n",
|
||||
"- **Limit the number of states in a cut.** Similarly, if there are too many states in a cut, there won't be many left for *A* or *B*.\n",
|
||||
"- **Make cuts contiguous.** Noncontiguous cuts can't be optimal for question 1, so I won't consider them for now.\n",
|
||||
"- **Make cuts go border-to-border.** A cut can produce exactly two regions only if (a) the cut runs from one place on the border to another place on the border or (b) the cut forms a \"donut\" that surrounds some interior region. The US map isn't big enough to support a decent-sized donut (there are only 14 non-border states, and only KS and NE are not neighbors of a border state). \n",
|
||||
"\n",
|
||||
"By default, the function `make_cuts` will yield all cuts that are contiguous regions up to twice the area and twice the number of states as the {IL, MO, NM, OK} cut, as long as they go from the north border of the US to the south border.\n",
|
||||
"\n",
|
||||
"It starts by building a set of regions where each region contains a single `start` state. Then in each iteration of the `while` loop, it yields each region from the current set of regions that intersects the `end` states, and creates a new set of regions formed by adding a neighboring state to a current region in all possible ways, as long as the area does not exceed `maxarea` and the size does not exceed `maxsize`. (On each iteration all the regions have the same size.)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"maxarea = 2 * area(states('IL MO NM OK'))\n",
|
||||
"\n",
|
||||
"def make_cuts(country, maxsize=8, maxarea=maxarea, start=north, end=south) -> Iterator[Region]:\n",
|
||||
" \"\"\"All contiguous regions up to `maxsize` and `maxarea` that contain a `start` and `end` state.\"\"\"\n",
|
||||
" regions = {Region({s}) for s in start & country} \n",
|
||||
" while regions:\n",
|
||||
" yield from filter(end.intersection, regions) \n",
|
||||
" regions = {region | {s1}\n",
|
||||
" for region in regions if len(region) + 1 <= maxsize \n",
|
||||
" for s in region for s1 in (neighbors[s] & country) - region\n",
|
||||
" if area(region) + areas[s1] <= maxarea} "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"For example, the north-south cuts of size up to 3 states:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{frozenset({'AZ', 'ID', 'UT'}),\n",
|
||||
" frozenset({'ID', 'NM', 'UT'}),\n",
|
||||
" frozenset({'CA', 'ID', 'OR'}),\n",
|
||||
" frozenset({'CA', 'ID', 'NV'}),\n",
|
||||
" frozenset({'AZ', 'ID', 'NV'}),\n",
|
||||
" frozenset({'CA', 'OR', 'WA'})}"
|
||||
]
|
||||
},
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"set(make_cuts(usa49, 3))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Making splits\n",
|
||||
"\n",
|
||||
"Now, given some cuts, the function `make_splits` creates **splits**: tuples `(A, B, C)`, where `A` and `B` are the two regions defined by the cut `C`, with `A` larger than `B`. A split requires that the cut divides the country into exactly two regions, but not all cuts do that. For example, the cut {WA, OR, CA} leaves only one region (consisting of all the other states). The cut {ID, OR, NV, AZ} leaves three regions: {WA}, {CA}, and {everything else}. To verify whether the cut makes two regions, `make_splits` first finds a maximal-size contiguous region `A` from the non-cut states, then finds a region `B` from the remaining states, then checks that `A` and `B` are non-empty and make up all the non-cut states.\n",
|
||||
"\n",
|
||||
"We find the extent of a region with the `floodfill` [algorithm](https://en.wikipedia.org/wiki/Flood_fill): it maintains a mutable `region` and a `frontier` of the states that neighbor the region but are not in the region. We iterate adding the frontier into the region and computing a new frontier until there is no new frontier. "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def make_splits(country, cuts) -> Iterator[Split]:\n",
|
||||
" \"\"\"For each cut C, find regions A and B and yield the Split (A, B, C) if valid.\"\"\"\n",
|
||||
" for C in cuts:\n",
|
||||
" noncut = country - C\n",
|
||||
" A = floodfill(noncut) \n",
|
||||
" B = floodfill(noncut - A)\n",
|
||||
" if A and B and (A | B | C == country):\n",
|
||||
" if area(B) > area(A): A, B = B, A # Ensure A larger than B\n",
|
||||
" B, A = sorted([A, B], key=area) \n",
|
||||
" yield (A, B, C)\n",
|
||||
" \n",
|
||||
"def floodfill(legal: States) -> Region:\n",
|
||||
" \"\"\"Starting at one state, fill out to all legal contiguous states.\"\"\"\n",
|
||||
" region = set() \n",
|
||||
" frontier = {min(legal)} if legal else None\n",
|
||||
" while frontier:\n",
|
||||
" region |= frontier\n",
|
||||
" frontier = {s1 for s in frontier for s1 in neighbors[s]\n",
|
||||
" if s1 in legal and s1 not in region}\n",
|
||||
" return Region(region)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"For example, the splits (*A*, *B*, *C*) of the western states from cuts *C* of size up to 3:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{(frozenset({'CO', 'MT', 'NM', 'WY'}),\n",
|
||||
" frozenset({'CA', 'NV', 'OR', 'WA'}),\n",
|
||||
" frozenset({'AZ', 'ID', 'UT'})),\n",
|
||||
" (frozenset({'CO', 'MT', 'NM', 'UT', 'WY'}),\n",
|
||||
" frozenset({'CA', 'OR', 'WA'}),\n",
|
||||
" frozenset({'AZ', 'ID', 'NV'})),\n",
|
||||
" (frozenset({'AZ', 'CO', 'MT', 'NM', 'UT', 'WY'}),\n",
|
||||
" frozenset({'OR', 'WA'}),\n",
|
||||
" frozenset({'CA', 'ID', 'NV'})),\n",
|
||||
" (frozenset({'AZ', 'CO', 'MT', 'NM', 'NV', 'UT', 'WY'}),\n",
|
||||
" frozenset({'WA'}),\n",
|
||||
" frozenset({'CA', 'ID', 'OR'}))}"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"set(make_splits(western, make_cuts(western, 3)))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# The answers\n",
|
||||
"\n",
|
||||
"The function `answers` puts it all together: makes cuts; makes splits from those cuts; finds the splits that answer the two questions; and depending on the value of the parameter `do`, either prints information in a pretty format, or returns the four values, or both. By default, just print."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def answers(country, maxsize=8, maxarea=maxarea, start=north, end=south, do='print') -> Optional[tuple]:\n",
|
||||
" \"\"\"Find the splits that answer the 2 questions.\n",
|
||||
" Print information in pretty format if 'print' is a substring of `do`.\n",
|
||||
" Return the tuple (cuts, splits, answer1, answer2) if 'return' is a substring of `do`.\"\"\"\n",
|
||||
" cuts = list(make_cuts(country, maxsize, maxarea, start, end))\n",
|
||||
" splits = list(make_splits(country, cuts))\n",
|
||||
" answer1 = max(splits, key=lambda s: area(s[1]))\n",
|
||||
" answer2 = min(splits, key=lambda s: area(s[0]) - area(s[1]))\n",
|
||||
" if 'print' in do:\n",
|
||||
" print(f'{len(country)} states ⇒ {len(cuts):,d} cuts',\n",
|
||||
" f'(maxsize ≤ {maxsize}, area ≤ {maxarea:,d}) ⇒ {len(splits):,d} splits.')\n",
|
||||
" show('1. Split that maximizes area(B)', country, answer1)\n",
|
||||
" show('2. Split that minimizes ∆ = area(A) - area(B)', country, answer2)\n",
|
||||
" if 'return' in do:\n",
|
||||
" return cuts, splits, answer1, answer2\n",
|
||||
" \n",
|
||||
"def show(title, country, split):\n",
|
||||
" \"\"\"Print a title, and a summary of the split in four rows. The columns shown are:\n",
|
||||
" 'region name|area|percent of country area|number of states in region|states in region'.\n",
|
||||
" The ∆ row of the table is not a region; it is the difference in area between A and B.\"\"\"\n",
|
||||
" A, B, C = split\n",
|
||||
" def print_row(name, region, sqmi): \n",
|
||||
" statelist = f'{len(region):2d}|{{{\",\".join(sorted(region))}}}' if region else ''\n",
|
||||
" print(f'{name}|{sqmi:9,d}|{sqmi/area(country):5.1%}|{statelist}')\n",
|
||||
" print(f'\\n{title}:')\n",
|
||||
" print_row('A', A, area(A))\n",
|
||||
" print_row('B', B, area(B))\n",
|
||||
" print_row('C', C, area(C))\n",
|
||||
" print_row('∆', '', area(A) - area(B))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"49 states ⇒ 43,901 cuts (maxsize ≤ 8, area ≤ 638,220) ⇒ 14,149 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,345,558|43.1%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"B|1,344,149|43.1%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"C| 430,653|13.8%| 5|{CO,IL,MO,NE,NM}\n",
|
||||
"∆| 1,409| 0.0%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,267,033|40.6%|14|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,UP,UT,WA,WI,WY}\n",
|
||||
"B|1,266,994|40.6%|27|{AL,AR,CT,DE,FL,GA,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TX,VA,VT,WV}\n",
|
||||
"C| 586,333|18.8%| 8|{CO,IL,IN,MO,NE,NM,SD,TN}\n",
|
||||
"∆| 39| 0.0%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"answers(usa49)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Adding DC\n",
|
||||
"\n",
|
||||
"Would anything change if we made DC a state (besides, obviously, the voting rights of the citizens)?"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"50 states ⇒ 45,810 cuts (maxsize ≤ 8, area ≤ 638,220) ⇒ 14,137 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,345,626|43.1%|30|{AL,AR,CT,DC,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"B|1,344,149|43.1%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"C| 430,653|13.8%| 5|{CO,IL,MO,NE,NM}\n",
|
||||
"∆| 1,477| 0.0%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,267,062|40.6%|28|{AL,AR,CT,DC,DE,FL,GA,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TX,VA,VT,WV}\n",
|
||||
"B|1,267,033|40.6%|14|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,UP,UT,WA,WI,WY}\n",
|
||||
"C| 586,333|18.8%| 8|{CO,IL,IN,MO,NE,NM,SD,TN}\n",
|
||||
"∆| 29| 0.0%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"answers(usa49 | {'DC'})"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The cuts are the same, but for question 2, adding DC's 68 square miles to the eastern region means that it is now only 29 square miles larger than the western region (previously it was 39 square miles smaller)."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Reuniting Michigan\n",
|
||||
"\n",
|
||||
"What if Michigan counts as one state, rather than two separate penninsulas? What if we then also add in DC?"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"48 states ⇒ 43,941 cuts (maxsize ≤ 8, area ≤ 638,220) ⇒ 19,811 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,348,646|43.2%|30|{AL,CT,DE,FL,GA,IA,IL,IN,KY,MA,MD,ME,MI,MN,MT,NC,ND,NH,NJ,NY,OH,PA,RI,SC,SD,TN,VA,VT,WI,WV}\n",
|
||||
"B|1,341,666|43.0%|12|{AZ,CA,CO,KS,LA,NM,NV,OK,OR,TX,UT,WA}\n",
|
||||
"C| 430,048|13.8%| 6|{AR,ID,MO,MS,NE,WY}\n",
|
||||
"∆| 6,980| 0.2%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,267,816|40.6%|13|{AZ,CA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UT,WA}\n",
|
||||
"B|1,267,672|40.6%|28|{AL,AR,CT,DE,FL,GA,IL,IN,KY,LA,MA,MD,ME,MI,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 584,872|18.7%| 7|{CO,IA,MO,NM,OK,WI,WY}\n",
|
||||
"∆| 144| 0.0%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"answers(usa48)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"49 states ⇒ 45,856 cuts (maxsize ≤ 8, area ≤ 638,220) ⇒ 19,860 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,348,714|43.2%|31|{AL,CT,DC,DE,FL,GA,IA,IL,IN,KY,MA,MD,ME,MI,MN,MT,NC,ND,NH,NJ,NY,OH,PA,RI,SC,SD,TN,VA,VT,WI,WV}\n",
|
||||
"B|1,341,666|43.0%|12|{AZ,CA,CO,KS,LA,NM,NV,OK,OR,TX,UT,WA}\n",
|
||||
"C| 430,048|13.8%| 6|{AR,ID,MO,MS,NE,WY}\n",
|
||||
"∆| 7,048| 0.2%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,267,816|40.6%|13|{AZ,CA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UT,WA}\n",
|
||||
"B|1,267,740|40.6%|29|{AL,AR,CT,DC,DE,FL,GA,IL,IN,KY,LA,MA,MD,ME,MI,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 584,872|18.7%| 7|{CO,IA,MO,NM,OK,WI,WY}\n",
|
||||
"∆| 76| 0.0%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"answers(usa48 | {'DC'})"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The results are not as good (I think because splitting MI allows IL and IN to be north border states rather than interior states)."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Four-state cuts\n",
|
||||
"\n",
|
||||
"If we are restricted to four-state cuts, the proposed {IL, MO, NM, OK} cut is indeed best:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"49 states ⇒ 61 cuts (maxsize ≤ 4, area ≤ 638,220) ⇒ 45 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,607,869|51.5%|18|{AZ,CA,CO,IA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"B|1,193,381|38.2%|27|{AL,AR,CT,DE,FL,GA,IN,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 319,110|10.2%| 4|{IL,MO,NM,OK}\n",
|
||||
"∆| 414,488|13.3%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,607,869|51.5%|18|{AZ,CA,CO,IA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"B|1,193,381|38.2%|27|{AL,AR,CT,DE,FL,GA,IN,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 319,110|10.2%| 4|{IL,MO,NM,OK}\n",
|
||||
"∆| 414,488|13.3%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"answers(usa49, 4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Achieving equality on question 2\n",
|
||||
"\n",
|
||||
"Can we find regions with *exactly* equal areas (to the nearest square mile)? The function `make_equals` generates contiguous regions (up to maxsize 10 by default), keeping track of the areas, and when it finds a second disjoint region with the same area, it yields the two regions with their area. \n",
|
||||
"\n",
|
||||
"With `make_cuts` and `make_splits` we generated a contiguous cut first, then checked that the cut formed two valid regions. Now with `make_equals` we generate two equal-area regions first, then check that they are separated by a not-necessarily-contiguous cut."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def make_equals(country, maxsize=10) -> Iterator[Tuple[int, Region, Region]]:\n",
|
||||
" \"\"\"Yield (area, A, B) for disjoint regions A, B up to `maxsize` with exactly equal area.\"\"\"\n",
|
||||
" table = defaultdict(set) # {area: [regions_with_that_area...]}\n",
|
||||
" for A in make_cuts(country, maxsize, area(country) / 2, country, country):\n",
|
||||
" a = area(A)\n",
|
||||
" for B in table[a]:\n",
|
||||
" if separated(A, B):\n",
|
||||
" yield (a, A, B)\n",
|
||||
" table[a].add(A)\n",
|
||||
" \n",
|
||||
"def separated(A, B) -> bool: \n",
|
||||
" \"\"\"Are regions A and B disjoint with no shared border?\"\"\"\n",
|
||||
" return A.isdisjoint(B) and all(neighbors[a].isdisjoint(B) for a in A)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This is the first computation that will take more than a couple of seconds:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 47.6 s, sys: 525 ms, total: 48.2 s\n",
|
||||
"Wall time: 48.2 s\n",
|
||||
"\n",
|
||||
"Split with ∆ = 0:\n",
|
||||
"A| 874,595|28.0%|10|{AL,FL,GA,KS,LA,MS,NC,NM,OK,TX}\n",
|
||||
"B| 874,595|28.0%|10|{CA,IA,ID,IL,IN,MT,ND,NV,SD,WA}\n",
|
||||
"C|1,371,170|43.9%|29|{AR,AZ,CO,CT,DE,KY,LP,MA,MD,ME,MN,MO,NE,NH,NJ,NY,OH,OR,PA,RI,SC,TN,UP,UT,VA,VT,WI,WV,WY}\n",
|
||||
"∆| 0| 0.0%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%time equals = list(make_equals(usa49, 10))\n",
|
||||
"(a, A, B) = max(equals)\n",
|
||||
"show('Split with ∆ = 0', usa49, (A, B, usa49 - A - B))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"There may be larger regions with equal area. I searched up to `maxsize=12` and didn't find anything.\n",
|
||||
"<img src=\"map6.png\" width=690>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"A difference in area of ∆ = 0 is obviously an optimal answer to question 2. How about question 1? \n",
|
||||
"\n",
|
||||
"# Proving optimality on question 1\n",
|
||||
"\n",
|
||||
"We arbitrarily limited cuts to 8 states, going from the north to south border. To prove that we have the best cut, we'll have to eliminate those constraints, allowing cuts of any number of states going between any border states. This will increase run time, probably by an order of magnitude. Fortunately, we can tighten the area constraint a bit. We found that the cut {CO, IL, MO, NE, NM} produces a region *B* with area 1,344,149, so that means that any cut that is better for question 1 must create a split where the areas of both *A* and *B* are greater than 1,344,149, Therefore, we can lower the `maxarea` for the cut to:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"432062"
|
||||
]
|
||||
},
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"area(usa49) - 2 * 1344149"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"49 states ⇒ 547,779 cuts (maxsize ≤ 49, area ≤ 432,062) ⇒ 42,685 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,345,558|43.1%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"B|1,344,149|43.1%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"C| 430,653|13.8%| 5|{CO,IL,MO,NE,NM}\n",
|
||||
"∆| 1,409| 0.0%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,345,558|43.1%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"B|1,344,149|43.1%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"C| 430,653|13.8%| 5|{CO,IL,MO,NE,NM}\n",
|
||||
"∆| 1,409| 0.0%|\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"answers(usa49, maxsize=49, maxarea=area(usa49) - 2 * 1344149, start=border, end=border)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This confirms that {CO, IL, MO, NE, NM} is indeed the optimal cut for question 1."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Unit tests\n",
|
||||
"\n",
|
||||
"Here are some unit tests; they also serve as examples of input/output of the various functions:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"'ok'"
|
||||
]
|
||||
},
|
||||
"execution_count": 16,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"def test():\n",
|
||||
" assert states('AZ CA OR') == frozenset({'AZ', 'CA', 'OR'})\n",
|
||||
"\n",
|
||||
" assert len(usa48) == 48 and len(usa49) == 49 and len(usa50) == 50\n",
|
||||
" assert len(western) == 11 and len(four) == 4\n",
|
||||
" \n",
|
||||
" assert set(areas) == set(neighbors)\n",
|
||||
" assert areas['MI'] == areas['UP'] + areas['LP'] \n",
|
||||
" assert area(states('AZ CA OR')) == area(states('IA IL KY NE SD VA WV')) == 376_064\n",
|
||||
"\n",
|
||||
" assert all((x in neighbors[y]) == (y in neighbors[x]) \n",
|
||||
" for x in neighbors for y in neighbors)\n",
|
||||
" \n",
|
||||
" assert set(make_cuts(western, 3)) == {\n",
|
||||
" states('AZ ID NV'),\n",
|
||||
" states('CA ID OR'),\n",
|
||||
" states('CA OR WA'),\n",
|
||||
" states('CA ID NV'),\n",
|
||||
" states('ID NM UT'),\n",
|
||||
" states('AZ ID UT')}\n",
|
||||
"\n",
|
||||
" assert set(make_splits(western, make_cuts(western, 3))) == {\n",
|
||||
" (states('CO MT NM WY'), states('CA NV OR WA'), states('AZ ID UT')),\n",
|
||||
" (states('CO MT NM UT WY'), states('CA OR WA'), states('AZ ID NV')),\n",
|
||||
" (states('AZ CO MT NM UT WY'), states('OR WA'), states('CA ID NV')),\n",
|
||||
" (states('AZ CO MT NM NV UT WY'), states('WA'), states('CA ID OR'))}\n",
|
||||
"\n",
|
||||
" assert set(make_cuts(four, 4, maxarea, four, four)) == {\n",
|
||||
" states('UT'), states('CO'), states('AZ'), states('NM'),\n",
|
||||
" states('AZ CO'), states('AZ NM'), states('CO NM'), states('NM UT'), states('AZ UT'), states('CO UT'),\n",
|
||||
" states('AZ CO UT'), states('AZ CO NM'), states('CO NM UT'), states('AZ NM UT'),\n",
|
||||
" states('AZ CO NM UT')}\n",
|
||||
"\n",
|
||||
" assert floodfill(western - states('AZ ID NV')) == states('CA OR WA')\n",
|
||||
" \n",
|
||||
" for country in (usa48, usa49, border, western, four):\n",
|
||||
" assert floodfill(country) == country\n",
|
||||
" \n",
|
||||
" assert set(make_equals(usa49, 5)) == {\n",
|
||||
" (207853, states('LP MD OH PA WV'), states('IA MO UP WI')),\n",
|
||||
" (258498, states('AL KY MO NC TN'), states('ID SD WY'))}\n",
|
||||
" \n",
|
||||
" assert not separated(south, states('GA SC'))\n",
|
||||
" assert separated(north, south)\n",
|
||||
" \n",
|
||||
" return 'ok'\n",
|
||||
" \n",
|
||||
"test()"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.7.6"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 4
|
||||
}
|
||||
File diff suppressed because one or more lines are too long
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ipynb/SquareSum15.jpg
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ipynb/SquareSum15.jpg
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|
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456
ipynb/StarBattle.ipynb
Normal file
456
ipynb/StarBattle.ipynb
Normal file
@@ -0,0 +1,456 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div align=\"right\" style=\"text-align: right\"><i>Peter Norvig<br>Aug 2021</i></div>\n",
|
||||
"\n",
|
||||
"# Star Battle Puzzles\n",
|
||||
"\n",
|
||||
"If you thought this notebook was going to be about a video game like StarCraft®, I'm sorry to disapoint you. Instead it is about [**Star Battle puzzles**](https://www.puzzle-star-battle.com/), a genre of Sudoku-like puzzles with these properties:\n",
|
||||
"\n",
|
||||
"- Like Sudoku, you start with an *N*×*N* board and fill in cells.\n",
|
||||
"- Like Sudoku, an *N*×*N* board has 3*N* **units**: *N* columns, *N* rows, and *N* boxes.\n",
|
||||
"- Like Sudoku, a well-formed puzzle has exactly one solution.\n",
|
||||
"- Unlike Sudoku, the boxes have irregular shapes (not squares) and differing numbers of cells.\n",
|
||||
"- Unlike Sudoku, there are only 2 possible values for each cell: star or blank (not 9 digits).\n",
|
||||
"- Unlike Sudoku,\n",
|
||||
"- The constraints are:\n",
|
||||
" - Each unit (column, row, or box) must have exactly *S* stars.\n",
|
||||
" - Two stars cannot be adjacent (not even diagonally).\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Here is a board (*S*=2, *N*=10) and its solution from a helpful [Star Battle Rules and Info](https://www.gmpuzzles.com/blog/star-battle-rules-and-info/) page:\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"This “24”-themed puzzle was created by Thomas Snyder for the 24-Hours Puzzle Championship in Hungary in 2012.\n",
|
||||
"\n",
|
||||
"# Representation\n",
|
||||
"\n",
|
||||
"Here's how I will represent Star Battle puzzles:\n",
|
||||
"\n",
|
||||
"- A **cell** is an integer in `range(N * N)`.\n",
|
||||
" - The top row is cells 0, 1, 2, ... left-to-right; the second row is *N*, *N* + 1, *N* + 2, ...; etc.\n",
|
||||
"- A **unit** is a set of cells.\n",
|
||||
"- A **board** is a named tuple with the attributes:\n",
|
||||
" - `N`: the number of cells on each side of the *N*×*N* board.\n",
|
||||
" - `S`: the number of stars per unit in a solution.\n",
|
||||
" - `units`: a list of all the units on the board.\n",
|
||||
" - `units_for`: a dict where `units_for[c]` is a list of the units that cell `c` is in.\n",
|
||||
" - `pic`: a string; a graphical picture of the differently-shaped boxes.\n",
|
||||
"- An intermediate **state** in a search for a solution is a named tuple with the attributes:\n",
|
||||
" - `units`: list of units that have not yet been filled with *S* stars each.\n",
|
||||
" - `stars`: set of cells that have been determined (or guessed) to contain a star.\n",
|
||||
" - `unknowns`: set of cells that might contain either a star or a blank.\n",
|
||||
"- A **solution** is a set of cells where the stars go.\n",
|
||||
"- A **failure** to find a solution is indicated by `None`."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from collections import namedtuple\n",
|
||||
"from functools import lru_cache\n",
|
||||
"from typing import Optional, Iterator, Set, List\n",
|
||||
"\n",
|
||||
"Cell = int\n",
|
||||
"Board = namedtuple('Board', 'N, S, units, units_for, pic')\n",
|
||||
"State = namedtuple('State', 'units, stars, unknowns')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Representing Boards\n",
|
||||
"\n",
|
||||
"We can describe the differently-shaped boxes with a **picture** consisting of of *N* lines of *N* non-whitespace characters, where each of *N* distinct characters in the picture corresponds to a box, as in this picture of a 5×5 board with 5 boxes:\n",
|
||||
" \n",
|
||||
" , + ' ' '\n",
|
||||
" , + : : '\n",
|
||||
" , + : : .\n",
|
||||
" , . . . .\n",
|
||||
" , . . . ."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def make_board(S, picture) -> Board:\n",
|
||||
" \"\"\"Create a `Board` from a picture of the boxes.\"\"\"\n",
|
||||
" pic = ''.join(picture.split()) # eliminate whitespace from picture\n",
|
||||
" N = int(len(pic) ** 0.5) # N is √(number of cells)\n",
|
||||
" assert len(pic) == N * N\n",
|
||||
" side = range(0, N)\n",
|
||||
" cols = [{N * r + c for r in side} for c in side]\n",
|
||||
" rows = [{N * r + c for c in side} for r in side]\n",
|
||||
" boxes = [indexes(pic, ch) for ch in set(pic)] \n",
|
||||
" units = cols + rows + boxes\n",
|
||||
" units_for = {c: [u for u in units if c in u]\n",
|
||||
" for c in range(N * N)}\n",
|
||||
" return Board(N, S, units, units_for, pic)\n",
|
||||
"\n",
|
||||
"def indexes(sequence, item) -> Set[int]:\n",
|
||||
" \"\"\"All indexes in sequence where item appears.\"\"\"\n",
|
||||
" return {i for i in range(len(sequence)) if sequence[i] == item}"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Here's the 5×5 board, and the [board](https://krazydad.com/play/starbattle/?kind=10x10&volumeNumber=1&bookNumber=24&puzzleNumber=18) Barry Hayes shared to introduce me to this type of puzzle, and the \"24\" board. Note that in the \"24\" board the boxes \"2\" and \"t\" form interlocking figure 2s and the boxes \"4\" and \"f\" form interlocking figure 4s."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"board5x5 = make_board(1, \"\"\"\n",
|
||||
", + ' ' '\n",
|
||||
", + : : '\n",
|
||||
", + : : .\n",
|
||||
", . . . .\n",
|
||||
", . . . .\n",
|
||||
"\"\"\")\n",
|
||||
"\n",
|
||||
"board1 = make_board(2, \"\"\"\n",
|
||||
"` . . . . . | ; ; ;\n",
|
||||
"` . . . . . | ; ; ;\n",
|
||||
"` ` ` . . . | ; ; ;\n",
|
||||
"` , ` . . . . ; ; ;\n",
|
||||
", , , . . + + = = =\n",
|
||||
", , : : + + + + + +\n",
|
||||
", : : ' ' ' ' ' ' +\n",
|
||||
", : : - - ' ' ' ' '\n",
|
||||
", : : : - - - ' ' '\n",
|
||||
", , , - - - - ' ' '\n",
|
||||
"\"\"\") \n",
|
||||
"\n",
|
||||
"board24 = make_board(2, \"\"\"\n",
|
||||
". . . ' ' , , , , ,\n",
|
||||
". 2 2 2 ' 4 , 4 , -\n",
|
||||
". . . 2 ' 4 , 4 - -\n",
|
||||
". 2 2 2 ' 4 4 4 - -\n",
|
||||
". 2 t t t ; f 4 f -\n",
|
||||
". 2 2 2 t ; f 4 f -\n",
|
||||
". . t t t ; f f f -\n",
|
||||
": : t ; ; ; ; ; f -\n",
|
||||
": : t t t : - ; f -\n",
|
||||
": : : : : : - - - -\n",
|
||||
"\"\"\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solving Strategy\n",
|
||||
"\n",
|
||||
"I will solve puzzles using **depth-first search** with **constraint propagation**. \n",
|
||||
"\n",
|
||||
"By \"depth-first search\" I mean a procedure that starts from a current state, then creates a new state with a guess that a star should go into some cell *c*, and then tries to solve the rest of the puzzle from the new state. If there is no solution, back up to the old state and guess a different cell for the star. \n",
|
||||
"\n",
|
||||
"By \"constraint propagation\" I mean that whenever a star is placed, check what implications this has for the rest of the board: what blanks and/or stars *must* be placed in what cells. Constraint propagation may be able to prove that the original guess leads to failure, and it may make future guesses easier. \n",
|
||||
"\n",
|
||||
"Note that search always creates a new state for each guess (leaving the old state unaltered so that we can back up to it) and constraint propagation always mutates the state (because the changes are inevitable consequences, not guesses). \n",
|
||||
"\n",
|
||||
"# Constraint Propagation\n",
|
||||
"\n",
|
||||
"The constraint propagation rules are:\n",
|
||||
" \n",
|
||||
"When we **put a star** in a cell:\n",
|
||||
" - Mutate the current state by adding the cell to the set of stars and removing it from the unknowns.\n",
|
||||
" - If any of the cell's units has more than *S* stars, then fail (return `None`).\n",
|
||||
" - Put a blank in each adjacent cell. If you can't, fail.\n",
|
||||
"\n",
|
||||
"When we **put a blank** in a cell:\n",
|
||||
" - Mutate the current state by removing the cell from the unknowns.\n",
|
||||
" - For each of the cell's units:\n",
|
||||
" - If the number of stars plus unknown cells in the unit is less than *S*, then fail.\n",
|
||||
" - If the number equals *S*, then put stars in the unknown cells. If you can't, fail."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def put_star(cell, board, state) -> Optional[State]:\n",
|
||||
" \"\"\"Put a star on the board in the given cell. Mutates state.\n",
|
||||
" Return `None` if it is not possible to place star.\"\"\"\n",
|
||||
" if cell in state.stars:\n",
|
||||
" return state # Already put star in cell\n",
|
||||
" state.unknowns.remove(cell)\n",
|
||||
" state.stars.add(cell)\n",
|
||||
" for unit in board.units_for[cell]:\n",
|
||||
" if count_stars(unit, state) > board.S:\n",
|
||||
" return None\n",
|
||||
" for c in neighbors(cell, board.N):\n",
|
||||
" if c in state.stars or not put_blank(c, board, state):\n",
|
||||
" return None\n",
|
||||
" return state\n",
|
||||
" \n",
|
||||
"def put_blank(cell, board, state) -> Optional[State]:\n",
|
||||
" \"\"\"Put a blank on the board in the given cell. Mutates state.\n",
|
||||
" Return `None` if it is not possible to place blank.\"\"\"\n",
|
||||
" if cell not in state.unknowns:\n",
|
||||
" return state # Already put blank in cell\n",
|
||||
" state.unknowns.remove(cell)\n",
|
||||
" for unit in board.units_for[cell]:\n",
|
||||
" s = count_stars(unit, state)\n",
|
||||
" unknowns = unit & state.unknowns\n",
|
||||
" if s + len(unknowns) < board.S:\n",
|
||||
" return None\n",
|
||||
" if s + len(unknowns) == board.S:\n",
|
||||
" if not all(put_star(c, board, state) for c in unknowns):\n",
|
||||
" return None\n",
|
||||
" return state"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def count_stars(unit, state) -> int: return len(unit & state.stars)\n",
|
||||
"\n",
|
||||
"@lru_cache()\n",
|
||||
"def neighbors(cell, N) -> Set[Cell]:\n",
|
||||
" \"\"\"The set of cells that neighbor a given cell on an N×N board.\"\"\"\n",
|
||||
" dxs = {0, +1 if cell % N != N - 1 else 0, -1 if cell % N != 0 else 0}\n",
|
||||
" dys = {0, +N if cell + N < N ** 2 else 0, -N if cell >= N else 0}\n",
|
||||
" return {cell + dx + dy \n",
|
||||
" for dy in dys for dx in dxs if dx or dy}"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Depth-First Search\n",
|
||||
"\n",
|
||||
"Here are the two more main functions to do search:\n",
|
||||
"1. `solve(board)`: a wrapper function that calls `search` and prints the results.\n",
|
||||
"2. `search(board, state)`: where the real work of searching for a solution is done."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def solve(board) -> Set[Cell]:\n",
|
||||
" \"\"\"Call `search` with an initial state; print board and return solution stars.\n",
|
||||
" Raise an error if there is no solution.\"\"\"\n",
|
||||
" stars = next(search(board, initial_state(board))).stars\n",
|
||||
" print_board(board, stars)\n",
|
||||
" return stars\n",
|
||||
"\n",
|
||||
"def search(board, state) -> Iterator[State]:\n",
|
||||
" \"\"\"Recursive depth-first search for solution(s) to a Star Battle puzzle.\"\"\"\n",
|
||||
" while state.units and count_stars(state.units[0], state) == board.S:\n",
|
||||
" state.units.pop(0) # Discard filled unit(s)\n",
|
||||
" if not state.units: # Succeed\n",
|
||||
" yield state\n",
|
||||
" else: # Guess and recurse\n",
|
||||
" for c in state.units[0] & state.unknowns:\n",
|
||||
" guess_state = put_star(c, board, copy_state(state))\n",
|
||||
" if guess_state is not None:\n",
|
||||
" yield from search(board, guess_state)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The inputs to `search` are the static `board` and the dynamic `state` of computation, but what the output should be is less obvious; I considered two choices:\n",
|
||||
"1. `search` returns the first state that represents a solution, or `None` if there is no solution.\n",
|
||||
"2. `search` is a generator that yields all states that represent a solution.\n",
|
||||
"\n",
|
||||
"I decided on the second choice for `search`, even though `solve` only looks at the first solution. That way `search` could be used to verify that puzzles are well-formed, for example.`search` works as follows:\n",
|
||||
" - While the state's first unit is already filled with *S* stars, discard that unit and move on to the next one.\n",
|
||||
" - If the state has no remaining unfilled units, then succeed: yield the state.\n",
|
||||
" - Otherwise, guess and recurse: for each unknown cell *c* in the first unit, create a new state with a star in cell *c*, and if placing the star does not lead to constraint-propagation failure then recursively search from that state.\n",
|
||||
"\n",
|
||||
"Below are the remaining minor functions. *Note:* in `initial_state`, the `units` are `sorted` smallest-unit first, because if, say, a board has *S*=2 and the smallest unit has 3 cells, then you have a 2/3 chance of guessing correctly where the 2 stars should go. With larger units you would be more likely to guess wrong and waste time backing up, so better to do small units first and large units later, when constraint propagation has eliminated some unknown cells."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def copy_state(s: State): return State(s.units[:], set(s.stars), set(s.unknowns))\n",
|
||||
"\n",
|
||||
"def initial_state(board) -> State: \n",
|
||||
" \"\"\"The initial state to start the search for a solution to `board`.\"\"\"\n",
|
||||
" return State(units=sorted(board.units, key=len), \n",
|
||||
" stars=set(), unknowns=set(range(board.N ** 2)))\n",
|
||||
"\n",
|
||||
"def print_board(board, stars) -> None:\n",
|
||||
" \"\"\"Print a representation of the board before and after placing the stars.\n",
|
||||
" The output is not beautiful, but it is readable.\"\"\"\n",
|
||||
" N = board.N\n",
|
||||
" def row(chars, i) -> str: return ' '.join(chars[i * N:(i + 1) * N])\n",
|
||||
" filled = [('*' if c in stars else ch) for c, ch in enumerate(board.pic)]\n",
|
||||
" for i in range(N):\n",
|
||||
" print(row(board.pic, i), ' ' * N, row(filled, i))\n",
|
||||
" print('Valid' if is_solution(board, stars) else 'Invalid', 'solution')\n",
|
||||
" \n",
|
||||
"def is_solution(board, stars) -> bool:\n",
|
||||
" \"\"\"Verify that all units have S stars and that stars are non-adjacent.\"\"\"\n",
|
||||
" return (all(len(stars & unit) == board.S\n",
|
||||
" for unit in board.units) and\n",
|
||||
" all(c1 not in neighbors(c2, board.N)\n",
|
||||
" for c1 in stars for c2 in stars))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solutions\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"solve(board5x5)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"` . . . . . | ; ; ; ` . . . . . * ; * ;\n",
|
||||
"` . . . . . | ; ; ; ` * . . * . | ; ; ;\n",
|
||||
"` ` ` . . . | ; ; ; ` ` ` . . . * ; * ;\n",
|
||||
"` , ` . . . . ; ; ; * , * . . . . ; ; ;\n",
|
||||
", , , . . + + = = = , , , . . + + * = *\n",
|
||||
", , : : + + + + + + , , : * + * + + + +\n",
|
||||
", : : ' ' ' ' ' ' + , * : ' ' ' ' ' ' *\n",
|
||||
", : : - - ' ' ' ' ' , : : * - * ' ' ' '\n",
|
||||
", : : : - - - ' ' ' * : : : - - - * ' '\n",
|
||||
", , , - - - - ' ' ' , , * - * - - ' ' '\n",
|
||||
"Valid solution\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{6, 8, 11, 14, 26, 28, 30, 32, 47, 49, 53, 55, 61, 69, 73, 75, 80, 87, 92, 94}"
|
||||
]
|
||||
},
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"solve(board1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
". . . ' ' , , , , , . . . ' ' , * , , *\n",
|
||||
". 2 2 2 ' 4 , 4 , - . 2 * 2 * 4 , 4 , -\n",
|
||||
". . . 2 ' 4 , 4 - - * . . 2 ' 4 , * - -\n",
|
||||
". 2 2 2 ' 4 4 4 - - . 2 * 2 * 4 4 4 - -\n",
|
||||
". 2 t t t ; f 4 f - . 2 t t t ; f * f *\n",
|
||||
". 2 2 2 t ; f 4 f - * 2 2 2 t * f 4 f -\n",
|
||||
". . t t t ; f f f - . . t * t ; f f * -\n",
|
||||
": : t ; ; ; ; ; f - : * t ; ; * ; ; f -\n",
|
||||
": : t t t : - ; f - : : t * t : - ; * -\n",
|
||||
": : : : : : - - - - : * : : : : * - - -\n",
|
||||
"Valid solution\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{6, 9, 12, 14, 20, 27, 32, 34, 47, 49, 50, 55, 63, 68, 71, 75, 83, 88, 91, 96}"
|
||||
]
|
||||
},
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"solve(board24)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 195 ms, sys: 2.98 ms, total: 198 ms\n",
|
||||
"Wall time: 197 ms\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%%time\n",
|
||||
"for board in (board5x5, board1, board24):\n",
|
||||
" assert next(search(board, initial_state(board))).stars"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.7.6"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 4
|
||||
}
|
||||
BIN
ipynb/Sudoku$1.class
Normal file
BIN
ipynb/Sudoku$1.class
Normal file
Binary file not shown.
BIN
ipynb/Sudoku$2.class
Normal file
BIN
ipynb/Sudoku$2.class
Normal file
Binary file not shown.
BIN
ipynb/Sudoku.class
Normal file
BIN
ipynb/Sudoku.class
Normal file
Binary file not shown.
1017
ipynb/Sudoku.ipynb
Normal file
1017
ipynb/Sudoku.ipynb
Normal file
File diff suppressed because it is too large
Load Diff
488
ipynb/Sudoku.java
Normal file
488
ipynb/Sudoku.java
Normal file
@@ -0,0 +1,488 @@
|
||||
import java.io.*;
|
||||
import java.lang.Integer.*;
|
||||
import java.util.*;
|
||||
import java.util.stream.*;
|
||||
import java.lang.StringBuilder;
|
||||
import java.util.concurrent.CountDownLatch;
|
||||
|
||||
//////////////////////////////// Solve Sudoku Puzzles ////////////////////////////////
|
||||
//////////////////////////////// @author Peter Norvig ////////////////////////////////
|
||||
|
||||
/** There are two representations of puzzles that we will use:
|
||||
** 1. A gridstring is 81 chars, with characters '0' or '.' for blank and '1' to '9' for digits.
|
||||
** 2. A puzzle grid is an int[81] with a digit d (1-9) represented by the integer (1 << (d - 1));
|
||||
** that is, a bit pattern that has a single 1 bit representing the digit.
|
||||
** A blank is represented by the OR of all the digits 1-9, meaning that any digit is possible.
|
||||
** While solving the puzzle, some of these digits are eliminated, leaving fewer possibilities.
|
||||
** The puzzle is solved when every square has only a single possibility.
|
||||
**
|
||||
** Search for a solution with `search`:
|
||||
** - Fill an empty square with a guessed digit and do constraint propagation.
|
||||
** - If the guess is consistent, search deeper; if not, try a different guess for the square.
|
||||
** - If all guesses fail, back up to the previous level.
|
||||
** - In selecting an empty square, we pick one that has the minimum number of possible digits.
|
||||
** - To be able to back up, we need to keep the grid from the previous recursive level.
|
||||
** But we only need to keep one grid for each level, so to save garbage collection,
|
||||
** we pre-allocate one grid per level (there are 81 levels) in a `gridpool`.
|
||||
** Do constraint propagation with `arcConsistent`, `dualConsistent`, and `nakedPairs`.
|
||||
**/
|
||||
|
||||
public class Sudoku {
|
||||
|
||||
//////////////////////////////// main; command line options //////////////////////////////
|
||||
|
||||
static final String usage = String.join("\n",
|
||||
"usage: java Sudoku -(no)[fghnprstuv] | -[RT]<number> | <filename> ...",
|
||||
"E.g., -v turns verify flag on, -nov turns it off. -R and -T require a number. The options:\n",
|
||||
" -f(ile) Print summary stats for each file (default on)",
|
||||
" -g(rid) Print each puzzle grid and solution grid (default off)",
|
||||
" -h(elp) Print this usage message",
|
||||
" -n(aked) Run naked pairs (default on)",
|
||||
" -p(uzzle) Print summary stats for each puzzle (default off)",
|
||||
" -r(everse) Solve the reverse of each puzzle as well as each puzzle itself (default off)",
|
||||
" -s(earch) Run search (default on, but some puzzles can be solved with CSP methods alone)",
|
||||
" -t(hread) Print summary stats for each thread (default off)",
|
||||
" -u(nitTest)Run a suite of unit tests (default off)",
|
||||
" -v(erify) Verify each solution is valid (default on)",
|
||||
" -T<number> Concurrently run <number> threads (default 26)",
|
||||
" -R<number> Repeat each puzzle <number> times (default 1)",
|
||||
" <filename> Solve all puzzles in filename, which has one puzzle per line");
|
||||
|
||||
boolean printFileStats = true; // -f
|
||||
boolean printGrid = false; // -g
|
||||
boolean runNakedPairs = true; // -n
|
||||
boolean printPuzzleStats = false; // -p
|
||||
boolean reversePuzzle = false; // -r
|
||||
boolean runSearch = true; // -s
|
||||
boolean printThreadStats = false; // -t
|
||||
boolean verifySolution = true; // -v
|
||||
int nThreads = 26; // -T
|
||||
int repeat = 1; // -R
|
||||
|
||||
int backtracks = 0; // count total backtracks
|
||||
|
||||
/** Parse command line args and solve puzzles in files. **/
|
||||
public static void main(String[] args) throws IOException {
|
||||
Sudoku s = new Sudoku();
|
||||
for (String arg: args) {
|
||||
if (!arg.startsWith("-")) {
|
||||
s.solveFile(arg);
|
||||
} else {
|
||||
boolean value = !arg.startsWith("-no");
|
||||
switch(arg.charAt(value ? 1 : 3)) {
|
||||
case 'f': s.printFileStats = value; break;
|
||||
case 'g': s.printGrid = value; break;
|
||||
case 'h': System.out.println(usage); break;
|
||||
case 'n': s.runNakedPairs = value; break;
|
||||
case 'p': s.printPuzzleStats = value; break;
|
||||
case 'r': s.reversePuzzle = value; break;
|
||||
case 's': s.runSearch = value; break;
|
||||
case 't': s.printThreadStats = value; break;
|
||||
case 'u': s.runUnitTests(); break;
|
||||
case 'v': s.verifySolution = value; break;
|
||||
case 'T': s.nThreads = Integer.parseInt(arg.substring(2)); break;
|
||||
case 'R': s.repeat = Integer.parseInt(arg.substring(2)); break;
|
||||
default: System.out.println("Unrecognized option: " + arg + "\n" + usage);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Handling Lists of Puzzles ////////////////////////////////
|
||||
|
||||
/** Solve all the puzzles in a file. Report timing statistics. **/
|
||||
void solveFile(String filename) throws IOException {
|
||||
List<int[]> grids = readFile(filename);
|
||||
long startFileTime = System.nanoTime();
|
||||
switch(nThreads) {
|
||||
case 1: solveList(grids); break;
|
||||
default: solveListThreaded(grids, nThreads); break;
|
||||
}
|
||||
if (printFileStats) printStats(grids.size() * repeat, startFileTime, filename);
|
||||
}
|
||||
|
||||
|
||||
/** Solve a list of puzzles in a single thread.
|
||||
** repeat -R<number> times; print each puzzle's stats if -p; print grid if -g; verify if -v. **/
|
||||
void solveList(List<int[]> grids) {
|
||||
int[] puzzle = new int[N * N]; // Used to save a copy of the original grid
|
||||
int[][] gridpool = new int[N * N][N * N]; // Reuse grids during the search
|
||||
for (int g=0; g<grids.size(); ++g) {
|
||||
int grid[] = grids.get(g);
|
||||
System.arraycopy(grid, 0, puzzle, 0, grid.length);
|
||||
for (int i = 0; i < repeat; ++i) {
|
||||
long startTime = printPuzzleStats ? System.nanoTime() : 0;
|
||||
int[] solution = initialize(grid); // All the real work is
|
||||
if (runSearch) solution = search(solution, gridpool, 0); // on these 2 lines.
|
||||
if (printPuzzleStats) {
|
||||
printStats(1, startTime, "Puzzle " + (g + 1));
|
||||
}
|
||||
if (i == 0 && (printGrid || (verifySolution && !verify(solution, puzzle)))) {
|
||||
printGrids("Puzzle " + (g + 1), grid, solution);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/** Break a list of puzzles into nThreads sublists and solve each sublist in a separate thread. **/
|
||||
void solveListThreaded(List<int[]> grids, int nThreads) {
|
||||
try {
|
||||
final long startTime = System.nanoTime();
|
||||
int nGrids = grids.size();
|
||||
final CountDownLatch latch = new CountDownLatch(nThreads);
|
||||
int size = nGrids / nThreads;
|
||||
for (int c = 0; c < nThreads; ++c) {
|
||||
int end = c == nThreads - 1 ? nGrids : (c + 1) * size;
|
||||
final List<int[]> sublist = grids.subList(c * size, end);
|
||||
new Thread() {
|
||||
public void run() {
|
||||
solveList(sublist);
|
||||
latch.countDown();
|
||||
if (printThreadStats) {
|
||||
printStats(repeat * sublist.size(), startTime, "Thread");
|
||||
}
|
||||
}
|
||||
}.start();
|
||||
}
|
||||
latch.await(); // Wait for all threads to finish
|
||||
} catch (InterruptedException e) {
|
||||
System.err.println("And you may ask yourself, 'Well, how did I get here?'");
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Utility functions ////////////////////////////////
|
||||
|
||||
/** Return an array of all squares in the intersection of these rows and cols **/
|
||||
int[] cross(int[] rows, int[] cols) {
|
||||
int[] result = new int[rows.length * cols.length];
|
||||
int i = 0;
|
||||
for (int r: rows) { for (int c: cols) { result[i++] = N * r + c; } }
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
/** Return true iff item is an element of array, or of array[0:end]. **/
|
||||
boolean member(int item, int[] array) { return member(item, array, array.length); }
|
||||
boolean member(int item, int[] array, int end) {
|
||||
for (int i = 0; i<end; ++i) {
|
||||
if (array[i] == item) { return true; }
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Constants ////////////////////////////////
|
||||
|
||||
final int N = 9; // Number of cells on a side of grid.
|
||||
final int[] DIGITS = {1<<0, 1<<1, 1<<2, 1<<3, 1<<4, 1<<5, 1<<6, 1<<7, 1<<8};
|
||||
final int ALL_DIGITS = Integer.parseInt("111111111", 2);
|
||||
final int[] ROWS = IntStream.range(0, N).toArray();
|
||||
final int[] COLS = ROWS;
|
||||
final int[] SQUARES = IntStream.range(0, N * N).toArray();
|
||||
final int[][] BLOCKS = {{0, 1, 2}, {3, 4, 5}, {6, 7, 8}};
|
||||
final int[][] ALL_UNITS = new int[3 * N][];
|
||||
final int[][][] UNITS = new int[N * N][3][N];
|
||||
final int[][] PEERS = new int[N * N][20];
|
||||
final int[] NUM_DIGITS = new int[ALL_DIGITS + 1];
|
||||
final int[] HIGHEST_DIGIT = new int[ALL_DIGITS + 1];
|
||||
|
||||
{
|
||||
// Initialize ALL_UNITS to be an array of the 27 units: rows, columns, and blocks
|
||||
int i = 0;
|
||||
for (int r: ROWS) {ALL_UNITS[i++] = cross(new int[] {r}, COLS); }
|
||||
for (int c: COLS) {ALL_UNITS[i++] = cross(ROWS, new int[] {c}); }
|
||||
for (int[] rb: BLOCKS) {for (int[] cb: BLOCKS) {ALL_UNITS[i++] = cross(rb, cb); } }
|
||||
|
||||
// Initialize each UNITS[s] to be an array of the 3 units for square s.
|
||||
for (int s: SQUARES) {
|
||||
i = 0;
|
||||
for (int[] u: ALL_UNITS) {
|
||||
if (member(s, u)) UNITS[s][i++] = u;
|
||||
}
|
||||
}
|
||||
|
||||
// Initialize each PEERS[s] to be an array of the 20 squares that are peers of square s.
|
||||
for (int s: SQUARES) {
|
||||
i = 0;
|
||||
for (int[] u: UNITS[s]) {
|
||||
for (int s2: u) {
|
||||
if (s2 != s && !member(s2, PEERS[s], i)) {
|
||||
PEERS[s][i++] = s2;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Initialize NUM_DIGITS[val] to be the number of 1 bits in the bitset val
|
||||
// and HIGHEST_DIGIT[val] to the highest bit set in the bitset val
|
||||
for (int val = 0; val <= ALL_DIGITS; val++) {
|
||||
NUM_DIGITS[val] = Integer.bitCount(val);
|
||||
HIGHEST_DIGIT[val] = Integer.highestOneBit(val);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Search algorithm ////////////////////////////////
|
||||
|
||||
/** Search for a solution to grid. If there is an unfilled square, select one
|
||||
** and try--that is, search recursively--every possible digit for the square. **/
|
||||
int[] search(int[] grid, int[][] gridpool, int level) {
|
||||
if (grid == null) {
|
||||
return null;
|
||||
}
|
||||
int s = select_square(grid);
|
||||
if (s == -1) {
|
||||
return grid; // No squares to select means we are done!
|
||||
}
|
||||
for (int d: DIGITS) {
|
||||
// For each possible digit d that could fill square s, try it
|
||||
if ((d & grid[s]) > 0) {
|
||||
// Copy grid's contents into gridpool[level], and use that at the next level
|
||||
System.arraycopy(grid, 0, gridpool[level], 0, grid.length);
|
||||
int[] result = search(fill(gridpool[level], s, d), gridpool, level + 1);
|
||||
if (result != null) {
|
||||
return result;
|
||||
}
|
||||
backtracks += 1;
|
||||
}
|
||||
}
|
||||
return null;
|
||||
}
|
||||
|
||||
|
||||
/** Verify that grid is a solution to the puzzle. **/
|
||||
boolean verify(int[] grid, int[] puzzle) {
|
||||
if (grid == null) { return false; }
|
||||
// Check that all squares have a single digit, and
|
||||
// no filled square in the puzzle was changed in the solution.
|
||||
for (int s: SQUARES) {
|
||||
if ((NUM_DIGITS[grid[s]] != 1) || (NUM_DIGITS[puzzle[s]] == 1 && grid[s] != puzzle[s])) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
// Check that each unit is a permutation of digits
|
||||
for (int[] u: ALL_UNITS) {
|
||||
int unit_digits = 0; // All the digits in a unit.
|
||||
for (int s : u) {unit_digits |= grid[s]; }
|
||||
if (unit_digits != ALL_DIGITS) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
/** Choose an unfilled square with the minimum number of possible values.
|
||||
** If all squares are filled, return -1 (which means the puzzle is complete). **/
|
||||
int select_square(int[] grid) {
|
||||
int square = -1;
|
||||
int min = N + 1;
|
||||
for (int s: SQUARES) {
|
||||
int c = NUM_DIGITS[grid[s]];
|
||||
if (c == 2) {
|
||||
return s; // Can't get fewer than 2 possible digits
|
||||
} else if (c > 1 && c < min) {
|
||||
square = s;
|
||||
min = c;
|
||||
}
|
||||
}
|
||||
return square;
|
||||
}
|
||||
|
||||
|
||||
/** fill grid[s] = d. If this leads to contradiction, return null. **/
|
||||
int[] fill(int[] grid, int s, int d) {
|
||||
if ((grid == null) || ((grid[s] & d) == 0)) { return null; } // d not possible for grid[s]
|
||||
grid[s] = d;
|
||||
for (int p: PEERS[s]) {
|
||||
if (!eliminate(grid, p, d)) { // If we can't eliminate d from all peers of s, then fail
|
||||
return null;
|
||||
}
|
||||
}
|
||||
return grid;
|
||||
}
|
||||
|
||||
|
||||
/** Eliminate digit d as a possibility for grid[s].
|
||||
** Run the 3 constraint propagation routines.
|
||||
** If constraint propagation detects a contradiction, return false. **/
|
||||
boolean eliminate(int[] grid, int s, int d) {
|
||||
if ((grid[s] & d) == 0) { return true; } // d already eliminated from grid[s]
|
||||
grid[s] -= d;
|
||||
return arc_consistent(grid, s) && dual_consistent(grid, s, d) && naked_pairs(grid, s);
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Constraint Propagation ////////////////////////////////
|
||||
|
||||
/** Check if square s is consistent: that is, it has multiple possible values, or it has
|
||||
** one possible value which we can consistently fill. **/
|
||||
boolean arc_consistent(int[] grid, int s) {
|
||||
int count = NUM_DIGITS[grid[s]];
|
||||
return count >= 2 || (count == 1 && (fill(grid, s, grid[s]) != null));
|
||||
}
|
||||
|
||||
|
||||
/** After we eliminate d from possibilities for grid[s], check each unit of s
|
||||
** and make sure there is some position in the unit where d can go.
|
||||
** If there is only one possible place for d, fill it with d. **/
|
||||
boolean dual_consistent(int[] grid, int s, int d) {
|
||||
for (int[] u: UNITS[s]) {
|
||||
int dPlaces = 0; // The number of possible places for d within unit u
|
||||
int dplace = -1; // Try to find a place in the unit where d can go
|
||||
for (int s2: u) {
|
||||
if ((grid[s2] & d) > 0) { // s2 is a possible place for d
|
||||
dPlaces++;
|
||||
if (dPlaces > 1) break;
|
||||
dplace = s2;
|
||||
}
|
||||
}
|
||||
if (dPlaces == 0 || (dPlaces == 1 && (fill(grid, dplace, d) == null))) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
/** Look for two squares in a unit with the same two possible values, and no other values.
|
||||
** For example, if s and s2 both have the possible values 8|9, then we know that 8 and 9
|
||||
** must go in those two squares. We don't know which is which, but we can eliminate
|
||||
** 8 and 9 from any other square s3 that is in the unit. **/
|
||||
boolean naked_pairs(int[] grid, int s) {
|
||||
if (!runNakedPairs) { return true; }
|
||||
int val = grid[s];
|
||||
if (NUM_DIGITS[val] != 2) { return true; } // Doesn't apply
|
||||
for (int s2: PEERS[s]) {
|
||||
if (grid[s2] == val) {
|
||||
// s and s2 are a naked pair; find what unit(s) they share
|
||||
for (int[] u: UNITS[s]) {
|
||||
if (member(s2, u)) {
|
||||
for (int s3: u) { // s3 can't have either of the values in val (e.g. 8|9)
|
||||
if (s3 != s && s3 != s2) {
|
||||
int d = HIGHEST_DIGIT[val];
|
||||
int d2 = val - d;
|
||||
if (!eliminate(grid, s3, d) || !eliminate(grid, s3, d2)) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Input ////////////////////////////////
|
||||
|
||||
/** The method `readFile` reads one puzzle per file line and returns a List of puzzle grids. **/
|
||||
List<int[]> readFile(String filename) throws IOException {
|
||||
BufferedReader in = new BufferedReader(new FileReader(filename));
|
||||
List<int[]> grids = new ArrayList<int[]>(1000);
|
||||
String gridstring;
|
||||
while ((gridstring = in.readLine()) != null) {
|
||||
grids.add(parseGrid(gridstring));
|
||||
if (reversePuzzle) {
|
||||
grids.add(parseGrid(new StringBuilder(gridstring).reverse().toString()));
|
||||
}
|
||||
}
|
||||
return grids;
|
||||
}
|
||||
|
||||
|
||||
/** Parse a gridstring into a puzzle grid: an int[] with values DIGITS[0-9] or ALL_DIGITS. **/
|
||||
int[] parseGrid(String gridstring) {
|
||||
int[] grid = new int[N * N];
|
||||
int s = 0;
|
||||
for (int i = 0; i<gridstring.length(); ++i) {
|
||||
char c = gridstring.charAt(i);
|
||||
if ('1' <= c && c <= '9') {
|
||||
grid[s++] = DIGITS[c - '1']; // A single-bit set to represent a digit
|
||||
} else if (c == '0' || c == '.') {
|
||||
grid[s++] = ALL_DIGITS; // Any digit is possible
|
||||
}
|
||||
}
|
||||
assert s == N * N;
|
||||
return grid;
|
||||
}
|
||||
|
||||
|
||||
/** Initialize a grid from a puzzle.
|
||||
** First initialize every square in the new grid to ALL_DIGITS, meaning any value is possible.
|
||||
** Then, call `fill` on the puzzle's filled squares to initiate constraint propagation. **/
|
||||
int[] initialize(int[] puzzle) {
|
||||
int[] grid = new int[N * N]; Arrays.fill(grid, ALL_DIGITS);
|
||||
for (int s: SQUARES) { if (puzzle[s] != ALL_DIGITS) { fill(grid, s, puzzle[s]); } }
|
||||
return grid;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Output and Tests ////////////////////////////////
|
||||
|
||||
boolean headerPrinted = false;
|
||||
|
||||
/** Print stats on puzzles solved, average time, frequency, threads used, and name. **/
|
||||
void printStats(int nGrids, long startTime, String name) {
|
||||
double usecs = (System.nanoTime() - startTime) / 1000.;
|
||||
String line = String.format("%7d %6.1f %7.3f %7d %10.1f %s",
|
||||
nGrids, usecs / nGrids, 1000 * nGrids / usecs, nThreads, backtracks * 1. / nGrids, name);
|
||||
synchronized (this) { // So that printing from different threads doesn't get garbled
|
||||
if (!headerPrinted) {
|
||||
System.out.println("Puzzles μsec KHz Threads Backtracks Name\n"
|
||||
+ "======= ====== ======= ======= ========== ====");
|
||||
headerPrinted = true;
|
||||
}
|
||||
System.out.println(line);
|
||||
backtracks = 0;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/** Print the original puzzle grid and the solution grid. **/
|
||||
void printGrids(String name, int[] puzzle, int[] solution) {
|
||||
String bar = "------+-------+------";
|
||||
String gap = " "; // Space between the puzzle grid and solution grid
|
||||
if (solution == null) solution = new int[N * N];
|
||||
synchronized (this) { // So that printing from different threads doesn't get garbled
|
||||
System.out.format("\n%-22s%s%s\n", name + ":", gap,
|
||||
(verify(solution, puzzle) ? "Solution:" : "FAILED:"));
|
||||
for (int r = 0; r < N; ++r) {
|
||||
System.out.println(rowString(puzzle, r) + gap + rowString(solution, r));
|
||||
if (r == 2 || r == 5) System.out.println(bar + gap + " " + bar);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/** Return a String representing a row of this puzzle. **/
|
||||
String rowString(int[] grid, int r) {
|
||||
String row = "";
|
||||
for (int s = r * 9; s < (r + 1) * 9; ++s) {
|
||||
row += (char) ((NUM_DIGITS[grid[s]] == 9) ? '.' : (NUM_DIGITS[grid[s]] != 1) ? '?' :
|
||||
('1' + Integer.numberOfTrailingZeros(grid[s])));
|
||||
row += (s % 9 == 2 || s % 9 == 5 ? " | " : " ");
|
||||
}
|
||||
return row;
|
||||
}
|
||||
|
||||
|
||||
/** Unit Tests. Just getting started with these. **/
|
||||
void runUnitTests() {
|
||||
assert N == 9;
|
||||
assert SQUARES.length == 81;
|
||||
for (int s: SQUARES) {
|
||||
assert UNITS[s].length == 3;
|
||||
assert PEERS[s].length == 20;
|
||||
}
|
||||
assert Arrays.equals(PEERS[19],
|
||||
new int[] {18, 20, 21, 22, 23, 24, 25, 26, 1, 10, 28, 37, 46, 55, 64, 73, 0, 2, 9, 11});
|
||||
assert Arrays.deepToString(UNITS[19]).equals(
|
||||
"[[18, 19, 20, 21, 22, 23, 24, 25, 26], [1, 10, 19, 28, 37, 46, 55, 64, 73], [0, 1, 2, 9, 10, 11, 18, 19, 20]]");
|
||||
System.out.println("Unit tests pass.");
|
||||
}
|
||||
}
|
||||
1355
ipynb/SudokuJava.ipynb
Normal file
1355
ipynb/SudokuJava.ipynb
Normal file
File diff suppressed because one or more lines are too long
10
ipynb/hardest.txt
Normal file
10
ipynb/hardest.txt
Normal file
@@ -0,0 +1,10 @@
|
||||
85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.
|
||||
..53.....8......2..7..1.5..4....53...1..7...6..32...8..6.5....9..4....3......97..
|
||||
12..4......5.69.1...9...5.........7.7...52.9..3......2.9.6...5.4..9..8.1..3...9.4
|
||||
...57..3.1......2.7...234......8...4..7..4...49....6.5.42...3.....7..9....18.....
|
||||
1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..
|
||||
1...34.8....8..5....4.6..21.18......3..1.2..6......81.52..7.9....6..9....9.64...2
|
||||
...92......68.3...19..7...623..4.1....1...7....8.3..297...8..91...5.72......64...
|
||||
.6.5.4.3.1...9...8.........9...5...6.4.6.2.7.7...4...5.........4...8...1.5.2.3.4.
|
||||
7.....4...2..7..8...3..8.799..5..3...6..2..9...1.97..6...3..9...3..4..6...9..1.35
|
||||
....7..2.8.......6.1.2.5...9.54....8.........3....85.1...3.2.8.4.......9.7..6....
|
||||
BIN
ipynb/map3.png
Normal file
BIN
ipynb/map3.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 47 KiB |
BIN
ipynb/map4.png
Normal file
BIN
ipynb/map4.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 136 KiB |
1
ipynb/one.txt
Normal file
1
ipynb/one.txt
Normal file
@@ -0,0 +1 @@
|
||||
..7........1....3..5..4.6...4....7...6...3........1..2.....7.......6..8...2.....1
|
||||
528
ipynb/risk.ipynb
528
ipynb/risk.ipynb
File diff suppressed because one or more lines are too long
500000
ipynb/sudata.txt
Normal file
500000
ipynb/sudata.txt
Normal file
File diff suppressed because it is too large
Load Diff
10000
ipynb/sudoku10k.txt
Normal file
10000
ipynb/sudoku10k.txt
Normal file
File diff suppressed because it is too large
Load Diff
10
ipynb/ten.txt
Normal file
10
ipynb/ten.txt
Normal file
@@ -0,0 +1,10 @@
|
||||
..7........1....3..5..4.6...4....7...6...3........1..2.....7.......6..8...2.....1
|
||||
..3..2.8.14......9.68.593.7..24.5...............2.85..9.457.86.6......75.8.6..4..
|
||||
.....4.....5.....3...8.1.6.......81..73........2..6.......2....14...........5...7
|
||||
......8..3...6.9.71.8.9..6..673...2....2.6....2...938..3..8.1.25.267...8..9......
|
||||
......7.4.1.5......6..........15.9..8.....3.....6.....4...97.....7..8..........1.
|
||||
..2..6..7......8.9.8..4..6.85.2..93.....3.....93..1.25.1..9..5.5.4......2..3..6..
|
||||
.....8......6.4.........1.7....9......5.....36......84..7.......4.....6.....269..
|
||||
....1......4....6....85............289............7.34.........15....8....3..4..7
|
||||
...9.........1..7..9...4.2..4.16.....5.3......1...7.533......1....58..4.8.....2..
|
||||
.......8...4....15..23.7........3...8.......1.....2..6........4....1.....26...7..
|
||||
48697
ipynb/usecs.txt
Normal file
48697
ipynb/usecs.txt
Normal file
File diff suppressed because it is too large
Load Diff
477
py/Sudoku.java
Normal file
477
py/Sudoku.java
Normal file
@@ -0,0 +1,477 @@
|
||||
import java.io.*;
|
||||
import java.lang.Integer.*;
|
||||
import java.util.*;
|
||||
import java.util.stream.*;
|
||||
import java.lang.StringBuilder;
|
||||
import java.util.concurrent.CountDownLatch;
|
||||
|
||||
//////////////////////////////// Solve Sudoku Puzzles ////////////////////////////////
|
||||
//////////////////////////////// See http://norvig.com/CQ ////////////////////////////////
|
||||
//////////////////////////////// @author Peter Norvig ////////////////////////////////
|
||||
|
||||
/** There are two representations of puzzles that we will use:
|
||||
** 1. A gridstring is 81 chars, with characters '0' or '.' for blank and '1' to '9' for digits.
|
||||
** 2. A puzzle grid is an int[81] with a digit d (1-9) represented by the integer (1 << (d - 1));
|
||||
** that is, a bit pattern that has a single 1 bit representing the digit.
|
||||
** A blank is represented by the OR of all the digits 1-9, meaning that any digit is possible.
|
||||
** While solving the puzzle, some of these digits are eliminated, leaving fewer possibilities.
|
||||
** The puzzle is solved when every square has only a single possibility.
|
||||
**
|
||||
** Search for a solution with `search`:
|
||||
** - Fill an empty square with a guessed digit and do constraint propagation.
|
||||
** - If the guess is consistent, search deeper; if not, try a different guess for the square.
|
||||
** - If all guesses fail, back up to the previous level.
|
||||
** - In selecting an empty square, we pick one that has the minimum number of possible digits.
|
||||
** - To be able to back up, we need to keep the grid from the previous recursive level.
|
||||
** But we only need to keep one grid for each level, so to save garbage collection,
|
||||
** we pre-allocate one grid per level (there are 81 levels) in a `gridpool`.
|
||||
** Do constraint propagation with `arcConsistent`, `dualConsistent`, and `nakedPairs`.
|
||||
**/
|
||||
|
||||
public class Sudoku {
|
||||
|
||||
//////////////////////////////// main; command line options //////////////////////////////
|
||||
|
||||
static final String usage = String.join("\n",
|
||||
"usage: java Sudoku -help | -(no)[fptgadnsrv] | -[RT]<number> | <filename> ...",
|
||||
"E.g., -v turns verify flag on, -nov turns it off. -R and -T require a number. The args are:\n",
|
||||
" -h(elp) Print this usage message",
|
||||
" -f(ile) Print summary stats for each file (default on)",
|
||||
" -p(uzzle) Print summary stats for each puzzle (default off)",
|
||||
" -t(hread) Print summary stats for each thread (default off)",
|
||||
" -g(rid) Print each puzzle grid and solution grid (default off)",
|
||||
" -a(rc) Run arc consistency (default on)",
|
||||
" -d(ual) Run dual consistency (default on)",
|
||||
" -n(aked) Run naked pairs (default on)",
|
||||
" -s(earch) Run search (default on, but some puzzles can be solved with CSP methods alone)",
|
||||
" -r(everse) Solve the reverse of each puzzle as well as each puzzle itself (default off)",
|
||||
" -v(erify) Verify each solution is valid (default off)",
|
||||
" -T<number> Concurrently run <number> threads (default 26)",
|
||||
" -R<number> Repeat each puzzle <number> times (default 1)",
|
||||
" <filename> Solve all puzzles in filename, which has one puzzle per line");
|
||||
|
||||
boolean printFileStats = true; // -f
|
||||
boolean printPuzzleStats = false; // -p
|
||||
boolean printThreadStats = false; // -t
|
||||
boolean printGrid = false; // -g
|
||||
boolean runArcCons = true; // -a
|
||||
boolean runDualCons = true; // -d
|
||||
boolean runNakedPairs = true; // -n
|
||||
boolean runSearch = true; // -s
|
||||
boolean reversePuzzle = false; // -r
|
||||
boolean verifySolution = false; // -v
|
||||
int nThreads = 26; // -T
|
||||
int repeat = 1; // -R
|
||||
|
||||
/** Parse command line args and solve puzzles in files. **/
|
||||
public static void main(String[] args) throws IOException {
|
||||
Sudoku s = new Sudoku();
|
||||
for (String arg: args) {
|
||||
if (!arg.startsWith("-")) {
|
||||
s.solveFile(arg);
|
||||
} else {
|
||||
boolean value = !arg.startsWith("-no");
|
||||
switch(arg.charAt(value ? 1 : 3)) {
|
||||
case 'h': if (value) { System.out.println(usage); } break;
|
||||
case 'f': s.printFileStats = value; break;
|
||||
case 'p': s.printPuzzleStats = value; break;
|
||||
case 't': s.printThreadStats = value; break;
|
||||
case 'a': s.runArcCons = value; break;
|
||||
case 'g': s.printGrid = value; break;
|
||||
case 'd': s.runDualCons = value; break;
|
||||
case 's': s.runSearch = value; break;
|
||||
case 'n': s.runNakedPairs = value; break;
|
||||
case 'r': s.reversePuzzle = value; break;
|
||||
case 'v': s.verifySolution = value; break;
|
||||
case 'T': s.nThreads = Integer.parseInt(arg.substring(2)); break;
|
||||
case 'R': s.repeat = Integer.parseInt(arg.substring(2)); break;
|
||||
default: System.out.println("Unrecognized option: " + arg + "\n" + usage);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
//////////////////////////////// Handling Lists of Puzzles ////////////////////////////////
|
||||
|
||||
/** Solve all the puzzles in a file. Report timing statistics. **/
|
||||
void solveFile(String filename) throws IOException {
|
||||
List<int[]> grids = readFile(filename);
|
||||
long startTime = System.nanoTime();
|
||||
switch(nThreads) {
|
||||
case 1: solveList(grids); break;
|
||||
default: solveListThreaded(grids, nThreads); break;
|
||||
}
|
||||
if (printFileStats) printStats(grids.size() * repeat, startTime, filename);
|
||||
}
|
||||
|
||||
|
||||
/** Solve a list of puzzles in a single thread.
|
||||
** repeat -R<number> times; print each puzzle's stats if -p; print grid if -g; verify if -v. **/
|
||||
void solveList(List<int[]> grids) {
|
||||
int[] puzzle = new int[N * N]; // Used to save a copy of the original grid
|
||||
int[][] gridpool = new int[N * N][N * N]; // Reuse grids during the search
|
||||
for (int g=0; g<grids.size(); ++g) {
|
||||
int grid[] = grids.get(g);
|
||||
System.arraycopy(grid, 0, puzzle, 0, grid.length);
|
||||
for (int i = 0; i < repeat; ++i) {
|
||||
long startTime = printPuzzleStats ? System.nanoTime() : 0;
|
||||
int[] solution = initialize(grid); // All the real work is
|
||||
if (runSearch) search(solution, gridpool, 0); // on these 2 lines.
|
||||
if (printPuzzleStats) {
|
||||
printStats(1, startTime, "Puzzle " + (g + 1));
|
||||
}
|
||||
if (i == 0 && (printGrid || (verifySolution && !isSolution(solution, puzzle)))) {
|
||||
printGrids("Puzzle " + (g + 1), grid, solution);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/** Break a list of puzzles into nThreads sublists and solve each sublist in a separate thread. **/
|
||||
void solveListThreaded(List<int[]> grids, int nThreads) {
|
||||
try {
|
||||
final long startTime = System.nanoTime();
|
||||
int nGrids = grids.size();
|
||||
final CountDownLatch latch = new CountDownLatch(nThreads);
|
||||
int size = nGrids / nThreads;
|
||||
for (int c = 0; c < nThreads; ++c) {
|
||||
final List<int[]> sublist = grids.subList(c * size,
|
||||
c == nThreads - 1 ? nGrids : (c + 1) * size);
|
||||
new Thread() {
|
||||
public void run() {
|
||||
solveList(sublist);
|
||||
latch.countDown();
|
||||
if (printThreadStats) {
|
||||
printStats(repeat * sublist.size(), startTime, "Thread");
|
||||
}
|
||||
}
|
||||
}.start();
|
||||
}
|
||||
latch.await(); // Wait for all threads to finish
|
||||
} catch (InterruptedException e) {
|
||||
System.err.println("And you may ask yourself, 'Well, how did I get here?'");
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Utility functions ////////////////////////////////
|
||||
|
||||
/** Return an array of ints {0, 1, ..., n-1} **/
|
||||
int[] range(int n) {
|
||||
int[] result = new int[n];
|
||||
for (int i = 0; i<n; ++i) { result[i] = i; }
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
/** Return an array of all squares in the intersection of these rows and cols **/
|
||||
int[] cross(int[] rows, int[] cols) {
|
||||
int[] result = new int[rows.length * cols.length];
|
||||
int i = 0;
|
||||
for (int r: rows) { for (int c: cols) { result[i++] = N * r + c; } }
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
/** Return true iff item is an element of array, or array[0:end]. **/
|
||||
boolean member(int item, int[] array) { return member(item, array, array.length); }
|
||||
boolean member(int item, int[] array, int end) {
|
||||
for (int i = 0; i<end; ++i) {
|
||||
if (array[i] == item) { return true; }
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Constants ////////////////////////////////
|
||||
|
||||
final int N = 9; // Number of cells on a side of grid.
|
||||
final int[] DIGITS = {1<< 0, 1<< 1, 1<< 2, 1<< 3, 1<< 4, 1<< 5, 1<< 6, 1<< 7, 1<< 8};
|
||||
final int ALL_DIGITS = Integer.parseInt("111111111", 2);
|
||||
final int[] ROWS = range(N);
|
||||
final int[] COLS = ROWS;
|
||||
final int[] SQUARES = range(N * N);
|
||||
final int[][] BLOCKS = {{0, 1, 2}, {3, 4, 5}, {6, 7, 8}};
|
||||
final int[][] ALL_UNITS = new int[3 * N][];
|
||||
final int[][][] UNITS = new int[N * N][3][N];
|
||||
final int[][] PEERS = new int[N * N][20];
|
||||
final int[] NUM_DIGITS = new int[ALL_DIGITS + 1];
|
||||
final int[] HIGHEST_DIGIT = new int[ALL_DIGITS + 1];
|
||||
|
||||
{
|
||||
// Initialize ALL_UNITS to be an array of the 27 units: rows, columns, and blocks
|
||||
int i = 0;
|
||||
for (int r: ROWS) {ALL_UNITS[i++] = cross(new int[] {r}, COLS); }
|
||||
for (int c: COLS) {ALL_UNITS[i++] = cross(ROWS, new int[] {c}); }
|
||||
for (int[] rb: BLOCKS) {for (int[] cb: BLOCKS) {ALL_UNITS[i++] = cross(rb, cb); } }
|
||||
|
||||
// Initialize each UNITS[s] to be an array of the 3 units for square s.
|
||||
for (int s: SQUARES) {
|
||||
i = 0;
|
||||
for (int[] u: ALL_UNITS) {
|
||||
if (member(s, u)) UNITS[s][i++] = u;
|
||||
}
|
||||
}
|
||||
|
||||
// Initialize each PEERS[s] to be an array of the 20 squares that are peers of square s.
|
||||
for (int s: SQUARES) {
|
||||
i = 0;
|
||||
for (int[] u: UNITS[s]) {
|
||||
for (int s2: u) {
|
||||
if (s2 != s && !member(s2, PEERS[s], i)) {
|
||||
PEERS[s][i++] = s2;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Initialize NUM_DIGITS[val] to be the number of 1 bits in the bitset val
|
||||
// and HIGHEST_DIGIT[val] to the highest bit set in the bitset val
|
||||
for (int val = 0; val <= ALL_DIGITS; val++) {
|
||||
NUM_DIGITS[val] = Integer.bitCount(val);
|
||||
HIGHEST_DIGIT[val] = Integer.highestOneBit(val);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Search algorithm ////////////////////////////////
|
||||
|
||||
/** Search for a solution to grid. If there is an unfilled square, select one
|
||||
** and try--that is, search recursively--every possible digit for the square. **/
|
||||
int[] search(int[] grid, int[][] gridpool, int level) {
|
||||
if (grid == null) {
|
||||
return null;
|
||||
}
|
||||
int s = select_square(grid);
|
||||
if (s == -1) {
|
||||
return grid; // No squares to select means we are done!
|
||||
}
|
||||
for (int d: DIGITS) {
|
||||
// For each possible digit d that could fill square s, try it
|
||||
if ((d & grid[s]) > 0) {
|
||||
// Copy grid's contents into the gridpool to be used at the next level
|
||||
System.arraycopy(grid, 0, gridpool[level], 0, grid.length);
|
||||
int[] result = search(assign(gridpool[level], s, d), gridpool, level + 1);
|
||||
if (result != null) {
|
||||
return result;
|
||||
}
|
||||
}
|
||||
}
|
||||
return null;
|
||||
}
|
||||
|
||||
|
||||
/** Check if grid is a solution to the puzzle. **/
|
||||
boolean isSolution(int[] grid, int[] puzzle) {
|
||||
if (grid == null) {
|
||||
return false;
|
||||
}
|
||||
// Check that all squares have a single digit, and
|
||||
// no filled square in the puzzle was changed in the solution.
|
||||
for (int s: SQUARES) {
|
||||
if (NUM_DIGITS[grid[s]] != 1 || (NUM_DIGITS[puzzle[s]] == 1 && grid[s] != puzzle[s])) return false;
|
||||
}
|
||||
// Check that each unit is a permutation of digits
|
||||
for (int[] u: ALL_UNITS) {
|
||||
if (IntStream.of(u).sum() != ALL_DIGITS) return false;
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
/** Choose an unfilled square with the minimum number of possible values.
|
||||
** If all squares are filled, return -1 (which means the puzzle is complete). **/
|
||||
int select_square(int[] grid) {
|
||||
int square = -1;
|
||||
int min = N + 1;
|
||||
for (int s: SQUARES) {
|
||||
int c = NUM_DIGITS[grid[s]];
|
||||
if (c == 2) {
|
||||
return s; // Can't get fewer than 2 possible digits
|
||||
} else if (c > 1 && c < min) {
|
||||
square = s;
|
||||
min = c;
|
||||
}
|
||||
}
|
||||
return square;
|
||||
}
|
||||
|
||||
|
||||
/** Assign grid[s] = d. If this leads to contradiction, return null. **/
|
||||
int[] assign(int[] grid, int s, int d) {
|
||||
if ((grid == null) || ((grid[s] & d) == 0)) { return null; } // d not possible for grid[s]
|
||||
grid[s] = d;
|
||||
for (int p: PEERS[s]) {
|
||||
if (!eliminate(grid, p, d)) { // If we can't eliminate d from all peers of s, then fail
|
||||
return null;
|
||||
}
|
||||
}
|
||||
return grid;
|
||||
}
|
||||
|
||||
|
||||
/** Remove digit d from possibilities for grid[s].
|
||||
** Run the 3 constraint propagation routines (unless a command line flag says not to).
|
||||
** If constraint propagation detects a contradiction return false. **/
|
||||
boolean eliminate(int[] grid, int s, int d) {
|
||||
if ((grid[s] & d) == 0) { return true; } // d already eliminated from grid[s]
|
||||
grid[s] -= d;
|
||||
return ((!runArcCons || arc_consistent(grid, s))
|
||||
&& (!runDualCons || dual_consistent(grid, s, d))
|
||||
&& (!runNakedPairs || naked_pairs(grid, s)));
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Constraint Propagation ////////////////////////////////
|
||||
|
||||
/** Check if square s is ok: that is, it has multiple possible values, or it has
|
||||
** one possible value which we can consistently assign. **/
|
||||
boolean arc_consistent(int[] grid, int s) {
|
||||
int c = NUM_DIGITS[grid[s]];
|
||||
return c >= 2 || (c == 1 && (assign(grid, s, grid[s]) != null));
|
||||
}
|
||||
|
||||
|
||||
/** After we eliminate d from possibilities for grid[s], check each unit of s
|
||||
** and make sure there is some position in the unit where d can go.
|
||||
** If there is only one possible place for d, assign it. **/
|
||||
boolean dual_consistent(int[] grid, int s, int d) {
|
||||
for (int[] u: UNITS[s]) {
|
||||
int dPlaces = 0; // The number of possible places for d within unit u
|
||||
int dplace = -1; // Try to find a place in the unit where d can go
|
||||
for (int s2: u) {
|
||||
if ((grid[s2] & d) > 0) { // s2 is a possible place for d
|
||||
dPlaces++;
|
||||
if (dPlaces > 1) break;
|
||||
dplace = s2;
|
||||
}
|
||||
}
|
||||
if (dPlaces == 0 || (dPlaces == 1 && (assign(grid, dplace, d) == null))) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
/** Look for two squares in a unit with the same two possible values, and no other values.
|
||||
** For example, if s and s2 both have the possible values 8|9, then we know that 8 and 9
|
||||
** must go in those two squares. We don't know which is which, but we can eliminate
|
||||
** 8 and 9 from any other square s3 that is in the unit. **/
|
||||
boolean naked_pairs(int[] grid, int s) {
|
||||
int val = grid[s];
|
||||
if (NUM_DIGITS[val] != 2) { return true; } // Doesn't apply
|
||||
for (int s2: PEERS[s]) {
|
||||
if (grid[s2] == val) {
|
||||
// s and s2 are a naked pair; find what unit(s) they share
|
||||
for (int[] u: UNITS[s]) {
|
||||
if (member(s2, u)) {
|
||||
for (int s3: u) { // s3 can't have either of the values in val (e.g. 8|9)
|
||||
if (s3 != s && s3 != s2) {
|
||||
int d = HIGHEST_DIGIT[val];
|
||||
int d2 = val - d;
|
||||
if (!eliminate(grid, s3, d) || !eliminate(grid, s3, d2)) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Input ////////////////////////////////
|
||||
|
||||
/** The method `readFile` reads one puzzle per file line and returns a List of puzzle grids. **/
|
||||
List<int[]> readFile(String filename) throws IOException {
|
||||
BufferedReader in = new BufferedReader(new FileReader(filename));
|
||||
List<int[]> grids = new ArrayList<int[]>(260000);
|
||||
String gridstring;
|
||||
while ((gridstring = in.readLine()) != null) {
|
||||
grids.add(parseGrid(gridstring));
|
||||
if (reversePuzzle) {
|
||||
grids.add(parseGrid(new StringBuilder(gridstring).reverse().toString()));
|
||||
}
|
||||
}
|
||||
return grids;
|
||||
}
|
||||
|
||||
|
||||
/** Parse a gridstring into a puzzle grid: an int[] with values 0-9. **/
|
||||
int[] parseGrid(String gridstring) {
|
||||
int[] grid = new int[N * N];
|
||||
int s = 0;
|
||||
for (int i = 0; i<gridstring.length(); ++i) {
|
||||
char c = gridstring.charAt(i);
|
||||
if ('1' <= c && c <= '9') {
|
||||
grid[s++] = DIGITS[c - '1']; // A single-bit set to represent a digit
|
||||
} else if (c == '0' || c == '.') {
|
||||
grid[s++] = ALL_DIGITS; // Any digit is possible
|
||||
}
|
||||
}
|
||||
assert s == N * N;
|
||||
return grid;
|
||||
}
|
||||
|
||||
|
||||
/** Initialize a grid from a puzzle.
|
||||
** First initialize every square in the new grid to ALL_DIGITS, meaning any value is possible.
|
||||
** Then, call `assign` on the puzzle's filled squares to initiate constraint propagation. **/
|
||||
int[] initialize(int[] puzzle) {
|
||||
int[] grid = new int[N * N];
|
||||
for (int s: SQUARES) { grid[s] = ALL_DIGITS; }
|
||||
for (int s: SQUARES) { if (puzzle[s] != ALL_DIGITS) { assign(grid, s, puzzle[s]); } }
|
||||
return grid;
|
||||
}
|
||||
|
||||
|
||||
//////////////////////////////// Output ////////////////////////////////
|
||||
|
||||
boolean headerPrinted = false;
|
||||
|
||||
/** Print stats on puzzles solved, average time, frequency, threads used, and name. **/
|
||||
void printStats(int nGrids, long startTime, String name) {
|
||||
double usecs = (System.nanoTime() - startTime) / 1000.;
|
||||
String line = String.format("%7d %8.1f %7.3f %7d %s",
|
||||
nGrids, usecs / nGrids, 1000 * nGrids / usecs, nThreads, name);
|
||||
synchronized (this) { // So that printing from different threads doesn't get garbled
|
||||
if (!headerPrinted) {
|
||||
System.out.println("Puzzles Avg μsec KHz Threads Name\n"
|
||||
+ "======= ======== ======= ======= ====");
|
||||
headerPrinted = true;
|
||||
}
|
||||
System.out.println(line);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/** Print the original puzzle grid and the solution grid. **/
|
||||
void printGrids(String name, int[] puzzle, int[] solution) {
|
||||
String bar = "------+-------+------";
|
||||
String gap = " "; // Space between the puzzle grid and solution grid
|
||||
if (solution == null) solution = new int[N * N];
|
||||
synchronized (this) { // So that printing from different threads doesn't get garbled
|
||||
System.out.format("\n%-22s%s%s\n", name + ":", gap,
|
||||
(isSolution(solution, puzzle) ? "Solution:" : "FAILED:"));
|
||||
for (int r = 0; r < N; ++r) {
|
||||
System.out.println(rowString(puzzle, r) + gap + rowString(solution, r));
|
||||
if (r == 2 || r == 5) System.out.println(bar + gap + bar);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/** Return a String representing a row of this puzzle. **/
|
||||
String rowString(int[] grid, int r) {
|
||||
String row = "";
|
||||
for (int s = r * 9; s < (r + 1) * 9; ++s) {
|
||||
row += (char) ((NUM_DIGITS[grid[s]] != 1) ? '.' : ('1' + Integer.numberOfTrailingZeros(grid[s])));
|
||||
row += (s % 9 == 2 || s % 9 == 5 ? " | " : " ");
|
||||
}
|
||||
return row;
|
||||
}
|
||||
}
|
||||
62
py/lispy.py
62
py/lispy.py
@@ -4,9 +4,7 @@
|
||||
|
||||
################ Symbol, Procedure, classes
|
||||
|
||||
from __future__ import division
|
||||
from __future__ import print_function
|
||||
import re, sys, StringIO
|
||||
import re, sys, io
|
||||
|
||||
class Symbol(str): pass
|
||||
|
||||
@@ -15,17 +13,17 @@ def Sym(s, symbol_table={}):
|
||||
if s not in symbol_table: symbol_table[s] = Symbol(s)
|
||||
return symbol_table[s]
|
||||
|
||||
_quote, _if, _set, _define, _lambda, _begin, _definemacro, = map(Sym,
|
||||
_quote, _if, _set, _define, _lambda, _begin, _definemacro, = map(Sym,
|
||||
"quote if set! define lambda begin define-macro".split())
|
||||
|
||||
_quasiquote, _unquote, _unquotesplicing = map(Sym,
|
||||
"quasiquote unquote unquote-splicing".split())
|
||||
|
||||
class Procedure(object):
|
||||
class Procedure:
|
||||
"A user-defined Scheme procedure."
|
||||
def __init__(self, parms, exp, env):
|
||||
self.parms, self.exp, self.env = parms, exp, env
|
||||
def __call__(self, *args):
|
||||
def __call__(self, *args):
|
||||
return eval(self.exp, Env(self.parms, args, self.env))
|
||||
|
||||
################ parse, read, and user interaction
|
||||
@@ -33,12 +31,12 @@ class Procedure(object):
|
||||
def parse(inport):
|
||||
"Parse a program: read and expand/error-check it."
|
||||
# Backwards compatibility: given a str, convert it to an InPort
|
||||
if isinstance(inport, str): inport = InPort(StringIO.StringIO(inport))
|
||||
if isinstance(inport, str): inport = InPort(io.StringIO(inport))
|
||||
return expand(read(inport), toplevel=True)
|
||||
|
||||
eof_object = Symbol('#<eof-object>') # Note: uninterned; can't be read
|
||||
|
||||
class InPort(object):
|
||||
class InPort:
|
||||
"An input port. Retains a line of chars."
|
||||
tokenizer = r"""\s*(,@|[('`,)]|"(?:[\\].|[^\\"])*"|;.*|[^\s('"`,;)]*)(.*)"""
|
||||
def __init__(self, file):
|
||||
@@ -63,7 +61,7 @@ def readchar(inport):
|
||||
def read(inport):
|
||||
"Read a Scheme expression from an input port."
|
||||
def read_ahead(token):
|
||||
if '(' == token:
|
||||
if '(' == token:
|
||||
L = []
|
||||
while True:
|
||||
token = inport.next_token()
|
||||
@@ -83,7 +81,7 @@ def atom(token):
|
||||
'Numbers become numbers; #t and #f are booleans; "..." string; otherwise Symbol.'
|
||||
if token == '#t': return True
|
||||
elif token == '#f': return False
|
||||
elif token[0] == '"': return token[1:-1].decode('string_escape')
|
||||
elif token[0] == '"': return token[1:-1]
|
||||
try: return int(token)
|
||||
except ValueError:
|
||||
try: return float(token)
|
||||
@@ -97,7 +95,7 @@ def to_string(x):
|
||||
if x is True: return "#t"
|
||||
elif x is False: return "#f"
|
||||
elif isa(x, Symbol): return x
|
||||
elif isa(x, str): return '"%s"' % x.encode('string_escape').replace('"',r'\"')
|
||||
elif isa(x, str): return repr(x)
|
||||
elif isa(x, list): return '('+' '.join(map(to_string, x))+')'
|
||||
elif isa(x, complex): return str(x).replace('j', 'i')
|
||||
else: return str(x)
|
||||
@@ -126,11 +124,11 @@ class Env(dict):
|
||||
def __init__(self, parms=(), args=(), outer=None):
|
||||
# Bind parm list to corresponding args, or single parm to list of args
|
||||
self.outer = outer
|
||||
if isa(parms, Symbol):
|
||||
if isa(parms, Symbol):
|
||||
self.update({parms:list(args)})
|
||||
else:
|
||||
else:
|
||||
if len(args) != len(parms):
|
||||
raise TypeError('expected %s, given %s, '
|
||||
raise TypeError('expected %s, given %s, '
|
||||
% (to_string(parms), to_string(args)))
|
||||
self.update(zip(parms,args))
|
||||
def find(self, var):
|
||||
@@ -158,16 +156,16 @@ def add_globals(self):
|
||||
self.update(vars(math))
|
||||
self.update(vars(cmath))
|
||||
self.update({
|
||||
'+':op.add, '-':op.sub, '*':op.mul, '/':op.div, 'not':op.not_,
|
||||
'>':op.gt, '<':op.lt, '>=':op.ge, '<=':op.le, '=':op.eq,
|
||||
'+':op.add, '-':op.sub, '*':op.mul, '/':op.truediv, 'not':op.not_,
|
||||
'>':op.gt, '<':op.lt, '>=':op.ge, '<=':op.le, '=':op.eq,
|
||||
'equal?':op.eq, 'eq?':op.is_, 'length':len, 'cons':cons,
|
||||
'car':lambda x:x[0], 'cdr':lambda x:x[1:], 'append':op.add,
|
||||
'car':lambda x:x[0], 'cdr':lambda x:x[1:], 'append':op.add,
|
||||
'list':lambda *x:list(x), 'list?': lambda x:isa(x,list),
|
||||
'null?':lambda x:x==[], 'symbol?':lambda x: isa(x, Symbol),
|
||||
'boolean?':lambda x: isa(x, bool), 'pair?':is_pair,
|
||||
'port?': lambda x:isa(x,file), 'apply':lambda proc,l: proc(*l),
|
||||
'boolean?':lambda x: isa(x, bool), 'pair?':is_pair,
|
||||
'port?': lambda x:isa(x,file), 'apply':lambda proc,l: proc(*l),
|
||||
'eval':lambda x: eval(expand(x)), 'load':lambda fn: load(fn), 'call/cc':callcc,
|
||||
'open-input-file':open,'close-input-port':lambda p: p.file.close(),
|
||||
'open-input-file':open,'close-input-port':lambda p: p.file.close(),
|
||||
'open-output-file':lambda f:open(f,'w'), 'close-output-port':lambda p: p.close(),
|
||||
'eof-object?':lambda x:x is eof_object, 'read-char':readchar,
|
||||
'read':read, 'write':lambda x,port=sys.stdout:port.write(to_string(x)),
|
||||
@@ -186,7 +184,7 @@ def eval(x, env=global_env):
|
||||
if isa(x, Symbol): # variable reference
|
||||
return env.find(x)[x]
|
||||
elif not isa(x, list): # constant literal
|
||||
return x
|
||||
return x
|
||||
elif x[0] is _quote: # (quote exp)
|
||||
(_, exp) = x
|
||||
return exp
|
||||
@@ -227,17 +225,17 @@ def expand(x, toplevel=False):
|
||||
elif x[0] is _quote: # (quote exp)
|
||||
require(x, len(x)==2)
|
||||
return x
|
||||
elif x[0] is _if:
|
||||
elif x[0] is _if:
|
||||
if len(x)==3: x = x + [None] # (if t c) => (if t c None)
|
||||
require(x, len(x)==4)
|
||||
return list(map(expand, x))
|
||||
elif x[0] is _set:
|
||||
require(x, len(x)==3);
|
||||
elif x[0] is _set:
|
||||
require(x, len(x)==3);
|
||||
var = x[1] # (set! non-var exp) => Error
|
||||
require(x, isa(var, Symbol), "can set! only a symbol")
|
||||
return [_set, var, expand(x[2])]
|
||||
elif x[0] is _define or x[0] is _definemacro:
|
||||
require(x, len(x)>=3)
|
||||
elif x[0] is _define or x[0] is _definemacro:
|
||||
require(x, len(x)>=3)
|
||||
_def, v, body = x[0], x[1], x[2:]
|
||||
if isa(v, list) and v: # (define (f args) body)
|
||||
f, args = v[0], v[1:] # => (define f (lambda (args) body))
|
||||
@@ -246,9 +244,9 @@ def expand(x, toplevel=False):
|
||||
require(x, len(x)==3) # (define non-var/list exp) => Error
|
||||
require(x, isa(v, Symbol), "can define only a symbol")
|
||||
exp = expand(x[2])
|
||||
if _def is _definemacro:
|
||||
if _def is _definemacro:
|
||||
require(x, toplevel, "define-macro only allowed at top level")
|
||||
proc = eval(exp)
|
||||
proc = eval(exp)
|
||||
require(x, callable(proc), "macro must be a procedure")
|
||||
macro_table[v] = proc # (define-macro v proc)
|
||||
return None # => None; add v:proc to macro_table
|
||||
@@ -256,18 +254,18 @@ def expand(x, toplevel=False):
|
||||
elif x[0] is _begin:
|
||||
if len(x)==1: return None # (begin) => None
|
||||
else: return [expand(xi, toplevel) for xi in x]
|
||||
elif x[0] is _lambda: # (lambda (x) e1 e2)
|
||||
elif x[0] is _lambda: # (lambda (x) e1 e2)
|
||||
require(x, len(x)>=3) # => (lambda (x) (begin e1 e2))
|
||||
vars, body = x[1], x[2:]
|
||||
require(x, (isa(vars, list) and all(isa(v, Symbol) for v in vars))
|
||||
or isa(vars, Symbol), "illegal lambda argument list")
|
||||
exp = body[0] if len(body) == 1 else [_begin] + body
|
||||
return [_lambda, vars, expand(exp)]
|
||||
return [_lambda, vars, expand(exp)]
|
||||
elif x[0] is _quasiquote: # `x => expand_quasiquote(x)
|
||||
require(x, len(x)==2)
|
||||
return expand_quasiquote(x[1])
|
||||
elif isa(x[0], Symbol) and x[0] in macro_table:
|
||||
return expand(macro_table[x[0]](*x[1:]), toplevel) # (m arg...)
|
||||
return expand(macro_table[x[0]](*x[1:]), toplevel) # (m arg...)
|
||||
else: # => macroexpand if m isa macro
|
||||
return list(map(expand, x)) # (f arg...) => expand each
|
||||
|
||||
@@ -305,7 +303,7 @@ macro_table = {_let:let} ## More macros can go here
|
||||
|
||||
eval(parse("""(begin
|
||||
|
||||
(define-macro and (lambda args
|
||||
(define-macro and (lambda args
|
||||
(if (null? args) #t
|
||||
(if (= (length args) 1) (car args)
|
||||
`(if ,(car args) (and ,@(cdr args)) #f)))))
|
||||
|
||||
@@ -1,44 +1,56 @@
|
||||
# Run "python pytudes.py" to create README.md for pytudes
|
||||
|
||||
def cols(items): "Make columns"; return '|' + '|'.join(items) + '|'
|
||||
|
||||
def table_head(*columns): return f'{cols(columns)}\n{cols(["---"]*len(columns))}\n'
|
||||
|
||||
def nbs(category, *notebooks):
|
||||
"""Make a table entry for jupyter/ipython notebooks."""
|
||||
header = f'|Run|Year|{category}|\n|---|----|---|\n'
|
||||
"""Make a table of multiple jupyter/ipython notebooks, under a header."""
|
||||
print(f'{len(notebooks)} notebooks in {category}')
|
||||
return header + '\n'.join(nb(*line) for line in notebooks)
|
||||
return table_head('Run', 'Year', category) + '\n'.join(nb(*line) for line in notebooks)
|
||||
|
||||
def nb(title, year, url, comment=''):
|
||||
"""Make a markdown table entry for a jupyter/ipython notebook."""
|
||||
urlb = f'/blob/master/ipynb/{url}'
|
||||
urlb = f'/blob/main/ipynb/{url}'
|
||||
co = f'[c](https://colab.research.google.com/github/norvig/pytudes{urlb})'
|
||||
dn = f'[d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmaster%2Fipynb%2F{url}) '
|
||||
my = f'[m](https://mybinder.org/v2/gh/norvig/pytudes/master?filepath=ipynb%2F{url})'
|
||||
dn = f'[d](https://beta.deepnote.org/launch?template=python_3.6&url=https%3A%2F%2Fgithub.com%2Fnorvig%2Fpytudes%2Fblob%2Fmain%2Fipynb%2F{url}) '
|
||||
my = f'[m](https://mybinder.org/v2/gh/norvig/pytudes/main?filepath=ipynb%2F{url})'
|
||||
nb = f'[n](https://nbviewer.jupyter.org/github/norvig/pytudes{urlb})'
|
||||
ti = f'<b><a href="ipynb/{url}" title="{comment}">{title}</a></b>'
|
||||
if year == 2020: year = f'<u>{year}</u>'
|
||||
return f'| {co} {dn} {my} {nb} | {year} | {ti} |'
|
||||
|
||||
def pys(*pyfiles):
|
||||
header = '| File | Description | Documentation |\n|:--|:----|----|\n'
|
||||
"""Make a table of multiple python programs."""
|
||||
print(f'{len(pyfiles)} pyfiles')
|
||||
return header + '\n'.join(py(*line) for line in pyfiles)
|
||||
return table_head('File', 'Description', 'Documentation') + '\n'.join(py(*line) for line in pyfiles)
|
||||
|
||||
def py(url, description, doc=''):
|
||||
"""Make a markdown table entry for a .py file."""
|
||||
if doc: doc = f'[documentation]({doc})'
|
||||
return f'|[{url}](/blob/master/py/{url})|*{description}*|{doc}|'
|
||||
return f'|[{url}](/py/{url})|*{description}*|{doc}|'
|
||||
|
||||
|
||||
body = f"""
|
||||
|
||||
<div align="right" style="text-align:right"><i>Peter Norvig<br><a href="https://github.com/norvig/pytudes/blob/master/LICENSE">MIT License</a><br>2015-2020</i></div>
|
||||
<div align="right" style="text-align:right"><i>Peter Norvig
|
||||
<br><a href="https://github.com/norvig/pytudes/blob/main/LICENSE">MIT License</a><br>2015-2020</i></div>
|
||||
|
||||
# pytudes
|
||||
|
||||
"An *étude* (a French word meaning *study*) is an instrumental musical composition, usually short, of considerable difficulty, and designed to provide practice material for perfecting a particular musical skill." — [Wikipedia](https://en.wikipedia.org/wiki/%C3%89tude)
|
||||
"An *étude* (a French word meaning *study*) is an instrumental musical composition, usually short, of considerable difficulty,
|
||||
and designed to provide practice material for perfecting a particular musical skill." — [*Wikipedia*](https://en.wikipedia.org/wiki/%C3%89tude)
|
||||
|
||||
This project contains **pytudes**—Python programs, usually short, for perfecting particular programming skills.
|
||||
Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each notebook you can:
|
||||
This project contains **pytudes**—Python programs, usually short, for perfecting particular programming skills.
|
||||
|
||||
# Who is this for?
|
||||
|
||||
To continue the musical analogy, some people think of programming like [Spotify](http://spotify.com): they want to know how to install the app, find a good playlist, and hit the "play" button; after that they don't want to think about it. There are plenty of other tutorials that will tell you how to do the equivalent of that for various programming tasks—this one won't help. But if you think of programming like playing the piano—a craft that can take [years](https://norvig.com/21-days.html) to perfect—then I hope this collection can help.
|
||||
|
||||
|
||||
# Index of Jupyter (IPython) Notebooks
|
||||
|
||||
For each notebook you can:
|
||||
- Click on [c](https://colab.research.google.com) to **run** the notebook on Colab
|
||||
- Click on [d](https://deepnote.com) to **run** the notebook on DeepNote
|
||||
- Click on [m](https://mybinder.org) to **run** the notebook on MyBinder
|
||||
@@ -47,21 +59,18 @@ Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each
|
||||
- Hover over the title to **view** a description.
|
||||
|
||||
|
||||
# Index of Jupyter (IPython) Notebooks
|
||||
|
||||
|
||||
{nbs('Programming Examples',
|
||||
('Advent of Code 2020', 2020, 'Advent-2020.ipynb', 'Puzzle site with a coding puzzle each day for Advent 2018 '),
|
||||
('Advent of Code 2020', 2020, 'Advent-2020.ipynb', 'Puzzle site with a coding puzzle each day for Advent 2020 '),
|
||||
('Advent of Code 2018', 2018, 'Advent-2018.ipynb', 'Puzzle site with a coding puzzle each day for Advent 2018 '),
|
||||
('Advent of Code 2017', 2017, 'Advent%202017.ipynb', 'Puzzle site with a coding puzzle each day for Advent 2017'),
|
||||
('Advent of Code 2016', 2016, 'Advent%20of%20Code.ipynb', 'Puzzle site with a coding puzzle each day for Advent 2016*'),
|
||||
("Beal's Conjecture Revisited", 2018, 'Beal.ipynb', "A search for counterexamples to Beal's Conjecture"),
|
||||
('Bicycling Statistics', 2020, 'Bike%20Speed%20versus%20Grade.ipynb', 'Visualizing statistics about bike routes.'),
|
||||
('Bicycling Statistics', 2020, 'Bike%20Speed%20versus%20Grade.ipynb', 'Visualizing statistics about bike routes'),
|
||||
("Can't Stop", 2018, 'Cant-Stop.ipynb', 'Optimal play in a dice board game'),
|
||||
('Chaos with Triangles', 2019, 'Sierpinski.ipynb', 'A surprising appearance of the Sierpinski triangle in a random walk between vertexes'),
|
||||
('Chaos with Triangles', 2019, 'Sierpinski.ipynb', 'A surprising appearance of the Sierpinski triangle in a random walk'),
|
||||
("Conway's Game of Life", 2017, 'Life.ipynb', 'The cellular automata zero-player game'),
|
||||
('Generating and Solving Mazes', 2020, 'Maze.ipynb', 'Make a maze by generating a random tree superimposed on a grid and solve it.'),
|
||||
('Photo Focal Lengths', 2020, 'PhotoFocalLengths.ipynb', 'Generate charts of what focal lengths were used on a photo trip.'),
|
||||
('Generating and Solving Mazes', 2020, 'Maze.ipynb', 'Make a maze by generating a random tree superimposed on a grid and solve it'),
|
||||
('Photo Focal Lengths', 2020, 'PhotoFocalLengths.ipynb', 'Generate charts of what focal lengths were used on a photo trip'),
|
||||
('Pickleball Tournament', 2018, 'Pickleball.ipynb', 'Scheduling a doubles tournament fairly and efficiently'),
|
||||
('Project Euler Utilities', 2017, 'Project%20Euler%20Utils.ipynb', 'My utility functions for the Project Euler problems, including `Primes` and `Factors`'),
|
||||
('Tracking Trump: Electoral Votes', 2020, 'Electoral%20Votes.ipynb', 'How many electoral votes would Trump get if he wins the state where he has positive net approval?'))}
|
||||
@@ -70,14 +79,18 @@ Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each
|
||||
('Cryptarithmetic', 2014, 'Cryptarithmetic.ipynb', 'Substitute digits for letters and make NUM + BER = PLAY'),
|
||||
("Euler's Sum of Powers Conjecture", 2018, "Euler's%20Conjecture.ipynb", 'Solving a 200-year-old puzzle by finding integers that satisfy a<sup>5</sup> + b<sup>5</sup> + c<sup>5</sup> + d<sup>5</sup> = e<sup>5</sup>'),
|
||||
('Four 4s, Five 5s, and Countdowns', 2020, 'Countdown.ipynb', 'Solving the equation 10 _ 9 _ 8 _ 7 _ 6 _ 5 _ 4 _ 3 _ 2 _ 1 = 2016. From an Alex Bellos puzzle'),
|
||||
('KenKen (Sudoku-like Puzzle)', 2021, 'KenKen.ipynb', 'A Sudoku-like puzzle, but with arithmetic.'),
|
||||
('Pairing Socks', 2019, 'Socks.ipynb', 'What is the probability that you will be able to pair up socks as you randomly pull them out of the dryer?'),
|
||||
('Sicherman Dice', 2018, 'Sicherman%20Dice.ipynb', 'Find a pair of dice that is like a regular pair of dice, only different'),
|
||||
("Sol Golomb's Rectangle Puzzle", 2014, 'Golomb-Puzzle.ipynb', 'A Puzzle involving placing rectangles of different sizes inside a square'),
|
||||
("Square Sum Puzzle", 2020, 'SquareSum.ipynb', 'Place the numbers from 1 to n in a chain such that adjacent pairs sum to a perfect square.'),
|
||||
("When is Cheryl's Birthday? (new: Mad Cheryl)", 2020, 'Cheryl.ipynb', "Solving the *Cheryl's Birthday* logic puzzle"),
|
||||
('Star Battle (Sudoku-like Puzzle)', 2021, 'StarBattle.ipynb', 'Fill-in-the-grid puzzle similar to Sudoku'),
|
||||
('Sudoku', 2006, 'Sudoku.ipynb', 'Classic fill-in-the-grid puzzle'),
|
||||
('Sudoku: 100,000 puzzles/second in Java', 2021, 'SudokuJava.ipynb', 'A version of the Sudoku solver using parallel threads and other optimizations'),
|
||||
('Square Sum Puzzle', 2020, 'SquareSum.ipynb', 'Place the numbers from 1 to n in a chain (or a circle) such that adjacent pairs sum to a perfect square'),
|
||||
("When is Cheryl's Birthday?", 2020, 'Cheryl.ipynb', "Solving the *Cheryl's Birthday* logic puzzle"),
|
||||
('When Cheryl Met Eve: A Birthday Story', 2015, 'Cheryl-and-Eve.ipynb', "Inventing new puzzles in the Style of Cheryl's Birthday"),
|
||||
('xkcd 1313: Regex Golf', 2015, 'xkcd1313.ipynb', 'Find the smallest regular expression; inspired by Randall Munroe'),
|
||||
('xkcd 1313: Regex Golf (Part 2: Infinite Problems)', 2015, 'xkcd1313-part2.ipynb', 'Regex Golf: better, faster, funner. With Stefan Pochmann.'))}
|
||||
('xkcd 1313: Regex Golf (Part 2: Infinite Problems)', 2015, 'xkcd1313-part2.ipynb', 'Regex Golf: better, faster, funner (with Stefan Pochmann)'))}
|
||||
|
||||
{nbs('The Riddler (from 538)',
|
||||
('Battle Royale', 2017, 'Riddler%20Battle%20Royale.ipynb', 'A puzzle involving allocating your troops and going up against an opponent'),
|
||||
@@ -87,6 +100,7 @@ Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each
|
||||
('How Many Soldiers to Beat the Night King?', 2019, 'NightKing.ipynb', 'A battle between the army of the dead and the army of the living'),
|
||||
('Misanthropic Neighbors', 2017, 'Mean%20Misanthrope%20Density.ipynb', 'How crowded will this neighborhood be, if nobody wants to live next door to anyone else?'),
|
||||
('Properly Ordered Card Hands', 2018, 'Orderable%20Cards.ipynb', 'Can you get your hand of cards into a nice order with just one move?'),
|
||||
('Split the States', 2021, 'SplitStates.ipynb', 'Split the US states into two near-halves by area.'),
|
||||
('Tour de 538', 2020, 'TourDe538.ipynb', 'Solve a puzzle involving the best pace for a bicycle race.'),
|
||||
('Weighing Twelve Balls', 2020, 'TwelveBalls.ipynb', 'A puzzle where you are given some billiard balls and a balance scale, and asked to find the one ball that is heavier or lighter, in a limited number of weighings'),
|
||||
('War. What is it Good For?', 2020, 'war.ipynb', 'How likely is it to win a game of war in 26 turns?'))}
|
||||
@@ -114,7 +128,7 @@ Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each
|
||||
('The Devil and the Coin Flip Game', 2019, 'Coin%20Flip.ipynb', 'How to beat the Devil at his own game'),
|
||||
('Dice Baseball', 2020, 'Dice%20Baseball.ipynb', 'Simulating baseball games'),
|
||||
('Economics Simulation', 2018, 'Economics.ipynb', 'A simulation of a simple economic game'),
|
||||
('Poker Hand Ranking', 2012, "poker.ipynb", 'How do we decide which poker hand wins? Several variants of poker are considered.'),
|
||||
('Poker Hand Ranking', 2012, "poker.ipynb", 'How do we decide which poker hand wins? Several variants of poker are considered'),
|
||||
('The Unfinished Game .... of Risk', 2020, "risk.ipynb", "Determining who is likely to win an interminably long game of Risk"),
|
||||
('WWW: Who Will Win (NBA Title)?', 2019, 'WWW.ipynb', 'Computing the probability of winning the NBA title, for my home town Warriors, or any other team'))}
|
||||
|
||||
@@ -125,7 +139,7 @@ Some programs are in Jupyter (`.ipynb`) notebooks, some in `.py` files. For each
|
||||
('Convex Hull Problem', 2017, 'Convex%20Hull.ipynb', 'A classic Computer Science Algorithm'),
|
||||
('How to Count Things', 2020, 'How%20To%20Count%20Things.ipynb', 'Combinatorial math: how to count how many things there are, when there are a lot of them'),
|
||||
('Stable Matching Problem', 2020, 'StableMatching.ipynb', 'What is the best way to pair up two groups with each other, obeying preferences?'),
|
||||
('Symbolic Algebra, Simplification, and Differentiation', 2017, 'Differentiation.ipynb', 'A computer algebra system that manipulates expressions, including symbolic differentiation'),
|
||||
('Symbolic Algebra, Simplification, and Differentiation', 2017, 'Differentiation.ipynb', 'A computer algebra system that, including symbolic differentiation'),
|
||||
('Traveling Salesperson Problem', 2018, 'TSP.ipynb', 'Another of the classics'))}
|
||||
|
||||
|
||||
@@ -160,5 +174,4 @@ that was very influential to me when I was first learning to program. I still ha
|
||||
"""
|
||||
|
||||
output = 'README.md'
|
||||
with open(output, 'w') as out:
|
||||
print(f'Wrote {output}; {out.write(body)}, characters')
|
||||
print(f'Wrote {open(output, "w").write(body)} characters to {output}')
|
||||
|
||||
34
py/sudoku.py
34
py/sudoku.py
@@ -27,22 +27,6 @@ units = dict((s, [u for u in unitlist if s in u])
|
||||
peers = dict((s, set(sum(units[s],[]))-set([s]))
|
||||
for s in squares)
|
||||
|
||||
################ Unit Tests ################
|
||||
|
||||
def test():
|
||||
"A set of tests that must pass."
|
||||
assert len(squares) == 81
|
||||
assert len(unitlist) == 27
|
||||
assert all(len(units[s]) == 3 for s in squares)
|
||||
assert all(len(peers[s]) == 20 for s in squares)
|
||||
assert units['C2'] == [['A2', 'B2', 'C2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2'],
|
||||
['C1', 'C2', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9'],
|
||||
['A1', 'A2', 'A3', 'B1', 'B2', 'B3', 'C1', 'C2', 'C3']]
|
||||
assert peers['C2'] == set(['A2', 'B2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2',
|
||||
'C1', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9',
|
||||
'A1', 'A3', 'B1', 'B3'])
|
||||
print('All tests pass.')
|
||||
|
||||
################ Parse a Grid ################
|
||||
|
||||
def parse_grid(grid):
|
||||
@@ -125,6 +109,22 @@ def search(values):
|
||||
result = search(assign(values.copy(), s, d))
|
||||
if result: return result
|
||||
|
||||
################ Unit Tests ################
|
||||
|
||||
def test():
|
||||
"A set of tests that must pass."
|
||||
assert len(squares) == 81
|
||||
assert len(unitlist) == 27
|
||||
assert all(len(units[s]) == 3 for s in squares)
|
||||
assert all(len(peers[s]) == 20 for s in squares)
|
||||
assert units['C2'] == [['A2', 'B2', 'C2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2'],
|
||||
['C1', 'C2', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9'],
|
||||
['A1', 'A2', 'A3', 'B1', 'B2', 'B3', 'C1', 'C2', 'C3']]
|
||||
assert peers['C2'] == set(['A2', 'B2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2',
|
||||
'C1', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9',
|
||||
'A1', 'A3', 'B1', 'B3'])
|
||||
print('All tests pass.')
|
||||
|
||||
################ System test ################
|
||||
|
||||
import time
|
||||
@@ -158,4 +158,4 @@ if __name__ == '__main__':
|
||||
solve_all(open("sudoku-easy50.txt"), "easy")
|
||||
solve_all(open("sudoku-top95.txt"), "hard")
|
||||
solve_all(open("sudoku-hardest.txt"), "hardest")
|
||||
|
||||
|
||||
|
||||
250000
py/sudoku.txt
Normal file
250000
py/sudoku.txt
Normal file
File diff suppressed because it is too large
Load Diff
28
tools.md
28
tools.md
@@ -1,21 +1,32 @@
|
||||
# Tools for Publishing Computational Content
|
||||
|
||||
## Notebooks
|
||||
## Notebooks: Run on Server; Interact in Browser
|
||||
|
||||
- Jupyter Notebook
|
||||
- Colab
|
||||
- Deepnote
|
||||
- Streamlit.io
|
||||
- [Epiphany](https://epiphany.pub/) "a new blogging experience"
|
||||
- [Iodide](https://github.com/iodide-project/iodide) Run notebook in the browser
|
||||
- [Pyodide](https://github.com/iodide-project/pyodide) Run Python in the browser
|
||||
- [Klipse](https://github.com/viebel/klipse) Run interactive code in tech blogs
|
||||
- Matlab / R
|
||||
- Mathematica
|
||||
|
||||
## Programming Environments
|
||||
## Notebooks: Run and Interact in Browser
|
||||
- - Observable
|
||||
- [Iodide](https://github.com/iodide-project/iodide) Run notebook in the browser
|
||||
- [Pyodide](https://github.com/iodide-project/pyodide) Run Python in the browser
|
||||
|
||||
- Jupyter Lab
|
||||
- Streamlit.io
|
||||
## Javascript Programming in Browser
|
||||
|
||||
- [Playcode](https://playcode.io/) Full-featured Live javascript IDE
|
||||
- [Code Sandbox](https://codesandbox.io/) Full-featured Live, colaborative javascript IDE
|
||||
- [jsfiddle](https://jsfiddle.net/) Classic javascript snippet site
|
||||
- [jsbin](https://jsbin.com/) Another javascript snippet site
|
||||
- [Code Pen](https://codepen.io/) Yet another javascript snippet site
|
||||
|
||||
## Interesting Full Programming Environments
|
||||
|
||||
- [Jupyter Lab](https://jupyterlab.readthedocs.io/en/stable/)
|
||||
- Kaggle
|
||||
- https://codereef.ai/
|
||||
- Light Table http://lighttable.com/
|
||||
@@ -25,7 +36,12 @@
|
||||
|
||||
- [distill.pub](https://distill.pub/)
|
||||
- [Papers with Code](https://paperswithcode.com/)
|
||||
- [Mathigon]()
|
||||
|
||||
## Debugging Aids
|
||||
|
||||
- [Python Tutor](http://www.pythontutor.com/) (Philip Guo)
|
||||
|
||||
## Project-Based Learning
|
||||
|
||||
- [tuvtran repository](https://github.com/tuvtran/project-based-learning#python)
|
||||
|
||||
8
txt/reviews.md
Normal file
8
txt/reviews.md
Normal file
@@ -0,0 +1,8 @@
|
||||
# Reviews of pytudes
|
||||
|
||||
Here's what some people are saying about `pytudes`:
|
||||
- "Everything I see from Peter Norvig is just always so incredibly well written and coded." — [Jonathan](https://news.ycombinator.com/user?id=jypepin), [Hacker News](https://news.ycombinator.com/item?id=27379366)
|
||||
- "Peter Norvig is my go to recommendation when someone is interested in becoming better at solving day to day problems ... I feel his skill of dividing a problem into small pieces and expressing them in code in a natural way is unparalleled." — [mikevin](https://news.ycombinator.com/user?id=mikevin), [Hacker News](https://news.ycombinator.com/item?id=27379366)
|
||||
- "I've never seen Peter Norvig choose anything but the most elegant and perfect data model for the problem at hand." — [spoonjim](https://news.ycombinator.com/user?id=spoonjim), [Hacker News](https://news.ycombinator.com/item?id=27379366)
|
||||
- "I just find Norvig's style of "functional Python" lovely in its own way (with noted disregard of Pep8 and other "best practices")" —[raverbashing](https://news.ycombinator.com/user?id=raverbashing), [Hacker News](https://news.ycombinator.com/item?id=25654955)
|
||||
- "You should check out Norvig's design of computer programs [course on Udacity](https://imp.i115008.net/c/2331964/788805/11298?u=https://www.udacity.com/course/design-of-computer-programs--cs212) where he uses these kinds of puzzle programs to teach programming design concepts. It is a hard but really rewarding course. — [nafizh](https://news.ycombinator.com/user?id=nafizh), [HN ACademy](https://yahnd.com/academy/r/udacity.com/course/design-of-computer-programs--cs212/)
|
||||
Reference in New Issue
Block a user