{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Traveling Salesperson Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the [*Traveling Salesperson Problem*](http://en.wikipedia.org/wiki/Traveling_salesman_problem): \n",
    "\n",
    "> *Given a set of cities and the distances between each pair of cities, what is the shortest possible tour that visits each city exactly once, and returns to the starting city?*\n",
    "\n",
    "In this notebook we will develop some solutions to the problem, and more generally show *how to think about* solving a problem like this. [Elsewhere](https://research.googleblog.com/2016/09/the-280-year-old-algorithm-inside.html) you can read about how the algorithms developed here are used in serious applications that millions of people rely on every day.\n",
    "\n",
    "<a href=\"http://www.math.uwaterloo.ca/tsp/history/pictorial/dfj.html\"><img src=\"http://www.math.uwaterloo.ca/tsp/history/img/dantzig.gif\"></a>\n",
    "<center>An example tour.</center>\n",
    "                                     \n",
    "# Understanding What We're Talking About (Vocabulary)\n",
    "\n",
    "Do we understand precisely what the problem is asking? Do we understand all the concepts that the problem talks about?  Do we understand them well enough to implement them in a programming language? Let's take a first pass:\n",
    "\n",
    "- **A set of cities**: We will need to represent a set of cities; Python's `set` datatype might be appropriate.\n",
    "- **Distance between each pair of cities**: If `A` and `B` are cities, this could be a function, `distance(A, B),` or a table lookup, `distance[A][B]`.  The resulting distance will be a real number.\n",
    "- **City**: All we have to know about an individual city is how far it is from other cities. We don't have to know its name, population, best restaurants, or anything else. So a city could be just an integer (0, 1, 2, ...) used as an index into a distance table, or a city could be a pair of (x, y) coordinates, if we are using straight-line distance on a plane.\n",
    "- **Tour**: A tour is a specified order in which to visit the cities; Python's `list` or `tuple` datatypes would work. For example, given the set of cities `{A, B, C, D}`, a tour might be the list `[B, D, A, C]`, which means to travel from `B` to `D` to `A` to `C` and finally back to `B`.\n",
    "- **Shortest possible tour**: The shortest tour is the one whose tour length is the minimum of all tours.\n",
    "- **Tour length**: The sum of the distances between adjacent cities in the tour (including the last city back to the first city).   Probably  a function, `tour_length(tour)`.\n",
    "- **What is ...**: We can define a function to answer the question *what is the shortest possible tour?*  The function takes a set of cities as input and returns a tour as output. I will use the convention that any such function will have a name ending in the letters \"`tsp`\", the traditional abbreviation for Traveling Salesperson Problem.\n",
    "\n",
    "At this stage I have a rough sketch of how to attack the problem.  I don't have all the answers, and I haven't committed to specific representations for all the concepts, but I know what all the pieces are, and I don't see anything that stops me from proceeding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the imports used throughout this notebook. I'm assuming Python 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import time\n",
    "import itertools\n",
    "import urllib\n",
    "import csv\n",
    "import functools\n",
    "from statistics import mean, stdev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All Tours Algorithm: `alltours_tsp`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with an algorithm that is guaranteed to solve the problem, although it is inefficient for large sets of cities:\n",
    "\n",
    "> **All Tours Algorithm**: *Generate all possible tours of the cities, and choose the shortest tour (the one with minimum tour length).*\n",
    "\n",
    "My design philosophy is to first write an English description of the algorithm, then write Python code that closely mirrors the English description. This will probably require some auxilliary functions and data structures; just assume they exist; put them on a TO DO list, and eventually define them with the same design philosophy.\n",
    "\n",
    "Here is the start of the implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def alltours_tsp(cities):\n",
    "    \"Generate all possible tours of the cities and choose the shortest tour.\"\n",
    "    return shortest_tour(alltours(cities))\n",
    "\n",
    "def shortest_tour(tours): \n",
    "    \"Choose the tour with the minimum tour length.\"\n",
    "    return min(tours, key=tour_length)\n",
    "\n",
    "# TO DO: Data types: cities, tours, Functions: alltours, tour_length"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: In Python `min(`*collection*`,key=`*function*`)` means to find the element *x* that is a member of *collection* such that *function(x)* is minimized. So `shortest` finds the tour whose `tour_length` in the minimal among the tours. \n",
    "\n",
    "This gives us a good start; the Python code closely matches the English description.  And we know what we need to do next: represent cities and tours, and implement the functions `alltours` and `tour_length`. Let's start with tours.\n",
    "\n",
    "\n",
    "Representing Tours\n",
    "------------------\n",
    "\n",
    "A tour starts in one city, and then visits each of the other cities in order, before returning to the start city.  A natural representation of a tour is a sequence of cities. For example `(1, 2, 3)` could represent a tour that starts in city 1, moves to 2, then 3, and finally returns to 1.  \n",
    "\n",
    "**Note**: I considered using `(1, 2, 3, 1)` as the representation of this tour. I also considered an ordered list of **edges** between cities: \n",
    "`((1, 2), (2, 3), (3, 1))`. In the end, I decided `(1, 2, 3)` was simplest.\n",
    "    \n",
    "\n",
    "Now for the `alltours` function.  If a tour is a sequence of cities, then all the tours are *permutations* of the set of all cities. A function to generate all permutations of a set is already provided in Python's standard `itertools` library module; we can use it as our implementation of `alltours`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alltours = itertools.permutations "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For *n* cities there are *n*! (that is, the factorial of *n*) permutations.\n",
    "Here's are all 3! = 6 tours of 3 cities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cities = {1, 2, 3}\n",
    "\n",
    "list(alltours(cities))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The length of a tour is the sum of the lengths of each edge in the tour; in other words, the sum of the distances between consecutive cities in the tour, including the distance form the last city back to the first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def tour_length(tour):\n",
    "    \"The total of distances between each pair of consecutive cities in the tour.\"\n",
    "    return sum(distance(tour[i], tour[i-1]) \n",
    "               for i in range(len(tour)))\n",
    "\n",
    "# TO DO: Functions: distance, Data types: cities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: I use one Python-specific trick: when `i` is 0, then `distance(tour[0], tour[-1])` gives us the wrap-around distance between the first and last cities, because `tour[-1]` is the last element of `tour`. \n",
    "\n",
    "Representing Cities\n",
    "--------------------------------\n",
    "\n",
    "We determined that the only thing that matters about cities is the distance between them. But before we can decide about how to represent cities, and before we can define `distance(A, B)`,  we have to make a choice. In the fully general version of the TSP, the \"distance\" between two cities could be anything: it could factor in the amount of time it takes to travel between cities, the twistiness of the road, or anything else. The `distance(A, B)` might be different from `distance(B, A)`. So the distances could be represented by a matrix `distance[A][B]`, where any entry in the matrix could be any (non-negative) numeric value.\n",
    "    \n",
    "But we will ignore the fully general TSP and concentrate on an important special case, the **Euclidean TSP**, where the distance between any two cities is the [Euclidean distance](http://en.wikipedia.org/wiki/Euclidean_distance), the straight-line distance between points in a two-dimensional plane. So a city can be represented by a two-dimensional point: a pair of *x* and *y* coordinates. We will use the constructor function `City`, so that `City(300, 0)` creates a city with x-coordinate of 300 and y coordinate of 0.  Then `distance(A, B)` will be a function that uses the *x* and *y* coordinates to compute the distance between `A` and `B`.\n",
    "\n",
    "Representing Points and Computing `distance`\n",
    "---\n",
    "        \n",
    "OK, so a city can be represented as just a two-dimensional point. But how will we represent points?  Here are some choices, with their pros and cons:\n",
    "\n",
    "* **tuple:** A point is a two-tuple of (*x*, *y*) coordinates, for example, `(300, 0)`. **Pro:** Very simple. \n",
    "**Con:** doesn't distinguish Points from other two-tuples.  \n",
    "            \n",
    "* **class:** Define a custom `Point` class with *x* and *y* slots. **Pro:** explicit, gives us `p.x` and `p.y` accessors.  **Con:** less efficient.\n",
    "            \n",
    "* **complex:** Python already has the two-dimensional point as a built-in numeric data type, but in a non-obvious way: as `complex` numbers, which inhabit the two-dimensional (real &times; imaginary) plane.  **Pro:** efficient. **Con:** a little confusing; doesn't distinguish Points from other complex numbers.\n",
    "* **subclass of complex:** All the pros of `complex`, and eliminating the major con.\n",
    "\n",
    "\n",
    "Any of these choices would work perfectly well; I decided to use a subclass of `complex`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Cities are represented as Points, which are a subclass of complex numbers\n",
    "\n",
    "class Point(complex):\n",
    "    x = property(lambda p: p.real)\n",
    "    y = property(lambda p: p.imag)\n",
    "    \n",
    "City = Point\n",
    "\n",
    "def distance(A, B): \n",
    "    \"The distance between two points.\"\n",
    "    return abs(A - B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example of computing the distance between two cities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = City(3, 0)\n",
    "B = City(0, 4)\n",
    "distance(A, B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random Sets of Cities\n",
    "---\n",
    "\n",
    "The input to a TSP algorithm should be a set of cities. I can make a random set of *n* cities by calling `City` *n* times, each with different random *x* and *y* coordinates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(193+375j), (427+384j), (497+585j), (179+546j), (224+543j), (245+643j)}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{City(random.randrange(1000), random.randrange(1000)) for c in range(6)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `Cities` does that (and a bit more):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def Cities(n, width=900, height=600, seed=42):\n",
    "    \"Make a set of n cities, each with random coordinates within a (width x height) rectangle.\"\n",
    "    random.seed(seed * n)\n",
    "    return frozenset(City(random.randrange(width), random.randrange(height))\n",
    "                     for c in range(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three complications that I decided to tackle in `Cities`:\n",
    "\n",
    "1. IPython's matplotlib plots (by default) in a rectangle that is 1.5 times wider than it is high; that's why I specified a width of 900 and a height of 600. If you want the coordinates of your cities to be bounded by a different size rectangle, you can change width or height.\n",
    "\n",
    "2. Sometimes I want `Cities(n)` to be a true function, returning the same result each time. This is very helpful for getting repeatable results: if I run a test twice, I get the same results twice. \n",
    "But other times I would like to be able to do an experiment, where, for example, I call `Cities(n)` 30 times and get 30 different sets, and I then compute the average tour length produced by my algorithm across these 30 sets. Can I get both behaviors out of one function? *Yes!*  The trick is the additional optional parameter, `seed`.  Two calls to `Cities` with the same `n` and `seed` parameters will always return the same set of cities, and two calls with different values for `seed` will return different sets. This is implemented by calling the function `random.seed`, which resets the random number generator.\n",
    "\n",
    "3. Once I create a set of Cities, I don't want anyone messing with my set. For example, I don't want an algorithm that claims to \"solve\" a problem by deleting half the cities from the input set, then finding a tour of the remaining cities.  Therefore, I make `Cities` return a `frozenset` rather than a `set`.  A `frozenset` is *immutable*; nobody can change it once it is created. (Likewise, each city is immutable.)\n",
    "\n",
    "For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)})"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A set of 5 cities\n",
    "Cities(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)}),\n",
       " frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)}),\n",
       " frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)})]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The exact same set of 5 cities each time\n",
    "[Cities(5) for i in range(3)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({(414+310j), (776+430j), (41+265j), (864+394j), (523+497j)}),\n",
       " frozenset({(814+542j), (29+476j), (637+261j), (759+367j), (794+255j)}),\n",
       " frozenset({(439+494j), (211+473j), (585+33j), (832+503j), (591+15j)})]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A different set of 5 cities each time\n",
    "[Cities(5, seed=i) for i in range(3)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to apply the `alltours_tsp` function to find the shortest tour:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((6+546j),\n",
       " (199+147j),\n",
       " (350+65j),\n",
       " (737+26j),\n",
       " (847+187j),\n",
       " (891+465j),\n",
       " (554+374j),\n",
       " (505+548j))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alltours_tsp(Cities(8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2509.307587720301"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tour_length(alltours_tsp(Cities(8)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quick, is that the right answer?  I have no idea, and you probably can't tell either. But if we could *plot* the tour we'd understand it better and might be able to see at a glance if the tour is optimal.\n",
    "\n",
    "Plotting Tours\n",
    "---\n",
    "\n",
    "I define `plot_tour(tour)` to plot the cities (as circles) and the tour (as lines):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_tour(tour): \n",
    "    \"Plot the cities as circles and the tour as lines between them.\"\n",
    "    plot_lines(list(tour) + [tour[0]])\n",
    "    \n",
    "def plot_lines(points, style='bo-'):\n",
    "    \"Plot lines to connect a series of points.\"\n",
    "    plt.plot([p.x for p in points], [p.y for p in points], style)\n",
    "    plt.axis('scaled'); plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c320630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_tour(alltours_tsp(Cities(8)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks much better!  To me, it looks like the shortest possible tour, although I don't have an easy way to prove it. Let's go one step further and define a function, `plot_tsp(algorithm, cities)` that will take a TSP algorithm (such as `alltours_tsp`) and a set of cities,  apply the algorithm to the cities to get a tour, check that the tour is reasonable, plot the tour,  and print information about the length of the tour and the time it took to find it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_tsp(algorithm, cities):\n",
    "    \"Apply a TSP algorithm to cities, plot the resulting tour, and print information.\"\n",
    "    # Find the solution and time how long it takes\n",
    "    t0 = time.clock()\n",
    "    tour = algorithm(cities)\n",
    "    t1 = time.clock()\n",
    "    assert valid_tour(tour, cities)\n",
    "    plot_tour(tour); plt.show()\n",
    "    print(\"{} city tour with length {:.1f} in {:.3f} secs for {}\"\n",
    "          .format(len(tour), tour_length(tour), t1 - t0, algorithm.__name__))\n",
    "    \n",
    "def valid_tour(tour, cities):\n",
    "    \"Is tour a valid tour for these cities?\"\n",
    "    return set(tour) == set(cities) and len(tour) == len(cities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c320518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 city tour with length 2509.3 in 0.110 secs for alltours_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(alltours_tsp, Cities(8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## All Non-Redundant Tours Algorithm (improved `alltours_tsp`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We said there are *n*! tours of *n* cities, and thus 6 tours of 3 cities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(alltours({1, 2, 3}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But this is redundant: `(1, 2, 3)`, `(2, 3, 1)`, and `(3, 1, 2)` are three ways of describing the same tour. So let's arbitrarily say that all tours must start with the first city in the set of cities. We'll just pull the first city out, and then tack it back on to all the permutations of the rest of the cities.  \n",
    "\n",
    "While we're re-assembling a tour from the start city and the rest, we'll take the opportunity to construct the tour as a *list* rather than a *tuple*. It doesn't matter much now, but later on we will want to represent *partial* tours, to which we will want to append cities one by one; appending can only be done to lists, not tuples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def alltours(cities):\n",
    "    \"Return a list of tours, each a permutation of cities, but each one starting with the same city.\"\n",
    "    start = first(cities)\n",
    "    return [[start] + Tour(rest)\n",
    "            for rest in itertools.permutations(cities - {start})]\n",
    "\n",
    "def first(collection):\n",
    "    \"Start iterating over collection, and return the first element.\"\n",
    "    return next(iter(collection))\n",
    "\n",
    "Tour = list  # Tours are implemented as lists of cities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can verify that for 3 cities there are now only 2 tours (not 6) and for 4 cities there are 6 tours (not 24):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3], [1, 3, 2]]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alltours({1, 2, 3})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3, 4],\n",
       " [1, 2, 4, 3],\n",
       " [1, 3, 2, 4],\n",
       " [1, 3, 4, 2],\n",
       " [1, 4, 2, 3],\n",
       " [1, 4, 3, 2]]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alltours({1, 2, 3, 4})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** We could say that there is only one tour of three cities, because `[1, 2, 3]` and `[1, 3, 2]` are in some sense the same tour, one going clockwise and the other counterclockwise.  However, I choose not to do that, for two reasons.  First, it would mean we can never handle TSP problems where the distance from A to B is different from B to A. Second, it would complicate the code (if only by a line or two).\n",
    "\n",
    "We can  verify that calling `alltours_tsp(Cities(8))` still works and gives the same tour with the same total distance. But it now runs faster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GDqRvzhR3eqLziEi1mbE58AzQ0YoTsxo00h8kd54Avg+cFp1FRNrCHsDDrSx8UOkP1bnA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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed960b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 city tour with length 2509.3 in 0.018 secs for alltours_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(alltours_tsp, Cities(8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try a much harder 10-city tour:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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48zuz0w+GRTfBzSPLd1x1HQgPz4GtJrfbHWDQ9+vC3sC1ZnS4c1nqmopMAVufscATqYuQ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10541ccf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2291.8 in 1.636 secs for alltours_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(alltours_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Complexity of `alltours_tsp`\n",
    "---\n",
    "\n",
    "It takes about 2 seconds on my machine to solve this 10-city problem. In general, the function `TSP` looks at (*n*-1)! tours for an *n*-city problem, and each tour has *n* cities, so the total time required for *n* cities should be roughly proportional to *n*!. This means that the time grows rapidly with the number of cities.  *Really* rapidly. This table shows the actual time for solving a 10 city problem, and the exepcted time for solving larger problems:\n",
    "\n",
    "<table>\n",
    "<tr><th>n <th>expected time for `alltours_tsp(Cities(n))`\n",
    "<tr><td>10<td>Covering 10! tours = 2 secs\n",
    "<tr><td>11<td>2 secs &times; 11! / 10! &approx; 22 secs\n",
    "<tr><td>12<td>2 secs &times; 12! / 10! &approx; 4 mins\n",
    "<tr><td>14<td>2 secs &times; 14! / 10! &approx; 13 hours\n",
    "<tr><td>16<td>2 secs &times; 16! / 10! &approx; 200 days\n",
    "<tr><td>18<td>2 secs &times; 18! / 10! &approx; 112 years\n",
    "<tr><td>25<td>2 secs &times; 25! / 10! &approx; <a href=\"https://www.google.com/search?q=2+seconds*25!+%2F+10!+in+years\">270 billion years</a>\n",
    "</table>\n",
    "\n",
    "There must be a better way ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximate Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we are willing to settle for a tour that is short, but not guaranteed to be shortest? Then we can save billions of years of compute time: we will show several *approximate* algorithms, which find tours that are typically within 10% of the shortest possible tour, and can handle thousands of cities in a few seconds. (**Note:** There are more sophisticated approximate algorithms that can handle hundreds of thousands of cities and come within 0.01% or better of the shortest possible tour.)\n",
    "\n",
    "So how do we come up with an approximate algorithm?   Here are two general plans of how to create a tour:\n",
    "\n",
    "* **Nearest Neighbor Algorithm**: Make the tour go from a city to its nearest neighbor. Repeat.\n",
    "* **Greedy Algorithm**: Find the shortest distance between any two cities and include that edge in the tour. Repeat.\n",
    "\n",
    "We will expand these ideas into full algorithms.\n",
    "\n",
    "In addition, here are four very general strategies that apply not just to TSP, but to any optimization problem. An **optimization problem** is one in which the goal is to find a solution that is best (or near-best) according to some metric,\n",
    "out of a pool of many candidate solutions. The strategies are:\n",
    "\n",
    "* **Repetition Strategy**: Take some algorithm and re-run it multiple times, varying some aspect each time, and take the solution with the best score.\n",
    "* **Alteration Strategy**: Use some algorithm to create a solution, then make small changes to the solution to improve it.\n",
    "* **Ensemble Strategy**: Take two or more algorithms, apply all of them to the problem, and pick the best solution.\n",
    "\n",
    "And here are two more strategies that work for a wide variety of problems:\n",
    "\n",
    "* **Divide and Conquer**: Split the input in half, solve the problem for each half, and then combine the two partial solutions.\n",
    "\n",
    "* **Stand on the Shoulders of Giants** *or* **Just Google It**: Find out what others have done in the past, and either copy it or build on it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nearest Neighbor Algorithm: `nn_tsp`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a description of the nearest neighbor algorithm:\n",
    "\n",
    "> **Nearest Neighbor Algorithm:** *Start at any city; at each step extend the tour by moving from the previous city to its nearest neighbor that has not yet been visited.*\n",
    "\n",
    "So now, instead of considering all *n*! tours, we are generating a single tour. It takes O(*n*<sup>2</sup> ) time to find the tour, because it has *n*-1 steps, and at each step we consider each of the remaining cities.\n",
    "I implement the algorithm as follows:\n",
    "\n",
    "* \"*Start at any city*\": arbitrarily pick the first city. \n",
    "* \"*extend the tour*\": append to the end of a list of cities.\n",
    "* \"*by moving from the previous city*\": previous city is `tour[-1]`.\n",
    "* \"*to its nearest neighbor*\": I will define the function `nearest_neighbor`.\n",
    "* \"*that has not yet been visited*\": I will keep a set of `unvisited` cities.\n",
    "\n",
    "That gives us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def nn_tsp(cities):\n",
    "    \"\"\"Start the tour at the first city; at each step extend the tour \n",
    "    by moving from the previous city to the nearest neighboring city, C,\n",
    "    that has not yet been visited.\"\"\"\n",
    "    start = first(cities)\n",
    "    tour = [start]\n",
    "    unvisited = set(cities - {start})\n",
    "    while unvisited:\n",
    "        C = nearest_neighbor(tour[-1], unvisited)\n",
    "        tour.append(C)\n",
    "        unvisited.remove(C)\n",
    "    return tour\n",
    "\n",
    "def nearest_neighbor(A, cities):\n",
    "    \"Find the city in cities that is nearest to city A.\"\n",
    "    return min(cities, key=lambda c: distance(c, A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** In Python, as in the formal mathematical theory of computability, `lambda` (or &lambda;) is the symbol for *function*, so \"`lambda c: distance(c, A)`\" means the function of `c` that computes the distance from `c` to the city `A`. \n",
    "\n",
    "We can compare the the slow (but optimal) `alltours_tsp` algorithm to the new fast (but approximate) `nn_tsp` algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x101b81358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2291.8 in 1.681 secs for alltours_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(alltours_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c328e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2381.4 in 0.000 secs for nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(nn_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the nearest neighbor algorithm is a lot faster, but it didn't find the shortest tour. To understand where it went wrong, it would be helpful to know what city it started from.  I can modify `plot_tour` by adding one line of code to highlight the start city with a red square:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_tour(tour):\n",
    "    \"Plot the cities as circles and the tour as lines between them. Start city is red square.\"\n",
    "    start = tour[0]\n",
    "    plot_lines(list(tour) + [start])\n",
    "    plot_lines([start], 'rs') # Mark the start city with a red square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c35b048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2381.4 in 0.000 secs for nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(nn_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the tour moves clockwise from the start city, and mostly makes good decisions, but not optimal ones.\n",
    "\n",
    "We can compare the performance of these two algorithms on, say, eleven different sets of cities instead of just one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 1.0118279018107388,\n",
       " 1.0121039193389436,\n",
       " 1.107851821362778,\n",
       " 1.139713084817861,\n",
       " 1.1531140497779002,\n",
       " 1.1972133336642432,\n",
       " 1.2160497559961319]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def length_ratio(cities): \n",
    "    \"The ratio of the tour lengths for nn_tsp and alltours_tsp algorithms.\"\n",
    "    return tour_length(nn_tsp(cities)) / tour_length(alltours_tsp(cities))\n",
    "\n",
    "sorted(length_ratio(Cities(8, seed=i*i)) for i in range(11))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ratio of `1.0` means the two algorithms got the same (optimal) result; that happened 4 times out of 10.  The other times, we see that the `nn_tsp` produces a longer tour, by anything up to 21% worse, with a median of 1% worse.\n",
    "\n",
    "But more important than that 1% (or even 21%) difference is that the nearest neighbor algorithm can quickly tackle problems that the all tours algorithm can't touch in the lifetime of the universe.  Finding a tour of 1000 cities takes well under a second:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UM526k9aAvAmyBZZsUK5uE1fD0HeUIedCw5U7Uu5xDRFO2gP/GFX43fbEdvu1\n28ED8geQn5cG73k1jpfJp59KIm2VA/zrVhUgZLJPpKfXjpDcz+NzPmQ5LDIG2ejh7LvN7DpZ9nhW\nN9lka5FGoRc3bbSuMqsYbb3NxAH5KcjrIM2D1MXq+bKv+wWJcdth1o9BzgJpol+7ZHBmtib1OXi0\nDRQqqS1VyBYH5GiQjiCjQH4O8gQsWg6TPy1euJFrc5J6whM/jpQbveA7yJEqP/zFj6VxhXdtqI1+\nOPJSiq46kL5ebnZ0ER6p6sHT/SCDLOadAg7NgopnjLLivy8/HWRL9H51QVI9Z6ahtoqK56T4iddf\nr5l6muy/PQq8OT7xO5j/qr8exMDF8Oc+IDeBvAhSCwveUircm8RbktGMy9ZVCq797PZVn4PbE0jl\nPsZq1gX7K/74+//WVxXDHLZe6fivWqeKLC/dCvIxylj6B5BrUaUOv+o+xc0bK05SuOgHiJr7yHVp\nEFExHnUqG7c0n7c9TN13uJaOJuIY+mURGVVkSwO+HIwOyA6QpvrfTbSmS4fQbgacfU8y6Tcbzx7V\nr9eoPyknOCRJCOhNEtc68iEC0hjGLdPj7boNID8GuRCkmWvN6kBaRJt/aQ3noTDVOwA+d8D+O/XG\nPV+qYoMxKywHS/NW+gyQV53pvx3IEpCdqApBj8DIuXoC6Rw5cjgeM4t309Abad19eSWneQJ9xK/G\n6efbqFlIh0nmDHKoksz8BvHsaThqOmRZAnJStHl7a8rmYxBevx3G1cVl2mnbOor7zqtk3F44SexA\n3n0zeFl89VzvF6LckEDmkcDff3/4NKEem+O0aAXdn4M7T4SmQB3Q/VP4EdAo9xkHfAGoWZ1/T2Rr\nteP0roZbTijusSlwdMvgUU+9Be7IjZd/584ToXyiCAOAF4th5GDgJODrMOQsGPM1+E2TArw3A79s\nDj952HG4GVgILBVhTxAUag4tOsOSWxTMNathbqXI1mrzW8e0LMDtnnO7Lo7DD4HFwKLcv2tEED2O\nry6DAxoV+joeheefArM3Qc1mePYEWJ/77tPcZ967bvj0fQ/v5jgtLhbZ+krQ/O2bac7GdT4DeE+E\nvUlHVvM79RYFwxrj+uS+GxBjiDVAS9R6edrcShjdthi3Y5bBG4OgfLSbZmBrS6ACZnSE8gn29ORu\nkfEc2Ipx9z+nwPc1Tx3d0hbHhefKW8LcOXDeHDj2UDjyi3DNcpG7fe/YtdWrFG7dc6/DzW+KYRhx\nKGy6x3FkUGfvAAAgAElEQVQWzImG3/2o1eeJo5cu8rk+giWW+FJvUsOSKVviuBW528HS4tuB/AiV\n6bM9lraDaPiqFaj4F0glyN0gs0DW5aTd2TBhuf6dC7eY8OfHkT6oreCl4O0j+s1HP19pq2IXIkn6\n14L8IvnYWadtaN5KFZUfPtdUWKf4BjFoBVT4SuaBtMjRXPdsaOviOuj4t2xiO9pU2QcOmqKs5RCU\nOq9bvHk/ey1M2JkEhjTooZSf+h3cyIDzOT/i57GPTty2us9LQr0kQA4GORWkD8hUkL+wz7NIPgZ5\nBb/t4IDom8k855ya41uKqZhwbNpIQaqfWlG1cec8WfBH9n6mWuNTP0/5JsjjICvguettC7Lk3g00\n4trDkKW6wxuxGewNFeTrDvJnkN+mAJMmL4w7Y6d93Wc/7kxzbG0s1ehRGwZG7YOcp/Jcdbg/WqlI\nOU4JSL+8SL1z2UsqeO91n9CQJT2E00rKxvUsAQ4nDPtiGwGb5zXlrmnj1ZH3C79sZxy/cMXMP1yg\nvH6in/goQ9Ax+G0H1reDqPrjIGI19RVu5K0V6PeKyruj+2262BU18doZ5BRU7eHVIOPIFTMvPHvZ\nyzDtE+h1mrm/G7YrY31SA2SvF/QHWvJUzMVrEh734D+E80b189aqamB6Y3B0mPJpNAaKPjf/pJUg\nx5sYUY6+28CEVX68VYva7+5cOUZvvbeC82cVrwUW8T2GvfgEyE2e74/M7cNrPfSQeWpuPU1nYFzP\nCuDwCdlJOeH9yJkgs+MhsP92JW1YZchrBaPnqeyY+et4ehZ59oPbgf89kzuniJp781bmPPFRM4KO\n3arcUeVakM8F4OlBkNFpb45iRlZ2Lwz7KIwZx1/raIV1iiO4vbeuKz9Kh/5sYBqzBJZshFHri2EY\ntBRemo4KVFqi0mKH484skPQ0ZJ70Brcpt894nnAyFORd3R4CORYliI0OhzU7ST+rMTMB1m5C+Unk\nExJ19eUAt+znEJTr24FpI7DACLq/ChfUlSpFs2d+treD2yjcDo7QzyNO7p2wtAbNy5QO311Kb+QW\ndTCagl1MfXa43wIfF4O8kebm0B8aQ+qg//I4B0nYlTy+pJ9eNHTwOpvHMQc5jlsG0gmkke0hrJ7T\nVbrqYohhcRfOKWRijSqFs0+tI98IoLMvg3xELvVJfej0s7pdZAKs3YTSmwjKjcq4gHoEBmfcNMcD\nZJuiOeK8vbeDv2K+HXTD8nZQPMYT42DCJ0HEXnyolD0Ow3YFPx+fmEGaoLIlnhLe36Sa3GHpmFUS\nuvxCebjzSeQmroYhb5vtCF6347Bkc2VfLzA7W53+gMXmNLxpqJzs7Ay2axcmaBR+n1gLHVa5cve3\nMh/ivaTYgSKv3gk/9IvXaNIqeO1nFrR2CsgakJ7FfUz9RKk2494kbW0O6Qa27eu3VAxKg1DjAsXo\n6z5CjHfhxsmoWSD9hL6/fCi+HYwmxu0g18+hisHe3dv2pmC3AZNK5vIjkJ+E9zf4LZAPlN7bq5IY\nsJh9uWyCmSlIFzy3i8LYtp4q+4yO3UCq4f1H4Py/FxfWCc3Pbjic0qr+1byVqs41Yp4JpjRUDmFS\ns/73vFFZh1Pd81dthzMeUUy2TZUKBnP/PtDWDncG6lbQxfXdSyDnpzVfzxq7D4YyU2BbonUuFSPy\nIyK9axLId0D+zx7xNlfqsEo+9S/px8RVlNvBMpCXiXA7sJEEDZt6j0rBG54+GuRrOQmsibm/fd4t\njrmQdp6JBtMD6naxFuTLfli8TNCkD6+YBfIoyIIoDMNMw8XzTJE+7gepyBKGaJJ5TwPTDrptnvUI\nDNnuZ5b6Q8MCJ2fnGH9Zzmi8CEYtTC6xlz9MLojQjNfTn9IFtiVa47SIJTpxXTYTpqxPwxAKchHI\nc3abJtg4Gb5QdsXC/9M++G8HL+XmvYVIt4Pism6mDea//t/SEeR9la303PvCc6/LqyBdzf1ZqZNy\ndGBz85Nfg9zgh8Pbt+kAqdypDtlvfDWJC14S+4y+H58HThVIryxhiFcDOj/myFXQZaOKlzHdimxu\n6fn1t3bvLFeOBkMjp4k2z/fGnbm9tQgmG2pZD9irezfRXs+CgdgtvPQDuS+lvlqipFSrIiNmV8Ow\nEoIVW5WR6boN8Px36gt3JVibxijp/8rc3xFuB4vXwPgdwVd3PdNTuu6xHm+gftU6ozCqIMZDdvMx\n5qVxqUuC8wuBnAPyvr9vG5/0cXUwrcxGSo6j+42+voE3o3+6D9Po/YbDHldFpPoftjqM6drV240u\nwMHlL+rhbh8Ct2m+HWvgnPvgtvNh6Ht6mDut1b2baP1LxUj8iJCrQO5MqS8Hdf1qaUeQI1bBgNDi\nxiaJBuR/c8zuhNLjrRRMQa7KMfJGFnh33w5yhbuXbIKb9sANdTDxI3jzDpChKqOpueaAeXNU+p4H\nORSWboFODwYX3Gk3AwZ9CJfs8Xtf/fqnMDG0apHq64gTYGod9H+jmBaa9VFl/dx99NwN3Wqgp8Dl\ntUo9EWSgdHtChUejJ1/foNgNeRakPB5d2gYOavPn1Omikm3htnvOTUfRnTICkuDtRt2CJ6NcyL2p\nljXr6g58G7DYXNS9dRWMqPHiNdH6Z8mgQhjGd0BuS7G/Z0EusifI/ssVQuNeUeVaVNrVQMaYLs5K\notM9KnegBQRA+apr5QKnptbBff1y/WhuB9euD2Z6thJafmzvrSDMGFixteAl8vRkkI/g5nPCVBUB\neM+5q+aDmvJ612cFBmo8nkzptIfNgeHfilNjId4am9UrKBtOh+h9RpPeiwWqbz0CVwd6fIXBHb5e\nIzbl9vtGf5lJfx/R5tj5IZArUCrAOagb8FMgN6oUzQOXFGhkgOgD31obU1LAk+Nh/LLU6k2UimFp\nmMsPQW5Msb+fgmhVLml4HGjGawzz31SufKUpT5fFPDTz+ivIj/3f6zZSvrqW3SEUnnbDFKHt08XO\nDJeaA6XZ3ihD8MnJ8N51u97zx2gYNnjfTFqpIo2zc8ksnk/ZvQG4eR2kbfQ+k7jhJpXgdSVJ84fK\niHkqtcLRHdTf56+Lu4f0e2CQThV4BEh3kP+D6zyCjjkYT6dZUJ++ryj343R4TGqEFIO5/Abk6mjv\nBOmDZSAGG0EWQQ4KliHWDC8dnGUbCo4KrllOLn948W+6DRetMpC+j3kCA3MJr3T6cL3XBQx5NwgX\nxbhy514v3whLPgZpnRzvfbbpGbyJeZ/9NvQ1pEbu9UKWwVfF83lpuj8N88i1ObXZv0HOiN6niSGf\nE2i3AzkERs4PXsv8vr/0HRjyqb2QIceBfKxy69jnOgrf93nGPPx9+PADkMPtacd+jbO62adGSNGJ\nZNwyGPGBvfU8zLdXTgeZp3+30wPpS/rZS90eAj4gSvH1GP0fiPLQ6WFHvCK2RdKD17B8W/GcXhHo\nIdDjE2izArp5vCWGLIe5z8AN24JwUVif5KkLzGt9/jp9rePOu/zPzxMYvLtwzZ8quWykZYUxdH1V\npJKx1LXOh4KshdsvKDCvix9T6RXkBJAPiJEvXq2tNzHe2G3w4Tz44Xl+taAcC3IryDp10zHdPLw0\nMy+Ht25G753cPPfl1tEb2+N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B3NcwkwpEV/krihdDmyrltdOxxpQ8qvj51lV+lU4+Olc/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LAxWJcH1KVp4dItjF3Sy2tpDZjJi2z0qrKecDTIzdWdO9kf/rc7jGwM9uHCnbDodSzZluw8EH5M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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6daa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 city tour with length 21275.9 in 0.145 secs for nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(nn_tsp, Cities(1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we do better?   Can we combine the speed of the nearest neighbor algorithm with the optimality of the all tours algorithm? \n",
    "\n",
    "Let's consider where `nn_tsp` can go wrong. At the end of `plot_tsp(nn_tsp, Cities(10))`, we see a very long edge, because there are no remaining cities near by.  In a way, this just seems like bad luck&mdash;we started in a place that left us with no good choices at the end.  Just as with buying lottery tickets, we could improve our chance of winning by trying more often; in other words, by using the **repetition strategy**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Repeated Nearest Neighbor Algorithm: `repeated_nn_tsp`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an easy way to apply the **repetition** strategy to improve **nearest neighbors**:\n",
    "\n",
    "> **Repeated Nearest Neighbor Algorithm:** *For each of the cities, run the nearest neighbor algorithm with that city as the starting point, and choose the resulting tour with the shortest total distance.*\n",
    "\n",
    "So, with *n* cities we could run the `nn_tsp` algorithm *n* times, regrettably making the total run time *n* times longer, but hopefully making at least one of the *n* tours shorter. \n",
    "\n",
    "To implement  `repeated_nn_tsp` we just take the shortest tour over all starting cities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def repeated_nn_tsp(cities):\n",
    "    \"Repeat the nn_tsp algorithm starting from each city; return the shortest tour.\"\n",
    "    return shortest_tour(nn_tsp(cities, start) \n",
    "                         for start in cities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To do that requires a modification of `nn_tsp` so that the `start` city can be specified as an optional argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def nn_tsp(cities, start=None):\n",
    "    \"\"\"Start the tour at the first city; at each step extend the tour \n",
    "    by moving from the previous city to its nearest neighbor \n",
    "    that has not yet been visited.\"\"\"\n",
    "    if start is None: start = first(cities)\n",
    "    tour = [start]\n",
    "    unvisited = set(cities - {start})\n",
    "    while unvisited:\n",
    "        C = nearest_neighbor(tour[-1], unvisited)\n",
    "        tour.append(C)\n",
    "        unvisited.remove(C)\n",
    "    return tour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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qfBetXJHSA5P9HC2uHRkhO0nWB/0S9AjXsoR/rO4dzEaGQ14yK970DTZAW1rn4qmgt4G+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\nFBH/D6i9NWsGaMGjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed685f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 city tour with length 6734.1 in 0.002 secs for nn_tsp\n"
     ]
    },
    {
     "data": {
      "image/png": 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ktJzESmACrLMU9hsTFzfRQGlhxp9xsSnHFHbceLk/x53IajAVOFLKTaqSXONd\n6Uez6oXABhU2ezOGAn8CuisqURYnoif6ZiQeALvB0LZwYaNMyzsGiptCzYLNuAt4P1UMS75IHZ8R\n7utUmHEALpXMNhKLfctTnTi4GO2FC8iqUPj7AoOAneKo8AGiwKNPo/Z/AGafTYAmu1b9ZGySvAXy\nQIpZcGezZvmYBe8E3J/jPtMglftzt/3NuAhXRvK9yntx5Y7Ec2b0gqn3mJ38a9zMYnFQ+itcNc3Y\nCPgX0F9igVepMmbubFiapJB78GMvXQoTBGjGqriaxFNz1Wf6pKoHO3sqsB7u99rSjLE4p4sxyWJt\nyo+eN0OHqTBm5QJMCDLCq59+ZCY5EHg2ilwdBfytuttmcRD82MuPVLPg3K3u3Gqi1xNw4e/Q9R73\n/0KS6r5+8TiJM6KN5W2B53Apt980Y4YZd5jRP3LIKEOWXgzDVq45IegwzKdU4H+mvy2wjISZ5GPg\nn14lypL65UkPFBtmtIMN2+czhXcS89GAQs8Wq97XbdrC5jtD9/OkB2cnPsOXuBn/v6KJXAegJy6N\n+P1mfIQzA40B3pT4pRCy+yX/E4Ks8ZyedEiUKvakqJpUE99pR0MLrbYGWhl0rksV/d/r4ajqlbkW\nw9ob5Was+KWGBh0HmpBuqcyoUlz3qKzpJNBi0POgs0Ad8lFyMw4tjteuovlOw3Ag8DUud0U/qUbu\nhEAgNkRFcCbjPMs6S13Og6d6QM+HoN842P/fMPhT+CZHaTdiOVt8AFe0vW86H5ZYLjFO4mKJTkA7\n3Kp+C+BpYL4ZD5pxdJRUsUSYfSlcsjyO5l5v5h2zHo/DrrvA79vAzqdLvYsiQ12g/DCjGTAMOAQ4\nFxgpudTR1bN4mrEWLuviQokb6jdyqk1Uf84BEr+bcS5wuxnPKkNTjVxk++NRw4yNcaagXsA/zJhP\nwhT0uipFHxdXkNj8P8HHU6HnZ7Ez9/pb/tS/MlJooeW7gfpEhbDvA62d5nfWB80BHVW/sZNVETv5\n+zj8VkAvgE7LcZ8NQJ1AF4PGRVX0XnNm4Hv75KqiWgHOTQvQIlBH37Ika96Cs8wqF9kIwR6BeBHl\ng7oFZ4Y4SRlGV5qxFTAOOEbixezlqJxD6odv4O5dYNOLJR7Kts9cYEZHnIvm5kozEWIWYzTBeQT1\nhAuPg6FrFEOQmBnDgW8lzvEtSzJ8e+9EeLdTBgIAmNEAGAwMxSn9wySWZ9qPxIdm9AVGm7G/xORs\n5EliPurvOCGUAAAgAElEQVQIjDXjY4l3sukzF0i8b8YzuARjF+RpjKXAC8ALZp9tB026V/1E/PSG\nGd2AHri4iljieyM3IgQxBfwTJTV7C7dJ2U3iimwUfgUS/wVOAJ42o30uZJTLNnsS8KQZLXPRZz24\nFDjRjA3zP1SqGhnrb1SY8esmytF1O3C2xE++5UmFR6Ufv13tQHlg1qydWdcRZv3HuteeW5lxI/Ai\n7kfbXa4iUr2ReBoYCjNfMevxeGLM7IOsJJ7ApWQYFVWV84LEfNxq6K/5Hy1ZkNjJs+DI0cC7Zgwz\nY/X8y1ErpwFfQcyr5Pnb7OgyAvqOda/x24wJrTRb8s3Rs36FqaNA6+ZvzEHf5HITErQS6CnQnX7P\np1YHzQftVJhrV1NvgNqCHgB9GcURrOThPLRxsRtq7/N6pNO8Z9kMBAqJj6yR+RozciV9E7hF4s76\nylkPOf6MKwvaXcKbQjGjE3ATsBpwlgqY2tiMfwMzJGJvsYiJTT8QyA9mrGHGHlE95Pth996FD3jK\nT5CVXNre3sAVZuxen77qyf3AOsBBHmVAYhIu3fk1wHAzRpmxSb7HNWNvXNGlv+V7rFwQlH6gJDDD\nzFjfjF5mXGrGE2bMAuYBVwPtgf/Ch+OTbwjm05Eg1SZk/ceUmAEcBTxixgb17S9LGX4DzgOui8o6\neiOyYDyK8555G5hoxvVmNM/HeGY0wuXOP0Pi53yMkWvKwrxTXJF85Uu61ylSLJsD2wHbR6/bAb/g\nitFXtPeAmapSd7nwlaAKMaYZ58Cnx8Gf34d1Whb6Po8SrY0BRkncUYgx08GM9XDR1AcClwP3Rg+p\nXPV/MdBZoleu+sw3Ja/0Q7m34iD1dfqmN7ywBgnFvj2wFa5mcWUFP0ViYfpjdShoNtTEmFt0gLVa\nwt1dcjmm6/+YaXBNU1/3uRnb4Tyg2itmFaMi2W4C1sXZ+8fkoM92uNXEziqmGgK+d5Lzv6tev2x3\nCY+BfsHTyMt1uvTXKDvjXaCTQV1Aq/uWN/vj1FpRpskGhTl/hc3qCBoOGub7PKeQzaK0Gp+BngVt\nUc/+ngIN8X1cmbaYROTmk9Ztkm+i7dHXjPHAN8C31Vr0t+sbQd974PaN4lb9pvRItdk5fYJE92Tf\nKEYkvouSinUgp5WwUp2/bTuZsZZcorNCmDqHAFPNuFNiXg77rTcSAp4y4wVc1PV4M0YCV1Scn3Qx\n40DcivOw3EuaX0pW6UfZDk9wRR+SZSqcNha4AVg7ausALXAbQNHfvusAtzfLdzm8AKTOKLngS08C\n5ZM3gS7kVOmnOn8NVwZmmvEsPPg09L46nzV9JeaZcSfOjn5sLvrMNXJR1jea8QBwBfCxGcOAO5RG\nXe6oyt8/cTmZso7Y9obvpUYelnBbg+4EfQ96EO7ulW12PmfSkWq2vmN9H2epNXj5HDjz12LIolj/\nY331Ihg8M5cmw+RBZ+78gdYGnQkX/lAIExCoGWghaDvf5zpNebcGvQT6GHRgXYVdQFeCHvUtd9bH\n61uAHF20lUAHgcZEN9vloPUS7yeP5Ku731R20kEfgRr6Pu5SaaDdQV/BdXuXeqS2uxePm5uPh1td\n93khJzHR/ssrdSnQuLTI3r8/6CPQy6AOKT63WRR528a3zFkfq28B6nmhmrsZjGaA3gYdBWqUu/6T\nzZ6OngUfjMWVjCvaCx+XFv2IFoJ6+JalMMfrb8O1kGODGkYKdD/f5zwLuQfj8uHfAVq3qjPH2fNh\nfCw3qtM+Rt8CpHchqnvQ/LU76BbQd6B/g7rma0aRbPYUrSwuweUc6e77/BRrizxZPgH9xbcshTtm\nfybD5JOY05fB+y+AmuXh+vYCfQBa2fd5z0L2tUA3wcxva+ZNOqqozY7eBaj75CdNkPUbTLwF1Nbz\njdEDtAB0IR6SPBVzA62Cq450o29ZCnvcfl0ra05itm2Pc4f9CK7dO5fuyZHJ5D+gP/s+79kfw76j\n4+AKm9Nj8i1A3Sc9Hv7HqeVTW9B/QU+D1vQtTzG0SBncBxpNjv3V496c0j3+i7htWMMrF7jJVG7l\nAu0UrYiLMraiFJ05iiD3Tn6SVeUKOV/kPYHPgbejQhyB2jkP2AEYoEopEsoB5xp5yPVw8RzoNw56\nPhSP6PChHeGqBjXdkzsMq0+vEm8DY3EF5YuQ/OVN8kUR+Omn8j+Oz0mX+AU4w4z/Ai+bvXo9DN0m\n5PqpiRn9gNNx+UqW+JbHD/s2h30flrjItyQJ8jq5ugRX6ORuucIrRcT0ITCoc830IMVb9KkIlH7x\nnHSJR8yu/wbmvwBjGoYo3qqYsRNwF7CvYhatWWA2ASb4FqIq+ZtcScwx417gSuDE+vZXSKTFs82a\n9XABmYXL1ZRPiiLhWiJ0fP0NYfNOMHkH6YUPfMuVDB9FOooBM9bHRaIOlnjKtzw+idJ/XCoxzrcs\nFSRPeDf0d2h3oHT6i/XvnzWAT4AecnV+A54ogpl+hR3UpT0w4ymgExBLpR/3PQgfRLVLnwFuLneF\nH7EJMNO3EJVJPqMd+hbsd5cZnSUW1K9/fohSHVwH7JcbqQPZUBRKvxrDgbNw1XpiSPz3IAqJGQ2A\nh4HJuFxHZY0ZjYG1gNjlFKo8uarAjDWBp812Owp+H1LPfaq7gNPN2Efi5dxIHciUojDvVMaMVXDV\nkLpI8ZotQcjfXx0zbgK2wdnx60xmVeqYsTWu0MgWvmVJB1ccZdoouGcfuKZJfe/paCP/MmCHcvPc\nigtF4LJZlchT5mHgaN+yJMP9CEb3cK54p86Ecz8qY4U/CLeUPzgo/BXEzrRTGxKCU/+XUPhQT3fO\nJ4GfcCUeAx4oOqUfMRw4xiye8kuLZ7tN29tOgju+LVOFvw+uPN0BEt97FidOFJXSd7RYL1f7VO4h\nwjnAsMjUFSgwsVSaaTAF+BHYw7cgdfAOsL1ZUe6dZE1kwhgBHBJHE5xnilDp5zZASWIi8AZwdn0l\nC2ROUSr9aLYwnJgWaahA4gdgPhSH/TYXmNEC56lzjsR43/LEBbNm7Zw773lHwKF93N5PsTB9CJw+\nL6H4cxIrcxFwlhkt6y9fIBOKbiO3AqdcPv8MjnsB1m4R18hXMx4CXpHi4W2Uz3J5ZqyKC7l/VWJo\nLvosBUphc9/s1fNh9CCYNztXAUpm3Ag0ljg5J0IG0sN38p/sEyE1bQenLYlb4qqacupM0O2+5Uic\ns+yqiKVxnAYaCXokZBytfm7inTQwzet7E+i8HPe5VpS3fivfx1dOrSjNO44Ow+DqXHkU5JF/fQEX\nHGrWf6xZ1xF+l/UdhiVmm5Djc3YZsDFwrMQfOeivhCiJgL0OwPRcdihXjPwa4Npc9huonSLeYIz/\nD8kp+D7XwR1rQ5Pu/vPw5OecmTEAOAaXRG1ZffoqTUoiYK8j5CV9wm3AYDO6K0ZpKUqZIp7pF0PK\n0w7D4I6Nfa9GEpuI322V63Nmxq7ATcBBEl/VR87SZfoQZ8PP3UZoxTUtxArSjHWBVclDFLHEcnj+\nRrjgcbP+4/yvhssA3/albFtk0/85zjb9OBRgqGrHny04S7k6Z6CNo8ph+/o+13FviYpVZ30FR0yo\nz32az72ZFNe5O2h8/s5L4Y4lNBWzeWfxcvj8V9hvNKzTMp4pTwu3rE/tlVPZjt8EOANnRp31Gywb\nB6/8JZtzFmVNfA4YJlHvLIylTkVeGzP+BvwsMTv73lLtzcwcRrXcOTki5/b8Sl0X+ljKniJW+hwK\nGz0pvX6sb0FSc+UUGHIIDFsln7UAkrsEnrW32VsPQ+eeVR86GwJXAafMhoe+yEb5mNEQeAx4WeK2\n+h9BWTEL6Fq/LlLtzbRuW79+U9IRFxCZB+K/N1dqFLFNnwHASN9CpMKMTaHHBdCul8vDk8/SeNtd\nXXO2dNN6cP8+sGhGcjv+Z9OAfpmGwrsEXNwC/EKIqMyGWTgvp3qQaj9rq65mPGfGYHf/5YwO5GcT\nl+LYmysxfNuXsmmgzUALQSv7liWFfA1Bb4HOyPM47UDXwCW/pNo7qM1mCnoRdGSGY54NmgZq6vs8\nF2OLrtnc+vWR6poesS3oUND90V7LZ6BbQPuDGmcpr4EWg9bMz/kINv1Ct2I17xwBPCLxm29BUjAU\n+AE3I84pUZK5HsCpwK7AA/DOC7C0V7K9g9rKvZnxL1wqi7RWTGb0wiXL6iLxU04PrGxo1wCOaW32\nwX9g/rxs9qES1/S7W2DbveA/T1bqZyrwaLQi2xaX5fQC4JGohvMLwIvAJxLphONvACxWnpLmuWPZ\nbn+4djp89CZ8+UX89uZKDN9PnUxbNPP4BLSLb1lSyNctWoW0ynG/zUGnR8c+FfRnUBP3XnazJVBj\n0PegNmmMvz3oa1An3+e4WFsuZ7Wur10fgiG/w+7/TuNaNwf1A90Dmgf6HHQ7qBdo9Vq+dyDoxfye\nF+0GmuT7+pRL8y5AxgKjHUEzQOZbliSyNY9+TL1y2GcH0B2Rcv539FCpcewJl8C+Y91reooEdC/o\n/Do+0wb0Behg3+e4mFvqdAxdM0rHkHh4fCi4XHCJoMdiaNotzWtu0X11LuhV0E/R67nR3y0xzvHv\nwWlzMrmnMj8vGgq6zvf1KZfmXYCMBUY3gq70LUcK2R4E3ZGDfhqCDgb9BzQfdFmuVw6VxtoN9EGq\nhyioCegd0EW+z2+xt9RxG5cK9BtoWWQ//yayyc8FzQR9HO2jvOP2is79yin8c6rFXBy+OLtVg1aP\nZvx3gGa7cd8bCScuKIStPXrg7O/7+pRL8y5ARsKiBpES3NK3LElkOzL6cWa1YRb1sV4065kHeh23\nKdcwz3KvBJoF2jHFe0+ChsdxZVVsrbbEa9GDvnG0WlwH1Aq0IWhT0JagbaJVbmc45h03w899Erdo\nFbAFHPt2IZLEgRpFK41mvq9PubRi28jdA1go8ZFvQSpjRjvgH7g6sD9n+F0DuuA2ZvcHHgX2l5iW\nazmTIfGHGQ/gcue8U+3ta4A1gcOktDb9ArUyfQgM6lwzxfL0IXLlJNMqKWn26UfQdod8+LdH1/lj\ns8WLC+Q/3wn4SGJxjvsNpKDYlP6RwEO+hYAqEbBtYOOtoM+90q7vpv99GuO8kE4FmuIST50qV3il\n0DwIvGnGuXI1iDHjRKAPzlPnFw8ylRy1eVJl1tP0IdCkFyxtmr9o74JFk+8J/CfHfQZqw/dSI90G\nWhX0Haitf1my98LA5au5HucJ8wxoX2KQfx4+mgSH/sfZnfuNgZlfg9r7liu0VNeraTdnw8+Pzb1Q\n/vPBnl/4VjSVs8zoC5wu0d2/LF1HwJgBNWdBPR9yBdGrf56VgD/hZvW7APcDd0rMKojAdeBWLUdM\ngr+vmzA7nP4lPNYt+EvHl8Rqsz6rBp/90wj4BmijYN4pGMWk9B8HXpS4178s/cfCqEoPnzm4kr1T\nv4eFz1cKfloTF/x0CvATcCvwb2Vo9883mT7EAoH64h4oe98Fm3eB15+u/kDJZ1nPcqcobPpmNAd6\nAn/2LYujsr1zDi7w9gqgyZqwdACctrvZlAmw3X64TJRHA29Jcd0MDUmvAoUjSYLAAZWLC6WoKeyx\n+FBpUSwJ1/oC45SnUPDMqVwUYziRwo/eawLcsj7cuhWwhcRAiTfjq/AhJL0KFJZU6ZRP/8CMeXD6\nB3ks61n2FIvSH0BMvHbAeWHA6B4ua+bU75PPkr/7TkVTSSr3lZ0CgdSkWlnOeA/oDDOnJH9/x25m\nbFIQEUuY2Ct9M1oBOwHP+palMtLi2c7evfD5Yp8lV32I5TMFdCAAqVeWc2dLzIM5nyd//7efgbfM\neMWMw6KN4ECm+HYfqquBzgAN9y1HavlCatjQQsuk1fWbqSMdeCPQ4ZGr5yLQ3+MYoR/nFnvvHTMm\nAUMkXvYtSyry7doWCJQadf1m0vlNRaaeE4DjgJnAPcBjipl3XNyItdI3YzNgPNBW8c2dHwgEPBKV\n7zwA593XGfg3cI+UrxKPxU3cbfpxL5YSKHHMmrUz6zrCrP9Y99qsnW+ZAlWR+FXiKYkDgO2ARcDT\nZkw24y9mNPUsYqyI7Uw/SkT2MXC0xETf8gTKjxT+4jPDJnf8MaMBsA9u9t8dGIUz/0yS4uw+nX/i\nPNPfAWgATPItSKBcSeVPvs1ffUoVqBuJ3yVekOgHbAnMwLl9TzXjtChavixXcnGOyD0SGFnuT+WA\nT1L5k+91hBk9gIXAV0leK//7G4k/CidzoDoSC4FrzLgOl9Xzz8BVZtPGwSE7wz/blFPkbyzNO9HS\n7Atgb8Usd36gfEidk+hPI2HCOcB6QMskr5X/vQYuqViqB0Tl1+8zfUCEHDXZYcY6cNyLcOuO5ZZz\nKq4z/VgWSwmUG6mKnky7JJo9Lqyrh8izZF1qPhg2xBUQqfz31c1YRN0Ph6+AH6DZhiFHTXZIfFPA\nQjGxIq5KPzbFUgLlS9WiJ1t0gBYbZLqJK1cRa37UaiWKMG1BzdXDJsCu1f6+Gpz2K1zcpOaew8xh\nQMnOVHNHwQrFxIrYmXfMWBX3A9lGYp5veQIBWFET4UPgJInXYiDPqnDEq/Bw15rvnjITbt9NYkHh\nJSseEt5ZF2/iqpT+Ckz8CSbuLy2e4Fm8vBFH7539gKlB4QfiRGRr/ydwhm9ZACT+lzpHzUoAH5rx\njBn9zFil8BLGnyjn1LFw5U9wLjAMeKop9B5eyl48cVT6scqoGQhU4gFgdzPa+RbEkSo76gM9gPWB\nx4HTgXlm3GTGNr4kjS8dBsG9TcspjXOslH6lYimjfMsSCFRHYgmugMJgz6IAtWdHlVgi8S+JPYEu\nwBLgWTPeNuNUM9byKnxsKL8CQrGy6ZtxLNBHoo9vWQKBZESz/LeBdtFDoGiIXKH3xiUo2w94EVev\n+RWJ333K5otyLBUaq5k+wbQTiDkSs4HXcSUwi4ooSvVliSOAjXDHMQyYbcYwMzb1K6EPyq+AUGxm\n+lGxlA+B1hLLfMsTCKTCjD2Au4CtSiHa1oyOuNn/AOAT4P+Ax4ttJZMtbtP2L2/BN/Ph0w9LPcAt\nTkr/DGB7iWN9yxII1EaUDPA94EKJF33LkysiL58DcA+A3YAncQ+AN0o9HYoZHwP9JD70LUu+iZN5\nZwAw0rcQgUBdRArwZmLivpkrJH6ReFKiFy5J2UfA3cAnZlxsRlu/EuaVVqQRQFcKxGKmH4qlBIqN\nKIhwDrCHxMe+5ckX0aqmE3A8cAgwEbf5O1piuU/ZcoUZTXD5kRqX+ooG4jPTD8VSAkWFC47ibpwf\nfMkSlVWdKHES0BYYAZwEfGnGLWZs71fCnNAKmF8OCh88K/2KXNZw8QXQu30pR8EFSpI7gCMqcrOX\nOhI/SzwksTewM/At8KQZU8w4w2WuLEpaUyamHfCo9BN5L8YMgL81hpH7Qu9XguIPFAsS84HnccW5\nywqJzyUuBzYGzsY9BGaY8bgZB5jFNpljMlpD+eQp8jjTT1WVqHTDnwMlyc3A4CJTcjlD4g+JsRID\ncemiXwaGAnPNuMaMzf1KmBZls4kLXpV++YU/B0oPiUk4hdHLtyy+kfhR4m6JzkAPnH55zYw3zDjR\njGaeRUxFmOkXhopc1pUp/VzWgZKk5Nw364vEhxLn4xK/XQPsj5v9/8uMPaNU1XEhzPQLQ/mFPwdK\nlieAjc3YzrcgcUPiV4lnogLl7YEpwC04+/9QMzbwKyFQZhu5Xv30E/U9W7eFLXeBJgdIF471JlAg\nkCVmXAS0lzjOtyxxJ/L93xEX+Xs48C4u8vcpiWWFrvtbTtG4EJPgLAAzhgFrSpzqW5ZAIFPMWBuY\nAWwusci3PMVCFOTWB/cA2Aneex5u3RP+2bZqXeLMylRmKMOPwIYSP+Sj/7gRJ6XfGvgA2KhcTn6g\ntDDjHmCuxFW+ZSlGnKnnxKfh5m0Lleq43KJxIT4RuWXt8xwoGf4JnBzKE2aHxFz4/rsCe/WVVTQu\nxEjpR1T4PDfwLUggkCkS7+OSlB3iW5bipeBefWW1iQsxU/qRz/NCgs9zwBMVqUHM+o91rxlHiN8M\nnBltVgYypuBefWXlow/EMorwZuBMXC7vQKBgJFKDVESKLwUGdTZrlskm4nPATbi6tP/Nj6Sli7R4\ntlmzHjBzmDPptN8eDrpcenB2noYsKx99iNFGbgVmNAQ+Bw6UmOJbnkD5kKt6qWacCXSROCznQpYZ\nZpyIq5t9YJ76vx74RuLafPQfR2Jl3gEXzAHcRohwDBSc1m1ytIn4f0BPM9bPjVxlzUNAp6jmRj4o\nu5l+7JR+xN1AHzNa+BYkUB6YsRtsul3yTcQlGbkQSywGHgROyZV85UpUL/te8le3IGzkxgGJb4HH\ngUG+ZQmUNma0NONfwEjY7ZKam4jnfgt37m7G4Rl2fQtwohmNcypweXI7MMCM5nnouxVltpEbO5t+\nBWZ0xKVp3VDiF9/yBEqLyC34ZOAyYDhwpcRPiRQA67V2boLTh8DitXFmhneAU9MNHjTjGeBpiXvy\ncxTlgxkPA5Mkbspxv2UVjQsxVvoAZrwCDJcY4VuWQOlgRmfc7HExTol/kMZ3GgPXAQcBx0j8J43v\n9AD+AXQsp+CffBBds5HAZhK/56jPsovGhZiadypxM3BG8HkO5AIz1jHjXmAUcAPQPR2FDytKBQ7G\nrQ5GmnGdGY3q+Nqr0eteWQsdAEDiLWAR7qFbb9yKbt+H4GJB1wfLqWJf3JX+c8CaOJ/nQCArzGhg\nxknAh8BPwFYSI7OZ3Uk8D2wLbAZMNKNDLZ8VLjVD8ETLDTmpW5CIxxjVG/62mnPTzbxUaw4C+fyg\nqNx9XBvoDNCjvuUIrTgbaCfQJNAE0LY57NdAJ4C+Bp0JWinF5xpHn9nE97ko9gZqCPqyvtcRuoyA\nJQJVaksEvV4AbQRqUncfTdvBwBmJfpbI/b9pO9/nqa4Wa5s+QFRibTawrcQXnsUJxJSaOdjbXQ8j\nBwF9gQuBByT+yP24bAKMAJYAx0p8Wfn9LmZ3N6Ntr19Ysg40kLH8t6Ys+XgRTH5T+kuu5Sl1zLgY\n2FTi+Oz76D8WRnWv+c4Fi+Ha74CWgHDmpK+i18rtK+h/PDzQo1DZQHNJHNMwVEFisRkPAqfifrwZ\nUeiCDIWgFI+pPiRPnzD0cHjvIdh+S4nv8zW2xEzn489FwLtmDJZ4rOL9FrDzaOa1rPSVlYHteudL\noNLnbuAzMy6Q+Dq7LiqSulVX2OOfkRgY7SE2AVrgHgAtKrWNgc7QvkvR1vj2vdRIc1m3abREbpzZ\n94p3CVZOx1T/c5Jqud5lRGHlUCfQp6B/gZpLojurL6smmATqzurLfJ+3Ym2ge0FDsv9+dr+hyFR3\nBOg5GLo8DvdcNi3uG7kASMwA3gQyXDZ1GJaY/YF7vXMT9/dipRSPqb60ah2HWZdcltjtgWXAFDN2\nE42SrqZT/T2QFjcDp2Rbt8Ctikf3gJ4PQb9x7jV5Za7ICWBvM4YDXwJHAyNh/HbFWuO7mG68m4F/\nmnGPlK7XRSpl0HVfM67C1eZ8B/gi/T5902Lj5Me07kY+pIkHqZbrecvBnhLJ/frNOAh4lBQu5cby\n3woqWAkh8b7ZiroFD2XXx+LZ1DKJNGOb6P0jcXb9EcCFEgvdJ8ZRNRvowqIxsxaT0h8L/AH0AMak\n95VUyuCL6biNmhOBO4AGZrwLK9o7wOfxfBAs3jj5MX3dypNAMWD6EBjUuVpKZK+zLolnzNiuAc0/\ngx+aVn+/CUtm+ZCrhLgZGGKWnettMsxoAxwBHIVzFR8B7KMUBdPrenDElaJR+hIyW+HznKbSv+xt\nuOQQ+OsqVZXBC8dKzK74VFSfdwdgR9xF/DuwepIHwQxV8wAp1KZqtJS9GrZaw2UOuILEMV0GrF5W\n+UMqk8jB3uwlN7OeNjkOsy6Jr7awH7/ak52awte4eYYB67KQGaGkYv2oqFvQGWf6zQozmgL9cL/7\nHYEncMndxlf/rZcKsXfZrIwZqwFzgF0lPqvjs62AKXDH8fDgEZkuwcxoibPPVjwMdgDWBt5jxUPg\nxoUw5c6aM8zk9sFMqPowWboY/rkRtP8cuv8Ctx8Cj+IWPisBhwLXToYnDi1nrx4zRgEPSzzuW5YK\nUrsH9hsnPREideuBGWcAXZVh3QIzVgZ64mb0+wOv4Wb1z0j8L+eCxoyimemDS7MahdGfDpyW6nOR\ny9VdwF3Syc/Byc9lMdZXwItRq+h3bRIPgoPg2/3gzqY1N1UbPWnGA7gNvWXA/yr9e1ktf//FrWiS\nuSCe8w2MjDz9/rZD1fcGz4Gj1oUm78F1a9Sj6lOxsx7O/hojUpkYm1bfmAlkzv3AZWasrzpieCKd\nULGSPxxXqOlB4HSJb/IuaYwoqpk+gBltgWnARhI/pvjMQOB8YCflMUNn6lncaXPglieB1ZK0VVP8\nfTWgAfA/GNoALmyUKvAjeSbIHa+DZw8pxmCRXGHGDGB/iU99y1JB8gf4xcvg7NVgQ4Dm0Gytcl6h\n1QczbgZ+lrgoxfvtgAE4Zd8QN6N/qC5LQSlTVDN9AIl5ZrwMHA8106xGZp0bgf3yqfAdqWZx70yQ\nOCvT3qJ0v6vCpy9Ck25V3024ICbbQDLrv05yr54O25uxOfBZqdooK9GSmM30a9Z8rXhI39wGmABz\nfoQjFsHfW5TxCq0eXPUE/PKS2cdd4Mt5USrsH3CePUcBW+FsoccDb8XTOaPA+A4UyDI4owtoFqhB\ntb8b6GnQlYWRIz+BUtkEG6X+zumzQbNB34NeBg0DHQRq6fs65vieaAJaBjLfsmQgcwM4Z2GxBvn4\nbsl/f4OXwKwfQY+BeoNW8S1n3Jp3AbK72DLQRFDvan8fCJpWyAvtbrwuI6DvWPda/8jYbB4mdX0H\n1BJ0IOgq0EvRQ2BO9OM4F7Q7aHXf17Ye98TGoNm+5chc7n5jkwTsCvqO9S1b3Fvqic6ej/iWLc6t\n6Mw7sMJ982bgTGA0FNqsU1mW3PvqpjIJ1Lbcr+s7chvTz0atYmNrU2AXoBNwMNAxsotPitpE4EOJ\nYogO8gAAAAJ6SURBVAgkip1pJz3iE1hWfKQKvlxzXR/SFAtFt5FbgfNbnzkXzngbGjWGDTaDw5+Q\ndgm5y7MkKgqyDe4h0An3QGiDc1OteAhMAuZK8bKNmtEHOF6il29ZMiH5Rm9u3H5LHbOuI1wu/PJ1\nXsiGIlb6zdrBgHfghrUSP5aTZ8JT4ceSQ8xYA9iJxIpgl+itSZXaZOUxk2U6mDEI2EGi6NIVJ/PG\nCvdw3YQHZnYUsdIPT3kfRGah9am6GtgBmE9Vs9BUieUFlOsyYGWJoYUaM+Cf8MDMnKK06TvikVmx\n3IjMOnOj9jisiHDcksRq4ASgvRnTSZiEJpFft9GWkDxHSqB0Kdb8Nz4pYqUfNsDiQrTR+37U7gUw\nowluBdAJOBC4CmhuxmQqrQiiDeZc0BIYl6O+AoGSpYjNO8GeV2xE+Yx2JrEi6AQspuom8bsSS7Lo\n+w1c6tvxuZM4ECg9ilbpQ7DnFTtJ3EY7AR2BmVQ1C32Qym00cQ/s2Q/eGwNvnBHugUAgNUWt9AOl\nRwq30ba4zKZV3Eah2YZhtRcIZEZQ+oHYk8Jt1ODsX+GqNsGDKxBInyLeyA2UCxI/AK9ErZLb6OLn\noEmbqp8OHlyBQG0URWH0QKAyUQqRufDh1ERh6gqCB1cgUBvBvBMIBAJlRJjpBwKBQBkRlH4gEAiU\nEUHpBwKBQBkRlH4gEAiUEUHpBwKBQBkRlH4gEAiUEUHpBwKBQBkRlH4gEAiUEUHpBwKBQBkRlH4g\nEAiUEUHpBwKBQBkRlH4gEAiUEUHpBwKBQBkRlH4gEAiUEUHpBwKBQBkRlH4gEAiUEUHpBwKBQBkR\nlH4gEAiUEUHpBwKBQBnx/x4YWJaHe6r2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed684a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 city tour with length 5912.6 in 0.157 secs for repeated_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "# Compare nn_tsp to repeated_nn_tsp\n",
    "plot_tsp(nn_tsp, Cities(100))\n",
    "plot_tsp(repeated_nn_tsp, Cities(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that `repeated_nn_tsp` does indeed take longer to run, and yields a tour that is shorter.  \n",
    "\n",
    "Let's try again with a smaller map that makes it easier to visualize the tours:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efb6b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2381.4 in 0.000 secs for nn_tsp\n"
     ]
    },
    {
     "data": {
      "image/png": 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m8X/PjUwB2zcjUYsgryYDpyYnQWrOjA+bMQV4ijArYbQ7VyUXN1ZdMhP308C3zTgzjdeQ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\nSEoUsCIiKfl/otWLcOBvkAEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f013cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2297.7 in 0.000 secs for repeated_nn_tsp\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x105373eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2291.8 in 1.619 secs for alltours_tsp\n"
     ]
    }
   ],
   "source": [
    "for f in [nn_tsp, repeated_nn_tsp, alltours_tsp]:\n",
    "    plot_tsp(f, Cities(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time the `repeated_nn_tsp` gives us a tour that is better than `nn_tsp`, but not quite optimal.  So, it looks like repetition is helping.  But if I want to tackle 1000 cities, I don't really want the run time to be 1000 times slower.  I'd like a way to moderate the repetition&mdash;to repeat the `nn_tsp` starting from *a sample* of the cities but not *all* the cities.\n",
    "\n",
    "# Sampled Repeated Nearest Neighbor Algorithm: revised `repeated_nn_tsp`\n",
    "\n",
    "\n",
    "We can give `repeated_nn_tsp` an optional argument specifying the number of different cities to try starting from. We will implement the function `sample` to draw a random sample of the specified size from all the cities.  Most of the work is done by the standard library function `random.sample`. What our `sample` adds is the same thing we did with the function `Cities`: we ensure that the function returns the same result each time for the same arguments, but can return different results if a `seed` parameter is passed in.  (In addition, if the sample size, `k` is `None` or is larger than the population, then return the whole population.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def repeated_nn_tsp(cities, repetitions=100):\n",
    "    \"Repeat the nn_tsp algorithm starting from specified number of cities; return the shortest tour.\"\n",
    "    return shortest_tour(nn_tsp(cities, start) \n",
    "                         for start in sample(cities, repetitions))\n",
    "\n",
    "def sample(population, k, seed=42):\n",
    "    \"Return a list of k elements sampled from population. Set random.seed with seed.\"\n",
    "    if k is None or k > len(population): \n",
    "        return population\n",
    "    random.seed(len(population) * k * seed)\n",
    "    return random.sample(population, k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare with 1, 10, and 100 starting cities on a 300 city map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def repeat_10_nn_tsp(cities): return repeated_nn_tsp(cities, 10)\n",
    "def repeat_100_nn_tsp(cities): return repeated_nn_tsp(cities, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KiMRlM/aVP/Pq52Svaz8jWVOIrvJMSKt8ZcuOOBWNzDsM9SI4M8Nzjhp+yn1z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\nREI/QoQIEcoRIqEfIUKECOUI/w8KjsgL2SCG7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef86e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299 city tour with length 12752.7 in 0.014 secs for nn_tsp\n"
     ]
    },
    {
     "data": {
      "image/png": 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WBZn7RykqoHPufOVHe8VBhNeVYj4wTinOAW4Tl9laleJw4C449swolkjdp8D0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\nXyBTQaokz2/3tIscSC+QTSB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l+5xIu6rAIVeUvNO9pp7c5tHHwnWvibxU4APKHs07Tu9s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\nMaMMXmqTZGOgckatqJKV4M5AgpwMstSlYsuhx53XQLsp6bl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C8wD4KUT0I3EIo+t1IC/6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2f8080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299 city tour with length 12070.6 in 0.127 secs for repeat_10_nn_tsp\n"
     ]
    },
    {
     "data": {
      "image/png": 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G7wArgPradmpnU/1mCnAnsAf8/k8f/CMz0DV6fQMRPlLq40egdCpMqVahwtCD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\nglH6BgYGBlkEo/QNDAwMsgj/Bd7vYgV5PruUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6c45c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299 city tour with length 11598.6 in 1.285 secs for repeat_100_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(nn_tsp, Cities(300))\n",
    "plot_tsp(repeat_10_nn_tsp, Cities(300))\n",
    "plot_tsp(repeat_100_nn_tsp, Cities(300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we add more starting cities, the run times get longer and the tours get shorter.\n",
    "\n",
    "I'd like to understand the tradefoff better.  I'd like to have a way to compare different algorithms (or different choices of parameters for one algorithm) over *multiple* trials, and summarize the results. That means we now have a new vocabulary item:\n",
    "\n",
    "# New Vocabulary: \"Maps\"\n",
    "\n",
    "\n",
    "We use the term *cities* and the function `Cities` to denote a set of cities.  But now I want to talk about multiple trials over a collection of sets of cities: a plural of a plural.  English doesn't give us a good way to do that, so it would be nice to have a *singular* noun that is a synonym for \"set of cities.\"  We'll use the term \"map\" for this, and the function `Maps` to create a collection of maps.  Just like `Cities`, the function `Maps` will give the same result every time it is called with the same arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def Maps(num_maps, num_cities):\n",
    "    \"Return a tuple of maps, each consisting of the given number of cities.\"\n",
    "    return tuple(Cities(num_cities, seed=(m, num_cities))\n",
    "                 for m in range(num_maps))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Benchmarking\n",
    "\n",
    "The term *benchmarking* means running a function on a standard collection of inputs, in order to compare its performance. We'll define a general-purpose function, `benchmark`, which takes a function and a collection of inputs for that function, and runs the function on each of the inputs.  It then returns two values: the average time taken per input, and the list of results of the function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@functools.lru_cache(None)\n",
    "def benchmark(function, inputs):\n",
    "    \"Run function on all the inputs; return pair of (average_time_taken, results).\"\n",
    "    t0           = time.clock()\n",
    "    results      = [function(x) for x in inputs]\n",
    "    t1           = time.clock()\n",
    "    average_time = (t1 - t0) / len(inputs)\n",
    "    return (average_time, results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Each time we develop a new algorithm, we would like to compare its performance to some standard old algorithms.\n",
    "The use of `@functools.lru_cache` here means that we don't need to to re-run the old algorithms on a standard data set each time; we can just cache the old results. \n",
    "\n",
    "We can use `benchmark` to see the average call to the absolute value function takes less than a microsecond:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.00000000069889e-07,\n",
       " [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "benchmark(abs, range(-10, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can see that `alltours_tsp` can handle 6-city maps in under a millisecond each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.00032370000000003785,\n",
       " [[(574+214j), (236+141j), (556+348j), (677+277j), (833+33j), (578+224j)],\n",
       "  [(433+6j), (396+143j), (527+431j), (167+227j), (113+100j), (127+105j)],\n",
       "  [(571+206j), (724+42j), (703+269j), (797+331j), (543+474j), (310+248j)],\n",
       "  [(12+30j), (344+45j), (693+77j), (548+186j), (279+508j), (171+229j)],\n",
       "  [(243+271j), (379+72j), (859+331j), (840+411j), (651+478j), (8+369j)],\n",
       "  [(672+502j), (820+460j), (887+489j), (853+65j), (422+69j), (433+135j)],\n",
       "  [(38+119j), (644+90j), (622+288j), (602+511j), (509+424j), (275+536j)],\n",
       "  [(18+208j), (832+456j), (483+477j), (314+533j), (314+539j), (23+596j)],\n",
       "  [(274+560j), (213+594j), (248+84j), (550+317j), (508+577j), (377+575j)],\n",
       "  [(813+467j), (438+216j), (270+118j), (71+18j), (125+320j), (199+578j)]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "benchmark(alltours_tsp, Maps(10, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Benchmarking Specifically for TSP Algorithms\n",
    "\n",
    "Now let's add another function, `benchmarks`, which builds on `benchmark` in two ways:\n",
    "\n",
    "1. It compares multiple algorithms, rather than just running one algorithm. (Hence the plural `benchmarks`.)\n",
    "2. It is specific to `TSP` algorithms, and rather than returning results, it prints summary statistics: the mean, standard deviation, min, and max of tour lengths, as well as the time taken and the number and size of the sets of cities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def benchmarks(tsp_algorithms, maps=Maps(30, 60)):\n",
    "    \"Print benchmark statistics for each of the algorithms.\"    \n",
    "    for tsp in tsp_algorithms:\n",
    "        time, results = benchmark(tsp, maps)\n",
    "        lengths = [tour_length(r) for r in results]\n",
    "        print(\"{:>25} |{:7.0f} ±{:4.0f} ({:5.0f} to {:5.0f}) |{:7.3f} secs/map | {} ⨉ {}-city maps\"\n",
    "              .format(tsp.__name__, mean(lengths), stdev(lengths), min(lengths), max(lengths),\n",
    "                      time, len(maps), len(maps[0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How Many Starting Cities is best for `nn_tsp`?\n",
    "---\n",
    "\n",
    "Now we are in a position to gain some insight into how many repetitions, or starting cities, we need to get a good result from `nn_tsp`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def repeat_25_nn_tsp(cities): return repeated_nn_tsp(cities, 25)\n",
    "def repeat_50_nn_tsp(cities): return repeated_nn_tsp(cities, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   nn_tsp |   5668 ± 488 ( 4674 to  6832) |  0.001 secs/map | 30 ⨉ 60-city maps\n",
      "         repeat_10_nn_tsp |   5232 ± 374 ( 4577 to  6172) |  0.006 secs/map | 30 ⨉ 60-city maps\n",
      "         repeat_25_nn_tsp |   5159 ± 394 ( 4620 to  6069) |  0.014 secs/map | 30 ⨉ 60-city maps\n",
      "         repeat_50_nn_tsp |   5118 ± 386 ( 4512 to  6069) |  0.029 secs/map | 30 ⨉ 60-city maps\n",
      "        repeat_100_nn_tsp |   5113 ± 384 ( 4512 to  6069) |  0.034 secs/map | 30 ⨉ 60-city maps\n"
     ]
    }
   ],
   "source": [
    "algorithms = [nn_tsp, repeat_10_nn_tsp, repeat_25_nn_tsp, repeat_50_nn_tsp, repeat_100_nn_tsp]\n",
    "\n",
    "benchmarks(algorithms, Maps(30, 60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that adding more starting cities results in shorter tours, but you start getting diminishing returns after 50 repetitions.\n",
    "\n",
    "Let's try again with bigger maps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   nn_tsp |   7789 ± 458 ( 6877 to  8632) |  0.002 secs/map | 30 ⨉ 120-city maps\n",
      "         repeat_10_nn_tsp |   7316 ± 334 ( 6646 to  7870) |  0.021 secs/map | 30 ⨉ 120-city maps\n",
      "         repeat_25_nn_tsp |   7242 ± 287 ( 6725 to  7870) |  0.053 secs/map | 30 ⨉ 120-city maps\n",
      "         repeat_50_nn_tsp |   7189 ± 295 ( 6646 to  7742) |  0.106 secs/map | 30 ⨉ 120-city maps\n",
      "        repeat_100_nn_tsp |   7173 ± 289 ( 6646 to  7736) |  0.213 secs/map | 30 ⨉ 120-city maps\n"
     ]
    }
   ],
   "source": [
    "benchmarks(algorithms, Maps(30, 120))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   nn_tsp |   8668 ± 485 ( 7183 to  9636) |  0.003 secs/map | 30 ⨉ 150-city maps\n",
      "         repeat_10_nn_tsp |   8220 ± 364 ( 7290 to  9197) |  0.033 secs/map | 30 ⨉ 150-city maps\n",
      "         repeat_25_nn_tsp |   8117 ± 326 ( 7222 to  8918) |  0.083 secs/map | 30 ⨉ 150-city maps\n",
      "         repeat_50_nn_tsp |   8086 ± 300 ( 7237 to  8676) |  0.166 secs/map | 30 ⨉ 150-city maps\n",
      "        repeat_100_nn_tsp |   8062 ± 284 ( 7174 to  8603) |  0.331 secs/map | 30 ⨉ 150-city maps\n"
     ]
    }
   ],
   "source": [
    "benchmarks(algorithms, Maps(30, 150))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are similar. So depending on what your priorities are (run time versus tour length), somewhere around 25 or 50 repetitions might be a good tradeoff.\n",
    "\n",
    "Next let's try to analyze where nearest neighbors goes wrong, and see if we can do something about it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Problem with Nearest Neighbors: Outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the 20-city map that we build below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAEACAYAAAAk4WSCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f00e7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outliers_list = [City(2, 2),  City(2, 3),  City(2, 4),  City(2, 5),  City(2, 6),  \n",
    "                 City(3, 6),  City(4, 6),  City(5, 6),  City(6, 6),  \n",
    "                 City(6, 5),  City(6, 4),  City(6, 3),  City(6, 2),  \n",
    "                 City(5, 2),  City(4, 2),  City(3, 2),  \n",
    "                 City(1, 6.8),  City(7.8, 6.4),  City(7, 1.2),  City(0.2, 2.8)]\n",
    "\n",
    "outliers = set(outliers_list)\n",
    "\n",
    "plot_lines(outliers, 'bo')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what a nearest neighbor search does on this map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cjvuSUqNke8gCLQnFpdyXlLKWZSOIUitDcSn3JaWsuHzOjfuSUho5N4IodTIUl3OafckP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\nUZIqDEVJqjAUJanCUJSkiv8HOSlz7KcrYmAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0590b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20 city tour with length 38.8 in 0.000 secs for nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(nn_tsp, outliers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tour starts out going around the inner square.  But then we are left with long lines to pick up the outliers. \n",
    "Let's try to understand what went wrong.  First we'll create a new tool to draw better diagrams:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_labeled_lines(points, *args):\n",
    "    \"\"\"Plot individual points, labeled with an index number.\n",
    "    Then, args describe lines to draw between those points.\n",
    "    An arg can be a matplotlib style, like 'ro--', which sets the style until changed,\n",
    "    or it can be a list of indexes of points, like [0, 1, 2], saying what line to draw.\"\"\"\n",
    "    # Draw points and label them with their index number\n",
    "    plot_lines(points, 'bo')\n",
    "    for (label, p) in enumerate(points):\n",
    "        plt.text(p.x, p.y, '  '+str(label))\n",
    "    # Draw lines indicated by args\n",
    "    style = 'bo-'\n",
    "    for arg in args:\n",
    "        if isinstance(arg, str):\n",
    "            style = arg\n",
    "        else: # arg is a list of indexes into points, forming a line\n",
    "            Xs = [points[i].x for i in arg]\n",
    "            Ys = [points[i].y for i in arg]\n",
    "            plt.plot(Xs, Ys, style)\n",
    "    plt.axis('scaled'); plt.axis('off'); plt.show()        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the diagram below, imagine we are running a nearest neighbor algorithm, and it has created a partial tour from city 0 to city 4.  Now there is a choice.  City 5 is the nearest neighbor.  But if we don't take city 16 at this point, we will have to pay a higher price sometime later to pick up city 16.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GeUoUndFaS1aQi2+C1V3ZnBoBlp0sVRZFDG8a5ymeU1PEW5qF6F4zVpiQ3a6elY2PS/li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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed8b978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_labeled_lines(outliers_list, 'bo-', [0, 1, 2, 3, 4], 'ro--', [4, 16], 'bo--', [4, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that picking up an outlier is *sometimes* a good idea, but sometimes going directly to the nearest neighbor is a better idea. So what can we do?  It is difficult to make the choice between an outlier and a nearest neighbor while we are constructing a tour, because we don't have the context of the whole tour yet. So here's an alternative idea: don't try to make the right choice while constructing the tour; just go ahead and make any choice, then when the tour is complete, *alter* it to correct problems caused by outliers (or other causes)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# New Vocabulary: \"Segment\"\n",
    "\n",
    "\n",
    "We'll define a *segment* as a subsequence of a tour: a sequence of consecutive cities within a tour. A tour forms a loop, but a segment does not have a loop; it is open-ended on both ends. So, if `[A, B, C, D]` is a 4-city tour, then segments include `[A, B]`, `[B, C, D]`, and many others.  Note that the segment `[A, B, C, D]` is different than the tour `[A, B, C, D]`; the tour returns from `D` to `A` but the segment does not. \n",
    "\n",
    "# Altering Tours by Reversing Segments\n",
    "\n",
    "\n",
    "One way we could try to improve a tour is by *reversing* a segment.  Consider this tour:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EPaKUPJy3EZuUmf1/M3vAzB40s1+Y2TVjfdDcm9Rwi+ZXuPsb3X1bYEPg6ObKksFGGzAa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\nNSkRyZqalIhkTU1KRLKmJiUiWfsv+abpfa0U1HMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed9d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cross = [City(9, 3),  City(3, 10),  City(2, 16),  City(3, 21),  City(9, 28), \n",
    "         City(26, 3), City(32, 10), City(33, 16), City(32, 21), City(26, 28)]\n",
    "\n",
    "plot_labeled_lines(cross, range(-1,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is clearly not an optimal tour.  We should \"uncross\" the lines, which can be achieved by reversing a segment.  The tour as it stands is `[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]`.  If we reverse the segment `[5, 6, 7, 8, 9]`, we get the tour `[0, 1, 2, 3, 4, 9, 8, 7, 6, 5]`, which is the optimal tour.  In the diagram below, reversing `[5, 6, 7, 8, 9]` is equivalent to deleting the  red  dashed lines and adding the green dotted lines. If the sum of the lengths of the green dotted lines is less than the sum of the lengths of the red dashed lines, then we know the reversal is an improvement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y2U/LT+V6ZPYmvbnPKlzmXQ1ciZm3l+Slt4PnxxFubeq3JO/dkwaNhH2/Dx96N8z4Pczp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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0130f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_labeled_lines(cross, 'bo-', range(5), range(5, 10), \n",
    "                          'g:', (4, 9), (0, 5), \n",
    "                          'r--', (4, 5), (0, 9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that reversing `[5, 6, 7, 8, 9]` works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SOnIQ3n7r2UG1CCzMRc1UK3tSI3YpTz2ymdfVFTPTMDXbBBM0X6dmm9e1Ga6kRuxJ+Ow+\nmjOo1bd70bNpdHI+eSKl7Xthdn+zxVuYg5npnE+eiJ6tNt7uSSqa2z1JRTOkJBXNkJJUNENKUtEM\nKUlFM6QkFc2QklQ0Q0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUNENKUtEMKUlFM6Qk\nFc2QklQ0Q0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUNENKUtEMKUlFM6QkFc2QklQ0\nQ0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUtP8HadpvJUCmS/cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed8b128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tour = Tour(cross)\n",
    "tour[5:10] = reversed(tour[5:10])\n",
    "plot_tour(tour)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is how we can check if reversing a segment is an improvement, and if so to do it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def reverse_segment_if_better(tour, i, j):\n",
    "    \"If reversing tour[i:j] would make the tour shorter, then do it.\" \n",
    "    # Given tour [...A-B...C-D...], consider reversing B...C to get [...A-C...B-D...]\n",
    "    A, B, C, D = tour[i-1], tour[i], tour[j-1], tour[j % len(tour)]\n",
    "    # Are old edges (AB + CD) longer than new ones (AC + BD)? If so, reverse segment.\n",
    "    if distance(A, B) + distance(C, D) > distance(A, C) + distance(B, D):\n",
    "        tour[i:j] = reversed(tour[i:j])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's write a function, `alter_tour`, which finds segments to swap. What segments should we consider? I don't know how to be clever about the choice, but I do know how to be fairly thorough: try all segments of all lengths at all starting positions. I have an intuition that trying longer ones first is better (although I'm not sure). \n",
    "\n",
    "I worry that even trying all segements won't be enough: after I reverse one segment, it might open up opportunities to reverse other segments.  So, after trying all possible segments, I'll check the tour length.  If it has been reduced, I'll go through the `alter_tour` process again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def alter_tour(tour):\n",
    "    \"Try to alter tour for the better by reversing segments.\"\n",
    "    original_length = tour_length(tour)\n",
    "    for (start, end) in all_segments(len(tour)):\n",
    "        reverse_segment_if_better(tour, start, end)\n",
    "    # If we made an improvement, then try again; else stop and return tour.\n",
    "    if tour_length(tour) < original_length:\n",
    "        return alter_tour(tour)\n",
    "    return tour\n",
    "\n",
    "def all_segments(N):\n",
    "    \"Return (start, end) pairs of indexes that form segments of tour of length N.\"\n",
    "    return [(start, start + length)\n",
    "            for length in range(N, 2-1, -1)\n",
    "            for start in range(N - length + 1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is what the list of all segments look like, for N=4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 4), (0, 3), (1, 4), (0, 2), (1, 3), (2, 4)]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_segments(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that altering the cross tour does straighten it out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SOnIQ3n7r2UG1CCzMRc1UK3tSI3YpTz2ymdfVFTPTMDXbBBM0X6dmm9e1Ga6kRuxJ+Ow+\nmjOo1bd70bNpdHI+eSKl7Xthdn+zxVuYg5npnE+eiJ6tNt7uSSqa2z1JRTOkJBXNkJJUNENKUtEM\nKUlFM6QkFc2QklQ0Q0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUNENKUtEMKUlFM6Qk\nFc2QklQ0Q0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUNENKUtEMKUlFM6QkFc2QklQ0\nQ0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUtP8HadpvJUCmS/cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f60080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_tour(alter_tour(Tour(cross)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Altered Nearest Neighbor Algorithm (`altered_nn_tsp`)\n",
    "----\n",
    "\n",
    "Let's see what happens when we alter the output of `nn_tsp`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def altered_nn_tsp(cities):\n",
    "    \"Run nearest neighbor TSP algorithm, and alter the results by reversing segments.\"\n",
    "    return alter_tour(nn_tsp(cities))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try this new algorithm on some test cases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SOnIQ3n7r2UG1CCzMRc1UK3tSI3YpTz2ymdfVFTPTMDXbBBM0X6dmm9e1Ga6kRuxJ+Ow+\nmjOo1bd70bNpdHI+eSKl7Xthdn+zxVuYg5npnE+eiJ6tNt7uSSqa2z1JRTOkJBXNkJJUNENKUtEM\nKUlFM6QkFc2QklQ0Q0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUNENKUtEMKUlFM6Qk\nFc2QklQ0Q0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUNENKUtEMKUlFM6QkFc2QklQ0\nQ0pS0QwpSUUzpCQVzZCSVDRDSlLRDClJRTOkJBXNkJJUtP8HadpvJUCmS/cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0d8e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 93.2 in 0.000 secs for altered_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(altered_nn_tsp, set(cross))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xM95jxiXA7wizErZxZ0Z8cGPDxXd3ewGnmnFmFteQNStqwN4FfDTVPxYpHnceBh4gbAQ1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\nSEYUsCIiGVHAiohkRAErIpKR/w/mf+vfo0FlFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f627f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2333.4 in 0.000 secs for altered_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(altered_nn_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It fails to get the optimal result here.  Let's try benchmarking:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   nn_tsp |   5668 ± 488 ( 4674 to  6832) |  0.001 secs/map | 30 ⨉ 60-city maps\n",
      "         repeat_50_nn_tsp |   5118 ± 386 ( 4512 to  6069) |  0.029 secs/map | 30 ⨉ 60-city maps\n",
      "           altered_nn_tsp |   4820 ± 233 ( 4450 to  5346) |  0.008 secs/map | 30 ⨉ 60-city maps\n"
     ]
    }
   ],
   "source": [
    "algorithms = [nn_tsp, repeat_50_nn_tsp, altered_nn_tsp]\n",
    "\n",
    "benchmarks(algorithms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is quite encouraging; `altered_nn_tsp` gives shorter tours and is  faster than repeating nearest neighbors from 50 starting cities. Could we do better?\n",
    "\n",
    "Altered Repeated Nearest Neighbor Algorithm (`altered_repeated_nn_tsp`)\n",
    "---\n",
    "\n",
    "We have seen that the *nearest neighbor* algorithm is improved by both the *alteration* and *repetition* strategies. So why not apply both strategies?  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def repeated_altered_nn_tsp(cities, repetitions=20): \n",
    "    \"Use alteration to improve each repetition of nearest neighbors.\"\n",
    "    return shortest_tour(alter_tour(nn_tsp(cities, start)) \n",
    "                         for start in sample(cities, repetitions))\n",
    "\n",
    "def repeat_5_altered_nn_tsp(cities): return repeated_altered_nn_tsp(cities, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see it in action:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pChI60o9cOQOAK4H/Al0lvvQqqlFOPhJevBT6rVSpeV4qCRfi2GnNzKPgd8cD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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c228e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 city tour with length 5701.6 in 0.541 secs for repeated_altered_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(repeated_altered_nn_tsp, Cities(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks like a good tour.  Let's gather more data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   nn_tsp |   5668 ± 488 ( 4674 to  6832) |  0.001 secs/map | 30 ⨉ 60-city maps\n",
      "         repeat_50_nn_tsp |   5118 ± 386 ( 4512 to  6069) |  0.029 secs/map | 30 ⨉ 60-city maps\n",
      "           altered_nn_tsp |   4820 ± 233 ( 4450 to  5346) |  0.008 secs/map | 30 ⨉ 60-city maps\n",
      "  repeated_altered_nn_tsp |   4640 ± 194 ( 4298 to  4991) |  0.148 secs/map | 30 ⨉ 60-city maps\n",
      "----------------------------------------------------------------------------------------------------\n",
      "                   nn_tsp |   7789 ± 458 ( 6877 to  8632) |  0.002 secs/map | 30 ⨉ 120-city maps\n",
      "         repeat_50_nn_tsp |   7189 ± 295 ( 6646 to  7742) |  0.106 secs/map | 30 ⨉ 120-city maps\n",
      "           altered_nn_tsp |   6589 ± 202 ( 6188 to  7016) |  0.036 secs/map | 30 ⨉ 120-city maps\n",
      "  repeated_altered_nn_tsp |   6402 ± 185 ( 6015 to  6779) |  0.701 secs/map | 30 ⨉ 120-city maps\n"
     ]
    }
   ],
   "source": [
    "algorithms = [nn_tsp, repeat_50_nn_tsp, altered_nn_tsp, repeated_altered_nn_tsp]\n",
    "\n",
    "benchmarks(algorithms)\n",
    "print('-' * 100)\n",
    "benchmarks(algorithms, Maps(30, 120))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, alteration gives the most gain, but alteration plus repetition gives a modest improvement in tour length, at the cost of 20 times more run time. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Non-Random Maps\n",
    "===="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I thought it would be fun to work on some *real* maps, instead of random maps. First I found [a page](http://www.realestate3d.com/gps/latlong.htm) that lists geographical coordinates of US cities.  Here is an excerpt from that page:\n",
    "\n",
    "<pre>\n",
    "[TCL]  33.23   87.62  Tuscaloosa,AL\n",
    "[FLG]  35.13  111.67  Flagstaff,AZ\n",
    "[PHX]  33.43  112.02  Phoenix,AZ\n",
    "</pre>\n",
    "\n",
    "I also found a [blog post](http://www.randalolson.com/2015/03/08/computing-the-optimal-road-trip-across-the-u-s/) by Randal S. Olson who chose 50 landmarks across the states and found a tour based on actual road-travel distances, not straight-line distance. His data looks like this:\n",
    "\n",
    "<pre>\n",
    "Mount Rushmore National Memorial, South Dakota 244, Keystone, SD\t43.879102\t-103.459067\n",
    "Toltec Mounds, Scott, AR\t34.647037\t-92.065143\n",
    "Ashfall Fossil Bed, Royal, NE\t42.425000\t-98.158611\n",
    "</pre> \n",
    "You can't see, but fields are separated by tabs in this data.\n",
    "\n",
    "Now we have a problem: we have two similar but different data formats, and we want to convert both of them to `Maps` (sets of cities).  Python provides a module, [`csv`](https://docs.python.org/3/library/csv.html) (for \"comma-separated values\"), to parse data like this.  The function `csv.reader` takes an input that should be an iterable over lines of text, and optionally you can tell it what character to use as a delimiter (as well as several other options). For each line, it generates a\n",
    "list of fields.  For example, for the line `\"[TCL]  33.23   87.62  Tuscaloosa,AL\"`  it would generate the list `['[TCL]', '33.23', '87.62', 'Tuscaloosa,AL']`.\n",
    "\n",
    "I define the function `Coordinate_map` to take an iterable of lines (a file object or a list of strings), parse it with `csv_reader`, pick out the latitude and longitude columns, and build a `City` out of each one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def lines(text): return text.strip().splitlines()\n",
    "\n",
    "def Coordinate_map(lines, delimiter=' ', lat_col=1, long_col=2, lat_scale=69, long_scale=-48):\n",
    "    \"\"\"Make a set of Cities from an iterable of lines of text.\n",
    "    Specify the column delimiter, and the zero-based column number of lat and long.\n",
    "    Treat long/lat as a square x/y grid, scaled by long_scale and lat_scale.\n",
    "    Source can be a file object, or list of lines.\"\"\"\n",
    "    return frozenset(City(long_scale * float(row[long_col]), \n",
    "                          lat_scale  * float(row[lat_col]))\n",
    "                     for row in csv.reader(lines, delimiter=delimiter, skipinitialspace=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might be wondering about the `lat_scale=69, long_scale=-48` part. The issue is that we have latitude and longitude for cities, and we want to compute the distance between cities. To do that accurately requires [complicated trigonometry](http://en.wikipedia.org/wiki/Haversine_formula).  But we can get an approximation by assuming the earth is flat, and that latitude and longitude are on a rectangular grid. (This is a bad approximation if you're talking about distances of 10,000 miles, but close enough for 100 miles, as long as you're not too close to the poles.)  I took the latitude of the center of the country (Wichita, KS: latitude 37.65) and plugged it into a [Length Of A Degree Of Latitude\n",
    "And Longitude Calculator](http://www.csgnetwork.com/degreelenllavcalc.html) to find that, in Wichita, one degree of latitude is 69 miles, and one degree of longitude is 48 miles.  (It is -48 rather than +48 because the US is west of the prime meridian.) \n",
    "\n",
    "Now let's create the map of USA cities, and find a tour for it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "USA_map = Coordinate_map(lines(\"\"\"\n",
    "[TCL]  33.23   87.62  Tuscaloosa,AL\n",
    "[FLG]  35.13  111.67  Flagstaff,AZ\n",
    "[PHX]  33.43  112.02  Phoenix,AZ\n",
    "[PGA]  36.93  111.45  Page,AZ\n",
    "[TUS]  32.12  110.93  Tucson,AZ\n",
    "[LIT]  35.22   92.38  Little Rock,AR\n",
    "[SFO]  37.62  122.38  San Francisco,CA\n",
    "[LAX]  33.93  118.40  Los Angeles,CA\n",
    "[SAC]  38.52  121.50  Sacramento,CA\n",
    "[SAN]  32.73  117.17  San Diego,CA\n",
    "[SBP]  35.23  120.65  San Luis Obi,CA\n",
    "[EKA]  41.33  124.28  Eureka,CA\n",
    "[DEN]  39.75  104.87  Denver,CO\n",
    "[DCA]  38.85   77.04  Washington/Natl,DC\n",
    "[MIA]  25.82   80.28  Miami Intl,FL\n",
    "[TPA]  27.97   82.53  Tampa Intl,FL\n",
    "[JAX]  30.50   81.70  Jacksonville,FL\n",
    "[TLH]  30.38   84.37  Tallahassee,FL\n",
    "[ATL]  33.65   84.42  Atlanta,GA\n",
    "[BOI]  43.57  116.22  Boise,ID\n",
    "[CHI]  41.90   87.65  Chicago,IL\n",
    "[IND]  39.73   86.27  Indianapolis,IN\n",
    "[DSM]  41.53   93.65  Des Moines,IA\n",
    "[SUX]  42.40   96.38  Sioux City,IA\n",
    "[ICT]  37.65   97.43  Wichita,KS\n",
    "[LEX]  38.05   85.00  Lexington,KY\n",
    "[NEW]  30.03   90.03  New Orleans,LA\n",
    "[BOS]  42.37   71.03  Boston,MA\n",
    "[PWM]  43.65   70.32  Portland,ME\n",
    "[BGR]  44.80   68.82  Bangor,ME\n",
    "[CAR]  46.87   68.02  Caribou Mun,ME\n",
    "[DET]  42.42   83.02  Detroit,MI\n",
    "[STC]  45.55   94.07  St Cloud,MN\n",
    "[DLH]  46.83   92.18  Duluth,MN\n",
    "[STL]  38.75   90.37  St Louis,MO\n",
    "[JAN]  32.32   90.08  Jackson,MS\n",
    "[BIL]  45.80  108.53  Billings,MT\n",
    "[BTM]  45.95  112.50  Butte,MT\n",
    "[RDU]  35.87   78.78  Raleigh-Durh,NC\n",
    "[INT]  36.13   80.23  Winston-Salem,NC\n",
    "[OMA]  41.30   95.90  Omaha/Eppley,NE\n",
    "[LAS]  36.08  115.17  Las Vegas,NV\n",
    "[RNO]  39.50  119.78  Reno,NV\n",
    "[AWH]  41.33  116.25  Wildhorse,NV\n",
    "[EWR]  40.70   74.17  Newark Intl,NJ\n",
    "[SAF]  35.62  106.08  Santa Fe,NM\n",
    "[NYC]  40.77   73.98  New York,NY\n",
    "[BUF]  42.93   78.73  Buffalo,NY\n",
    "[ALB]  42.75   73.80  Albany,NY\n",
    "[FAR]  46.90   96.80  Fargo,ND\n",
    "[BIS]  46.77  100.75  Bismarck,ND\n",
    "[CVG]  39.05   84.67  Cincinnati,OH\n",
    "[CLE]  41.42   81.87  Cleveland,OH\n",
    "[OKC]  35.40   97.60  Oklahoma Cty,OK\n",
    "[PDX]  45.60  122.60  Portland,OR\n",
    "[MFR]  42.37  122.87  Medford,OR\n",
    "[AGC]  40.35   79.93  Pittsburgh,PA\n",
    "[PVD]  41.73   71.43  Providence,RI\n",
    "[CHS]  32.90   80.03  Charleston,SC\n",
    "[RAP]  44.05  103.07  Rapid City,SD\n",
    "[FSD]  43.58   96.73  Sioux Falls,SD\n",
    "[MEM]  35.05   90.00  Memphis Intl,TN\n",
    "[TYS]  35.82   83.98  Knoxville,TN\n",
    "[CRP]  27.77   97.50  Corpus Chrst,TX\n",
    "[DRT]  29.37  100.92  Del Rio,TX\n",
    "[IAH]  29.97   95.35  Houston,TX\n",
    "[SAT]  29.53   98.47  San Antonio,TX\n",
    "[LGU]  41.78  111.85  Logan,UT\n",
    "[SLC]  40.78  111.97  Salt Lake Ct,UT\n",
    "[SGU]  37.08  113.60  Saint George,UT\n",
    "[CNY]  38.77  109.75  Moab,UT\n",
    "[MPV]  44.20   72.57  Montpelier,VT\n",
    "[RIC]  37.50   77.33  Richmond,VA\n",
    "[BLI]  48.80  122.53  Bellingham,WA\n",
    "[SEA]  47.45  122.30  Seattle,WA\n",
    "[ALW]  46.10  118.28  Walla Walla,WA\n",
    "[GRB]  44.48   88.13  Green Bay,WI\n",
    "[MKE]  42.95   87.90  Milwaukee,WI\n",
    "[CYS]  41.15  104.82  Cheyenne,WY\n",
    "[SHR]  44.77  106.97  Sheridan,WY\n",
    "\"\"\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BAoAiwQKAIsECgCLBAoAiwQKAIsECgCLBAoAiwQKAIsECgCLBAoAiwQKAIsECgCLBAoAi\nwQKAIsECgCLBAoAiwQKAIsECgCLBAoAiwQKAIsECgCLBAoAiwQKAIsECgKL/A16f7ZbG/yzJAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116d3e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lines(USA_map, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HwJDfEVt4+t1whU/ND+Dwf6juGXfBnh64egqJJWd6WToCarrDy09mfUVcKaiy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\nhmEYRlFMWRiGYRhF+X/yRvdjURKB8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef5aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 13562.6 in 0.297 secs for repeated_altered_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(repeated_altered_nn_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad! There are no obvious errors in the tour (although I'm not at all confident it is the optimal tour). \n",
    "\n",
    "Now let's do the same for Randal Olson's landmarks.  Note that the data is delimited by tabs, not spaces, and the longitude already has a minus sign, so we don't need another one in `long_scale`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "USA_landmarks_map = Coordinate_map(lines(\"\"\"\n",
    "Mount Rushmore National Memorial, South Dakota 244, Keystone, SD\t43.879102\t-103.459067\n",
    "Toltec Mounds, Scott, AR\t34.647037\t-92.065143\n",
    "Ashfall Fossil Bed, Royal, NE\t42.425000\t-98.158611\n",
    "Maryland State House, 100 State Cir, Annapolis, MD 21401\t38.978828\t-76.490974\n",
    "The Mark Twain House & Museum, Farmington Avenue, Hartford, CT\t41.766759\t-72.701173\n",
    "Columbia River Gorge National Scenic Area, Oregon\t45.711564\t-121.519633\n",
    "Mammoth Cave National Park, Mammoth Cave Pkwy, Mammoth Cave, KY\t37.186998\t-86.100528\n",
    "Bryce Canyon National Park, Hwy 63, Bryce, UT\t37.593038\t-112.187089\n",
    "USS Alabama, Battleship Parkway, Mobile, AL\t30.681803\t-88.014426\n",
    "Graceland, Elvis Presley Boulevard, Memphis, TN\t35.047691\t-90.026049\n",
    "Wright Brothers National Memorial Visitor Center, Manteo, NC\t35.908226\t-75.675730\n",
    "Vicksburg National Military Park, Clay Street, Vicksburg, MS\t32.346550\t-90.849850\n",
    "Statue of Liberty, Liberty Island, NYC, NY\t40.689249\t-74.044500\n",
    "Mount Vernon, Fairfax County, Virginia\t38.729314\t-77.107386\n",
    "Fort Union Trading Post National Historic Site, Williston, North Dakota 1804, ND\t48.000160\t-104.041483\n",
    "San Andreas Fault, San Benito County, CA\t36.576088\t-120.987632\n",
    "Chickasaw National Recreation Area, 1008 W 2nd St, Sulphur, OK 73086\t34.457043\t-97.012213\n",
    "Hanford Site, Benton County, WA\t46.550684\t-119.488974\n",
    "Spring Grove Cemetery, Spring Grove Avenue, Cincinnati, OH\t39.174331\t-84.524997\n",
    "Craters of the Moon National Monument & Preserve, Arco, ID\t43.416650\t-113.516650\n",
    "The Alamo, Alamo Plaza, San Antonio, TX\t29.425967\t-98.486142\n",
    "New Castle Historic District, Delaware\t38.910832\t-75.527670\n",
    "Gateway Arch, Washington Avenue, St Louis, MO\t38.624647\t-90.184992\n",
    "West Baden Springs Hotel, West Baden Avenue, West Baden Springs, IN\t38.566697\t-86.617524\n",
    "Carlsbad Caverns National Park, Carlsbad, NM\t32.123169\t-104.587450\n",
    "Pikes Peak, Colorado\t38.840871\t-105.042260\n",
    "Okefenokee Swamp Park, Okefenokee Swamp Park Road, Waycross, GA\t31.056794\t-82.272327\n",
    "Cape Canaveral, FL\t28.388333\t-80.603611\n",
    "Glacier National Park, West Glacier, MT\t48.759613\t-113.787023\n",
    "Congress Hall, Congress Place, Cape May, NJ 08204\t38.931843\t-74.924184\n",
    "Olympia Entertainment, Woodward Avenue, Detroit, MI\t42.387579\t-83.084943\n",
    "Fort Snelling, Tower Avenue, Saint Paul, MN\t44.892850\t-93.180627\n",
    "Hoover Dam, Boulder City, CO\t36.012638\t-114.742225\n",
    "White House, Pennsylvania Avenue Northwest, Washington, DC\t38.897676\t-77.036530\n",
    "USS Constitution, Boston, MA\t42.372470\t-71.056575\n",
    "Omni Mount Washington Resort, Mount Washington Hotel Road, Bretton Woods, NH\t44.258120\t-71.441189\n",
    "Grand Canyon National Park, Arizona\t36.106965\t-112.112997\n",
    "The Breakers, Ochre Point Avenue, Newport, RI\t41.469858\t-71.298265\n",
    "Fort Sumter National Monument, Sullivan's Island, SC\t32.752348\t-79.874692\n",
    "Cable Car Museum, 94108, 1201 Mason St, San Francisco, CA 94108\t37.794781\t-122.411715\n",
    "Yellowstone National Park, WY 82190\t44.462085\t-110.642441\n",
    "French Quarter, New Orleans, LA\t29.958443\t-90.064411\n",
    "C. W. Parker Carousel Museum, South Esplanade Street, Leavenworth, KS\t39.317245\t-94.909536\n",
    "Shelburne Farms, Harbor Road, Shelburne, VT\t44.408948\t-73.247227\n",
    "Taliesin, County Road C, Spring Green, Wisconsin\t43.141031\t-90.070467\n",
    "Acadia National Park, Maine\t44.338556\t-68.273335\n",
    "Liberty Bell, 6th Street, Philadelphia, PA\t39.949610\t-75.150282\n",
    "Terrace Hill, Grand Avenue, Des Moines, IA\t41.583218\t-93.648542\n",
    "Lincoln Home National Historic Site Visitor Center, 426 South 7th Street, Springfield, IL\t39.797501\t-89.646211\n",
    "Lost World Caverns, Lewisburg, WV\t37.801788\t-80.445630\n",
    "\"\"\"), delimiter='\\t', long_scale=48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAADTCAYAAABwSj+lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nioQFAEXCAoAiYQFA0f8ADudCIBijUDgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed705f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lines(USA_landmarks_map, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kThKhI/Asbs9tSxQlwJKFKVSsk4XTbQ/odoUqz/iOJNAdeKOuzkoWoTXwPHC9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed8b710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50 city tour with length 10236.7 in 0.125 secs for repeated_altered_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(repeated_altered_nn_tsp, USA_landmarks_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare that to the tour that Randal Olson computed as the shortest based on road distances:\n",
    "\n",
    "<a href=\"http://www.randalolson.com/2015/03/08/computing-the-optimal-road-trip-across-the-u-s/\">\n",
    "<img src=\"http://norvig.com/ipython/best-road-trip-major-landmarks.jpg\">\n",
    "</a>\n",
    "\n",
    "The two tours are similar but not the same.  I think the difference is that roads through the rockies and along the coast of the Carolinas tend to be very windy, so Randal's tour avoids them, whereas my  program assumes staright-line roads and thus includes them. William Cook provides an\n",
    "analysis, and a [tour that is shorter](http://www.math.uwaterloo.ca/tsp/usa50/index.html) than either Randal's or mine.\n",
    "\n",
    "Now let's go back to the [original web page](http://www.realestate3d.com/gps/latlong.htm) to get a bigger map with over 1000 cities. A shell command fetches the file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "! [ -e latlong.htm ] || curl -O http://www.realestate3d.com/gps/latlong.htm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I note that the page has some lines that I don't want, so I will filter out lines that are not in the continental US (that is, cities in Alaska or Hawaii), as well as header lines that do not start with `'['`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def continental_USA(line): \n",
    "    \"Does line denote a city in the continental United States?\"\n",
    "    return line.startswith('[') and ',AK' not in line and ',HI' not in line\n",
    "\n",
    "USA_big_map = Coordinate_map(filter(continental_USA, open('latlong.htm')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O8iCp6b6KbhSUz2Ut4/Du0Q4ScdFf8e/JJXhDBBUVtCGEG8iQSl47KICNHwBr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\niRIlSpTIS/8/TuRYhKOqNG4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed6e668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lines(USA_big_map, 'bo')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get a baseline tour with `nn_tsp`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DEqlepx7rDrfkgb61yDcA8ZtFrga5179xgosa8t3vB/KwmzOXDEgvkL+hOP87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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c35d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1089 city tour with length 52879.1 in 0.177 secs for nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(nn_tsp, USA_big_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try to improve on that with `repeat_100_nn_tsp` and with `repeat_5_altered_nn_tsp` (which will take a while with over 1000 cities):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qxb/3vf4t+yEcVwwFwPrXgfe8fnUuhFufglO7BtfkKoHrgAec97rrZ9mJcOYT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\nYN+c9lBC34KvN2ddVuxNvol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vLy8bh7DbvTZsGvaDMKbR7uaIEvrmi9rT/mdH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\nURRFiUSFhaIoihLJ/wI5QrssPkko5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111a14400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1089 city tour with length 50802.6 in 17.126 secs for repeat_100_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(repeat_100_nn_tsp, USA_big_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HZ18xEXjX3u+KOij7kSMs9XvQepL32ztALbDwaLXvzNDhHaj99lD2/27AWGDt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\nz6t5umop3LETZvdONw5ZBL+7Xs3zmLZ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Kr2tkoh5C84dWrpWuoopQuTC+3zXzFCdi8YuZ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\nEAL5fxkVHTv2ITP1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efa4198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1089 city tour with length 44234.6 in 23.149 secs for repeat_5_altered_nn_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(repeat_5_altered_nn_tsp, USA_big_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again we see that we do better by spending our run time budget on alteration rather than on repetition. This time we saved over 8,000 miles of travel in half a minute of computation!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Greedy Algorithm: `greedy_tsp`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the start of the *Approximate Algorithms* section, we mentioned two ideas:\n",
    "\n",
    "1. **Nearest Neighbor Algorithm:** Make the tour go from a city to its nearest neighbor. Repeat.\n",
    "2. **Greedy Algorithm:** Find the shortest distance between any two cities and include that in the tour. Repeat.\n",
    "\n",
    "It is time to develop the *greedy algorithm*, so-called because at every step it greedily adds to the tour the edge that is shortest (even if that is not best in terms of long-range planning).  The nearest neighbor algorithm always extended the tour by adding on to the end.  The greedy algorithm is different in that it doesn't have a notion of *end* of the tour; instead it keeps a *set* of partial segments. Here's a brief statement of the algorithm:\n",
    "\n",
    "> **Greedy Algorithm:** *Maintain a set of segments; intially each city defines its own 1-city segment. Find the shortest possible edge that connects two endpoints of two different segments, and join those segments with that edge. Repeat until we form a segment that tours all the cities.*\n",
    "\n",
    "On each step of the algorithm, we want to \"find the shortest possible edge that connects two endpoints.\" That seems like an expensive operation to do on each step. So we will add in some data structures to enable us to speed up the computation.  Here's a more detailed sketch of the algorithm:\n",
    "\n",
    "1. Pre-compute a list of **edges**, sorted by shortest edge first. An edge is a pair of cities; if the list contains `(A, B)` then it does not contain `(B, A)`, and it never contains `(A, A)`.\n",
    "2. Maintain a dict that maps **endpoints** to **segments**, e.g. `{A: [A, B, C, D], D: [A, B, C, D]}`. Initially, each city is the endpoint of its own 1-city-long segment, but as we join segments together, some cities are no longer endpoints and are removed from the dict.\n",
    "3. Go through the edges in shortest-first order. When you find an edge `(A, B)` such that both `A` and `B` are endpoints of different segments, then join the two segments together.  Maintain the endpoints dict to reflect this new segment. Stop when you create\n",
    "a segment that contains all the cities.\n",
    "\n",
    "\n",
    "Let's consider an example: assume we have seven cities,  labeled A through G.  Suppose CG happens to be the shortest edge.  We would add the edge to the partial tour, by joining the segment that contains C with the segment that contains G.  In this case, the joining is easy, because each segment is one city long; we join them to form a segment two cities long. We then look at the next shortest edge and continue the process, joining segments as we go, as shown in the table below. Some edges cannot be used.  For example, FD cannot be used, because by the time it becomes the shortest edge, D is already in the interior of a segment. Next, AE cannot be used, even though both A and E are endpoints, because it would make a loop out of ACGDE.  Finally, note that sometimes we may have to reverse a segment.  For example, EF can merge AGCDE and BF, but first we have to reverse BF to FB. \n",
    "\n",
    "\n",
    "<table>\n",
    "<tr><th>Shortest Edge<th>Usage of edge<th>Resulting Segments\n",
    "<tr><td>&mdash;<td>&mdash;<td> A; B; C; D; E; F; G\n",
    "<tr><td>CG<td>Join C to G<td>A; B; <b>CG</b>; D; E; F\n",
    "<tr><td>DE<td>Join D to E<td>A; B; CG; <b>DE</b>; F\n",
    "<tr><td>AC<td>Join A to CG<td>B; <b>AC</b>G; DE; F\n",
    "<tr><td>GD<td>Join ACG to D<td>B; AC<b>GD</b>E; F\n",
    "<tr><td>FD<td>Discard<td>B; ACGDE; F\n",
    "<tr><td>AE<td>Discard<td>B; ACGDE; F\n",
    "<tr><td>BF<td>Join B to F<td><b>BF</b>; ACGDE\n",
    "<tr><td>CF<td>Discard<td>BF; ACGDE\n",
    "<tr><td>EF<td>Join ACGDE to FB<td>ACGD<b>EF</b>B\n",
    "</table>\n",
    "\n",
    "Here is the code:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def greedy_tsp(cities):\n",
    "    \"\"\"Go through edges, shortest first. Use edge to join segments if possible.\"\"\"\n",
    "    endpoints = {c: [c] for c in cities} # A dict of {endpoint: segment}\n",
    "    for (A, B) in shortest_edges_first(cities):\n",
    "        if A in endpoints and B in endpoints and endpoints[A] != endpoints[B]:\n",
    "            new_segment = join_endpoints(endpoints, A, B)\n",
    "            if len(new_segment) == len(cities):\n",
    "                return new_segment\n",
    "            \n",
    "# TO DO: functions: shortest_edges_first, join_endpoints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**Note:** The `endpoints` dict is serving two purposes. First, the keys of the dict are all the cities that are endpoints of some segments,\n",
    "making it possible to ask \"`A in endpoints`\" to see if city `A` is an endpoint. Second, the values of the dict are all the segments, making it possible to ask \"`endpoints[A] != endpoints[B]`\" to make sure that the two cities are endpoints of different segments, not of the same segment.\n",
    "\n",
    "The `shortest_edges_first` function is easy: generate all `(A, B)` pairs of cities, and sort by the distance between the cities.  (Note: I use the conditional `if id(A) < id(B)` so that I won't have both `(A, B)` and `(B, A)` in my list of edges, and I won't ever have `(A, A)`.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def shortest_edges_first(cities):\n",
    "    \"Return all edges between distinct cities, sorted shortest first.\"\n",
    "    edges = [(A, B) for A in cities for B in cities \n",
    "                    if id(A) < id(B)]\n",
    "    return sorted(edges, key=lambda edge: distance(*edge))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the `join_endpoints` function, I first make sure that A is the last element of one segment and B is the first element of the other, by reversing segments if necessary.  Then I add the B segment on to the end of the A segment. Finally, I update the `endpoints` dict. This is a bit tricky!  My first thought was that A and B are no longer endpoints, because they have been joined together in the interior of the segment.  However, that isn't always true.  If A was the endpoint of a 1-city segment, then when you join it to B, A is still an endpoint.  I could have had complicated logic to handle the case when A, B, or both, or neither were 1-city segments, but I decided on a different tactic: first unconditionally delete A and B from the endpoints dict, no matter what.  Then add the two endpoints of the new segment (which is `Asegment`) to the endpoints dict.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def join_endpoints(endpoints, A, B):\n",
    "    \"Join B's segment onto the end of A's and return the segment. Maintain endpoints dict.\"\n",
    "    Asegment, Bsegment = endpoints[A], endpoints[B]\n",
    "    if Asegment[-1] is not A: Asegment.reverse()\n",
    "    if Bsegment[0] is not B: Bsegment.reverse()\n",
    "    Asegment.extend(Bsegment)\n",
    "    del endpoints[A], endpoints[B] # A and B are no longer endpoints\n",
    "    endpoints[Asegment[0]] = endpoints[Asegment[-1]] = Asegment\n",
    "    return Asegment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try out the `greedy_tsp` algorithm on the two USA maps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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n6UjBzKJykXgRTgFOB8b6tKl2bN0x+/T7RzsD9wAdgC1FWAqnN3GRXqWxritC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\nH76Nk+B8wxPEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efaf7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 16087.5 in 0.006 secs for greedy_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(greedy_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yDoB5g7kXzOYTrVvP6FFh9ddhnkGdkKT+gV914TeG1uyG2YZ8TzbVzJjnoLzb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\nUpHNWpKISpRosllot3F339HZldN7qswmTSYl9OZ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33VcvvHN4DuosVDWKrDHMv23O3eel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\nUBRFUWJRZaEoiqLEospCURRFieX/AY5SUy5TwxCZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2f8080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1089 city tour with length 46981.5 in 1.052 secs for greedy_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(greedy_tsp, USA_big_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The greedy algorithm is worse than nearest neighbors, but it is fast (especially on the big map). Let's see if the *alteration* strategy can help:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def altered_greedy_tsp(cities):\n",
    "    \"Run greedy TSP algorithm, and alter the results by reversing segments.\"\n",
    "    return alter_tour(greedy_tsp(cities))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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32GhzGHOO6sxZUctlREOa7Py4RcQtBTYhcGVRPGZZERoB2wJ278aQondwVz0Y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\nMmLKwjAMw8jI/wPmeYcBxNnlLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111fd7ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 14133.3 in 0.022 secs for altered_greedy_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(altered_greedy_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PNDXAwxW2+vW+zGR4F/A0MBr4g6XuyTBruT8vvPDsqycDr7tDsFf+3N5X69+E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\naM2HSv2xEErfcC9od+8IF3jWQu8s2VqAWehqgLvXw333A68H9xEWiR1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x101b81358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1089 city tour with length 43769.9 in 4.177 secs for altered_greedy_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(altered_greedy_tsp, USA_big_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's the best result yet on the big map. Let's look at some benchmarks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           altered_nn_tsp |   4820 ± 233 ( 4450 to  5346) |  0.008 secs/map | 30 ⨉ 60-city maps\n",
      "       altered_greedy_tsp |   4766 ± 207 ( 4320 to  5185) |  0.009 secs/map | 30 ⨉ 60-city maps\n",
      "  repeated_altered_nn_tsp |   4640 ± 194 ( 4298 to  4991) |  0.148 secs/map | 30 ⨉ 60-city maps\n",
      "----------------------------------------------------------------------------------------------------\n",
      "           altered_nn_tsp |   6589 ± 202 ( 6188 to  7016) |  0.036 secs/map | 30 ⨉ 120-city maps\n",
      "       altered_greedy_tsp |   6539 ± 240 ( 5994 to  7203) |  0.037 secs/map | 30 ⨉ 120-city maps\n",
      "  repeated_altered_nn_tsp |   6402 ± 185 ( 6015 to  6779) |  0.701 secs/map | 30 ⨉ 120-city maps\n"
     ]
    }
   ],
   "source": [
    "algorithms = [altered_nn_tsp, altered_greedy_tsp, repeated_altered_nn_tsp]\n",
    "\n",
    "benchmarks(algorithms)\n",
    "print('-' * 100)\n",
    "benchmarks(algorithms, Maps(30, 120))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So overall, the altered greedy algorithm looks slightly better than the altered nearest neighbor algorithm and runs in about the same time. However, the repeated altered nearest neighbor algorithm does best of all (although it takes much longer).\n",
    "\n",
    "What about a repeated altered greedy algorithm?  That might be a good idea, but there is no obvious way to do it.  We can't just start from a sample of cities, because the greedy algorithm doesn't have a notion of starting city.\n",
    "\n",
    "Visualizing the Greedy Algorithm\n",
    "---\n",
    "\n",
    "I would like to see how the process of joining segments unfolds.  Although I dislike copy-and-paste (because it violates the *[Don't Repeat Yourself](http://en.wikipedia.org/wiki/Don%27t_repeat_yourself)* principle), I'll copy  `greedy_tsp` and make a new version called `visualize_greedy_tsp` which adds one line to plot the segments several times as the algorithm is running:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def visualize_greedy_tsp(cities, plot_sizes):\n",
    "    \"\"\"Go through edges, shortest first. Use edge to join segments if possible.\n",
    "    Plot segments at specified sizes.\"\"\"\n",
    "    edges = shortest_edges_first(cities) # A list of (A, B) pairs\n",
    "    endpoints = {c: [c] for c in cities} # A dict of {endpoint: segment}\n",
    "    for (A, B) in edges:\n",
    "        if A in endpoints and B in endpoints and endpoints[A] != endpoints[B]:\n",
    "            new_segment = join_endpoints(endpoints, A, B)\n",
    "            plot_segments(endpoints, plot_sizes, distance(A, B)) # <<<< NEW\n",
    "            if len(new_segment) == len(cities):\n",
    "                return new_segment\n",
    "        \n",
    "def plot_segments(endpoints, plot_sizes, dist):\n",
    "    \"If the number of distinct segments is one of plot_sizes, then plot segments.\"\n",
    "    segments = set(map(tuple, endpoints.values()))\n",
    "    if len(segments) in plot_sizes:\n",
    "        for s in segments:\n",
    "            plot_lines(s)\n",
    "        plt.show()\n",
    "        print('{} segments, longest edge = {:.0f}'.format(\n",
    "              len(segments), dist))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed8c240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50 segments, longest edge = 119\n"
     ]
    },
    {
     "data": {
      "image/png": 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Gd4DDgaHuvJ9G3EVmxjXAn925InQsEo6ShRSKGT8FXnDn4gr/fiBwP7CPOy9m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\nKiULERGpSslCRESq+v925hp4HkFWDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed96c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25 segments, longest edge = 190\n"
     ]
    },
    {
     "data": {
      "image/png": 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LR1lmT+8Iy/uvem09fCtc+D2iMvObFn72AbaBzbZNyVjQFsC8mB9TySKn6iRZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed629e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 segments, longest edge = 255\n"
     ]
    },
    {
     "data": {
      "image/png": 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eaLTe3XvDe5Ot9lP6ZT5Z+Hu6mDYczl8a5lBXEdYD1iO2C2Aq1oWop/ppCIZ3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111a35eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 segments, longest edge = 335\n"
     ]
    },
    {
     "data": {
      "image/png": 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+yiJ2ZRHwOHCwp76XIkJX3MTgPN+yGMXJXG4oWFqPejLQX5U3fMtTkyAS5QVg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\nopiyMAzDMIpiysIwDMMoyv8D+nb7pKw2teEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0d85c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 segments, longest edge = 597\n"
     ]
    },
    {
     "data": {
      "image/png": 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4ALgDaK/Kkao82EihgOTPLGIXi4CHgMM8jb0GEXriHgzO9W2LUZzM1YaCNf2o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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c306dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 segments, longest edge = 1021\n"
     ]
    }
   ],
   "source": [
    "visualize_greedy_tsp(USA_map, (50, 25, 10, 5, 2, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Divide and Conquer Strategy\n",
    "\n",
    "The next general strategy to consider is *divide and conquer*.  Suppose we have an algorithm, like `alltours_tsp`, that is inefficient for large *n* (the `alltours_tsp` algorithm is O(*n!*) for *n* cities).  So we can't apply `alltours_tsp` directly to a large set of cities.  But we can divide the problem into smaller pieces, and then combine those pieces:\n",
    "\n",
    "1. Split the set of cities in half.\n",
    "2. Find a tour for each half.\n",
    "3. Join those two tours into one.\n",
    "\n",
    "The trick is that when *n* is small, then step 2 can be done directly.  But when *n* is large, step 2 is done with a recursive call, breaking the half into two smaller halves.\n",
    "\n",
    "Let's work out by hand an example with a small map of just six cities. Here are the cities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ4AAAEACAYAAABCu5jVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2f2f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cities = Cities(6)\n",
    "\n",
    "plot_labeled_lines(cities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 1 is to divide this set in half.  I'll divide it into a left half (blue circles) and a right half (black squares):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ4AAAEACAYAAABCu5jVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116c8550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_labeled_lines(list(cities), 'bo', [3, 4, 0], 'ks', [1, 2, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 2 is to find a tour for each half:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Q+A5psljjt5V0H0cXJHYDfkianfgf2ZYFlZLYGjgngs2qrqUfSfoRcGNEfK+k8+9I6og9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111fe0cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_labeled_lines(list(cities), 'bo-', [0, 3, 4, 0], 'ks-', [1, 2, 5, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 3 is to combine the two halves.  We do that by choosing an edge from each half to delete (the edges marked by red dashes) and replacing those two edges by two edges that connect the halves (the blue dash-dot edges). Note that there are two choices of ways to connect the new dash-dot lines.  Pick the one that yields the shortest tour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116ecef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# One way to connect the two segments, giving the tour [1, 3, 4, 0, 2, 5]\n",
    "plot_labeled_lines(list(cities), 'bo-', [0, 3, 4], 'ks-', [1, 2, 5],\n",
    "                   'b-.', [0, 1], [4, 5],\n",
    "                   'r--', [0, 4], [1, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have a feel for what we have to do.  Let's define the divide and conquer algorithm, which we will call `dq_tsp`. Like all `tsp` algorithms it gets a set of cities as input and returns a tour. If the size of the set of cities is 3 or less, then just listing the cities in any order produces an optimal tour. If there are more than 3 cities, then split the cities in half (using `split_cities`), find a tour for each half (using `dq_tsp` recursively), and join the two tours together (using `join_tours`): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def dq_tsp(cities):\n",
    "    \"\"\"Find a tour by divide and conquer: if number of cities is 3 or less,\n",
    "    any tour is optimal.  Otherwise, split the cities in half, solve each\n",
    "    half recursively, then join those two tours together.\"\"\"\n",
    "    if len(cities) <= 3:\n",
    "        return Tour(cities)\n",
    "    else:\n",
    "        Cs1, Cs2 = split_cities(cities)\n",
    "        return join_tours(dq_tsp(Cs1), dq_tsp(Cs2))\n",
    "    \n",
    "# TO DO: functions: split_cities, join_tours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's verify that `dq_tsp` works for three cities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef28710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 city tour with length 1203.4 in 0.000 secs for dq_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(dq_tsp, Cities(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have more than 3 cities, how do we split them?  My approach is to imagine drawing an axis-aligned rectangle that is just big enough to contain all the cities. If the rectangle  is wider than it is tall, then order all the cities by *x* coordiante and split that ordered list in half.  If the rectangle is taller than it is wide, order and split the cities by *y* coordinate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def split_cities(cities):\n",
    "    \"Split cities vertically if map is wider; horizontally if map is taller.\"\n",
    "    width, height = extent([c.x for c in cities]), extent([c.y for c in cities])\n",
    "    key = 'x' if (width > height) else 'y'\n",
    "    cities = sorted(cities, key=lambda c: getattr(c, key))\n",
    "    mid = len(cities) // 2\n",
    "    return frozenset(cities[:mid]), frozenset(cities[mid:])\n",
    "\n",
    "def extent(numbers): return max(numbers) - min(numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's show that split_cities is working:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qdWC02c0DYNQK+jU6fRqM1Wu3oWXeUpg1w/3srl6THWYMovPpzj2Bv9FeDv+VPb7S26XX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\ncYhItP8Hf62p30lzGqcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef86e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Cs1, Cs2 = split_cities(cities)\n",
    "plot_tour(dq_tsp(Cs1))\n",
    "plot_tour(dq_tsp(Cs2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for the tricky part: joining two tours together. First we consider all ways of deleting one edge from each of the two tours.  If we delete a edge from a tour we get a segment.  We are representing segments as lists of cities, the same surface representation as tours.  But there is a difference in their interpretation.  The tour `[0, 2, 5]` is a triangle of three edges, but the segment `[0, 2, 5]` consists of only two edges, from `0` to `2` and from `2` to `5`. The segments that result from deleting an edge from the tour `[0, 2, 5]` are:\n",
    "\n",
    "<pre>\n",
    "[0, 2, 5],    [2, 5, 0],    [5, 0, 2]\n",
    "</pre>\n",
    "\n",
    "You may recognize these as the *rotations* of the segment `[0, 2, 5]`. So any candidate combined tour consists of taking a rotation of the first tour, and appending to it a rotation of the second tour, with one caveat: when we go to append the two segments, there are two ways of doing it: either keep the second segment as is, or reverse the second segment.\n",
    "\n",
    "**Note:** In Python, `sequence[::-1]` means to reverse the sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def join_tours(tour1, tour2):\n",
    "    \"Consider all ways of joining the two tours together, and pick the shortest.\"\n",
    "    segments1, segments2 = rotations(tour1), rotations(tour2)\n",
    "    tours = [s1 + s2\n",
    "             for s1 in segments1\n",
    "             for s  in segments2\n",
    "             for s2 in (s, s[::-1])]\n",
    "    return shortest_tour(tours)\n",
    "\n",
    "def rotations(sequence):\n",
    "    \"All possible rotations of a sequence.\"\n",
    "    # A rotation is some suffix of the sequence followed by the rest of the sequence.\n",
    "    return [sequence[i:] + sequence[:i] for i in range(len(sequence))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if it works, first on the 6 city example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xAXAN4fT9E2Kh1CSNOMrMnecIP21eJJw2dppGH8XkzifuXAJcDDxmxqmpM7WURhwVZMbe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\nmYpDRDL7f32INzgSOu2iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114f680b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 city tour with length 1431.7 in 0.000 secs for dq_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(dq_tsp, Cities(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is indeed the optimal tour, achieved by deleting the two dashed red lines and adding the dotted blue lines.\n",
    "\n",
    "Now for the USA map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V8Htp48dSE1RADwIdCfoN6FjQY2tL5knxdz8F3dPv/WMj/fPGOyeGg34CWuK3rKnIHPS5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\nBDopa1IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x101930710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 14883.2 in 0.142 secs for dq_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(dq_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not quite as good as `altered_greedy_tsp`. Let's alter it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def altered_dq_tsp(cities): return alter_tour(dq_tsp(cities))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0DmmsU1LF7TfV7PNU0HFBn/eqZQzfbGXQN0EvCKbvygWJgj5HleULv0Kr6S0G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\nElMWhmEYRkpMWRiGYRgp+X8tJqUfXSTwBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114f68828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 14209.6 in 0.109 secs for altered_dq_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(altered_dq_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's just remind ourselves how the algorithms behave on the standard test cases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   nn_tsp |   5668 ± 488 ( 4674 to  6832) |  0.001 secs/map | 30 ⨉ 60-city maps\n",
      "               greedy_tsp |   5392 ± 306 ( 4554 to  5967) |  0.002 secs/map | 30 ⨉ 60-city maps\n",
      "                   dq_tsp |   5268 ± 236 ( 4743 to  5752) |  0.042 secs/map | 30 ⨉ 60-city maps\n",
      "           altered_dq_tsp |   4953 ± 221 ( 4575 to  5399) |  0.049 secs/map | 30 ⨉ 60-city maps\n",
      "           altered_nn_tsp |   4820 ± 233 ( 4450 to  5346) |  0.008 secs/map | 30 ⨉ 60-city maps\n",
      "       altered_greedy_tsp |   4766 ± 207 ( 4320 to  5185) |  0.009 secs/map | 30 ⨉ 60-city maps\n",
      "  repeated_altered_nn_tsp |   4640 ± 194 ( 4298 to  4991) |  0.148 secs/map | 30 ⨉ 60-city maps\n"
     ]
    }
   ],
   "source": [
    "algorithms = [nn_tsp, greedy_tsp, dq_tsp, altered_dq_tsp, altered_nn_tsp, altered_greedy_tsp, \n",
    "              repeated_altered_nn_tsp]\n",
    "\n",
    "benchmarks(algorithms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of the non-altered algorithms (the first three lines), divide and conquer (`dq_tsp`) does best.  But interestingly, divide and conquer is helped less by `alter_tour` than is the greedy algorithm or nearest neighbor algorithm.  Perhaps it is because divide and conquer constructs its tour by putting together pieces that are already good, so `alter_tour` is less able to improve it. ALso, `dq_tsp` has a standard deviation that is much smaller than the other two&mdash;this suggests that `dq_tsp` is not producing really bad tours that can be easily improved by `alter_tour`.  In any event, `altered_dq_tsp` is the worst of the `altered` algorithms, both in average tour length and in run time.  \n",
    "\n",
    "`repeated_altered_nn_tsp` remains the best in tour length, although the worst in run time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shoulders of Giants: Minimum Spanning Tree Algorithm: `mst_tsp`\n",
    "\n",
    "\n",
    "<a href=\"https://en.wikipedia.org/wiki/Joseph_Kruskal\">\n",
    "<img src=\"http://people.inf.elte.hu/hytruongson/Kruskal/J.Kruskal.jpg\">\n",
    "<center>Joseph Kruskal (Wikipedia)</center></a>\n",
    "\n",
    "\n",
    "I hope you now believe that you could have come up with some ideas for solving the TSP. But even if you can't come up with something all on your own, you can always [Google it](http://bit.ly/XNGt2y), in which case you'll no doubt find a giant of a mathematician, [Joseph Kruskal](http://en.wikipedia.org/wiki/Joseph_Kruskal), who, in 1956, \n",
    "published [a paper](http://www.cmat.edu.uy/~marclan/TAG/Sellanes/Kruskal.pdf) that led to an algorithm that\n",
    "most people would not have thought of on their own\n",
    " (I know I wouldn't have):\n",
    "> **Minimum Spanning Tree Traversal Algorithm:** *Construct a Minimum Spanning Tree, then do a pre-order traversal.  That will give you a tour that is guaranteed to be no more than twice as long as the minimal tour.* \n",
    "\n",
    "What does all this jargon mean? It is part of *graph theory*, the study of vertexes and edges.  Here is a glossary of terms:\n",
    "\n",
    "* A **graph** is a collection of vertexes and edges.\n",
    "* A **vertex** is a point (such as a city).\n",
    "* An **edge** is a link between two vertexes. Edges have lengths.\n",
    "\n",
    "* A **directed graph** is a graph where the edges have a direction.  We say that the edge goes from the **parent** vertex to the **child** vertex.\n",
    "\n",
    "* A **tree** is a directed graph in which there is one distinguished vertex called the **root** that has no parent; every other vertex has exactly one parent. \n",
    "\n",
    "* A **spanning tree** (of a set of vertexes) is a tree that contains all the vertexes.    \n",
    "\n",
    "* A **minimum spanning tree** is a spanning tree with the smallest possible sum of edge lengths.\n",
    "\n",
    "* A **traversal** of a tree is a way of visiting all the vertexes in some order.\n",
    "\n",
    "* A **pre-order traversal** means that you visit the root first, then do a pre-order traversal of each of the children.\n",
    "\n",
    "* A **guarantee** means that, no matter what set of cities is selected, the tour found by the minimum spanning tree traversal algorithm will never be more than twice as long as the shortest possible tour. None of the other algorithms has any guarantee at all (except for `alltours_tsp`, which is guaranteed to find the optimal algorithm, if it has enough time to complete).\n",
    "\n",
    "We will implement a vertex as a Point, and a directed graph as a dict of `{parent: [child, ...]}` pairs. \n",
    "\n",
    "Visualizing Graphs and Trees\n",
    "---\n",
    "\n",
    "I think we will need visualization right away, so before doing anything else I will define `plot_graph`. I will make it plot in red so that we can easily tell a tour (blue) from a graph (red)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_graph(graph):\n",
    "    \"Given a graph of the form {parent: [child...]}, plot the vertexes and edges.\"\n",
    "    vertexes = {v for parent in graph for v in graph[parent]} | set(graph)\n",
    "    edges = {(parent, child) for parent in graph for child in graph[parent]}\n",
    "    for edge in edges:\n",
    "        plot_lines(edge, 'ro-')\n",
    "    total_length = sum(distance(p, c) for (p, c) in edges)\n",
    "    print('{} node Graph of total length: {:.1f}'.format(len(vertexes), total_length))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try it out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 node Graph of total length: 10.9\n"
     ]
    },
    {
     "data": {
      "image/png": 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vSYUw8CWpEAa+JBXi/wHexqNhYBwX7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e68f940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ps = [Point(0, 0.1), \n",
    "      Point(-2, -1), Point(0, -1), Point(2, -1), \n",
    "      Point(-2.9, -1.9), Point(-1, -1.9), Point(1, -1.9), Point(2.9, -1.9)]\n",
    "\n",
    "Ptree = {Ps[0]: Ps[1:4], Ps[1]: Ps[4:6], Ps[3]: Ps[6:8]}\n",
    "\n",
    "plot_graph(Ptree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now our plan is:\n",
    "\n",
    "1. Implement an algorithm to create a minimum spanning tree.\n",
    "2. Implement a tree traversal; that will give us our `mst_tsp` algorithm.\n",
    "3. Understand the guarantee,  \n",
    "\n",
    "Creating a Minimum Spanning Tree (`mst`)\n",
    "---\n",
    "\n",
    "Now let's see how to create a minimum spanning tree (or MST).  Kruskal has a very nice algorithm to find MSTs, but with what we have done so far, it will be a bit easier to implement another Giant's algorithm:\n",
    "\n",
    "> **[Prim's algorithm for creating a MST](http://en.wikipedia.org/wiki/Prim%27s_algorithm):** *List all the edges and sort them, shortest first.  Initialize a tree to be a single root city (we'll arbitrarily shoose the first city). Now repeat the following until the tree contains all the cities: find the shortest edge that links a city (A) that is in the tree to a city (B) that is not yet in the tree, and add B to the list of A's children in the tree.*\n",
    "\n",
    "Here's the code. One tricky bit: In the first line inside the `while` loop, we define `(A, B)` to be an edge in which one of `A` or `B` is in the tree, using the exclusive-or operator, `^`.  Then in the next line, we make sure that `A` is the one that is in the tree and B is not, by swapping if necessary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mst(vertexes):\n",
    "    \"\"\"Given a set of vertexes, build a minimum spanning tree: a dict of the form {parent: [child...]}, \n",
    "    where parent and children are vertexes, and the root of the tree is first(vertexes).\"\"\"\n",
    "    tree  = {first(vertexes): []} # the first city is the root of the tree.\n",
    "    edges = shortest_edges_first(vertexes)\n",
    "    while len(tree) < len(vertexes):\n",
    "        (A, B) = shortest_usable_edge(edges, tree)\n",
    "        tree[A].append(B)\n",
    "        tree[B] = []\n",
    "    return tree\n",
    "\n",
    "def shortest_usable_edge(edges, tree):\n",
    "    \"Find the ehortest edge (A, B) where A is in tree and B is not.\"\n",
    "    (A, B) = first((A, B) for (A, B) in edges if (A in tree) ^ (B in tree)) # ^ is \"xor\" \n",
    "    return (A, B) if (A in tree) else (B, A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what a minimum spanning tree looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 node Graph of total length: 11518.4\n"
     ]
    },
    {
     "data": {
      "image/png": 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NVaX9Dtx6COwW9vMjUL4fbbw+aha7wesKO/l+fzy/B9sn62GFrjBfaM+bkMRc9FpUMFpd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114f48e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graph(mst(USA_map))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This algorithm clearly produced a spanning tree.  It looks pretty good, but how can we be sure the algorithm will *always* produce a minimum spanning tree?  \n",
    "\n",
    "1. The output is a **tree** because (1) every city is connected by a path from the root, and (2) every city only gets one parent (we only add a B that is not in tree), so there can be no loops. \n",
    "2. The output is a **spanning tree** because it contains all the cities.\n",
    "3. The output is a **minimum spanning tree** because each city was added with the shortest possible edge.  Suppose this algorithm produces the tree T. For another putative spanning tree to be shorter, it would have to contain at least one city C whose edge from its parent was shorter than the edge in T. But that is not possible, because the algorithm always chooses the shortest possible edge from C's parent to C.\n",
    "\n",
    "\n",
    "\n",
    "**Note:** There are refinements to Prim's algorithm to make it more efficient.  I won't bother with them because they complicate the code, and because `mst` is already fast enough for our purposes.\n",
    "\n",
    "Turning a Minimum Spanning Tree into a Tour (`mst_tsp`)\n",
    "---\n",
    "\n",
    "Given a minimum spanning tree, we can generate a tour by doing a pre-order traversal, which means the tour starts at the root, then visits all the cities in the pre-order traversal of the first child of the root, followed by the pre-order traversals of any other children."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def mst_tsp(cities):\n",
    "    \"Create a minimum spanning tree and walk it in pre-order, omitting duplicates.\"\n",
    "    return preorder_traversal(mst(cities), first(cities))\n",
    "\n",
    "def preorder_traversal(tree, root):\n",
    "    \"Traverse tree in pre-order, starting at root of tree.\"\n",
    "    result = [root]\n",
    "    for child in tree.get(root, ()):\n",
    "        result.extend(preorder_traversal(tree, child))\n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better understand pre-order traversal, let's go back to the `Ptree` example, and this time label the vertexes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 node Graph of total length: 10.9\n"
     ]
    },
    {
     "data": {
      "image/png": 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PFYxJIyEXeMUpAyFQjDUATf7JUMGY1FKBV/xSXBPIfwBo8k+WCsakTAVeyUkpBPJ9CUiT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\ngVIAiIgESgEgIhKo/wdXi4DvW4BqgwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c35fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = [Point(0, 0.1), \n",
    "     Point(-2, -1), Point(0, -1), Point(2, -1), \n",
    "     Point(-2.9, -1.9), Point(-1, -1.9), Point(1, -1.9), Point(2.9, -1.9)]\n",
    "\n",
    "Ptree = {P[0]: P[1:4], P[1]: P[4:6], P[3]: P[6:8]}\n",
    "\n",
    "plot_graph(Ptree)\n",
    "plot_labeled_lines(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A pre-order traversal starting at 0 would go to the first child, 1, then to its children, 4 and 5, then since there are no children of 4 and 5, it would continue with the other children of 0, hitting 2, then 3, and finally the children of 3, namely 6 and 7.  So the following should be true:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preorder_traversal(Ptree, P[0]) == [P[0], P[1], P[4], P[5], P[2], P[3], P[6], P[7]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And this is what the pre-order traversal looks like as a tour:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Cdh7z2ReAk++GW1a3tS6N97vnwrVHvP46HXlj5v0r21qVpsbXWSlOvwQu+ZXZvs4av+9z\n5vZcsvVfDqpfL10OfKiFBWlCS5dPfJ0WL2ljNZouX2dlWLB4FK+zDgf+k5uq72Djv6OtW5uJO8eO\niFh3A7wwwQ7xqU1trUnT4eusBKN6nXX4Lp0NF8Lpj1V/Kag+nv5Y9Xl1h9epbF6/MozmOnX2DB/G\n3j2wuL77YwbvSqtxXqeyef3KMIrr1OnAlySNToePdCRJo2TgS9JAGPiSNBAGviQNhIEvSQNh4EvS\nQBj4kjQQBr4kDYSBL0kDYeBL0kAY+JI0EAa+JA2EgS9JA2HgS9JAGPiSNBAGviQNhIEvSQNh4EvS\nQBj4kjQQBr4kDYSBL0kDYeBL0kD8H0VC3Z07TYQ6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0204e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_tour([P[0], P[1], P[4], P[5], P[2], P[3], P[6], P[7]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can think of this as starting at the root (at the top) and going around the outside of the tree counterclockwise, as if you were walking with your left hand always touching an edge, but skipping cities you have already been to.\n",
    "\n",
    "We see that the result is a tour, but not an optimal one.  \n",
    "\n",
    "Let's see what `mst_tsp` can do on the USA map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DOsaMYuBroMwbz3h/56myXmT6cGdCq/49yqv3ss6SxMrVc3a/BDyoujFwoAqV33+/v7uf\n86kfqO421l8ZC5Swlza5Wmr6uz/tDvpuCp/7EnSXsI+Pjfy4bjKXU3uAjg9a5vj7OmsxTL0d9DnP\nzPor6FzQ0aA3g54CunsyM038ufsvg3nLQfv6lVhbm9kOdAjomETF/wo5eTOQ6zJsAfy+IHKzP90D\n9NMUPje7tgJkNurWdZO5nHo/6JWV/6+oBtx/Ngz4KncPRYmOz7mf4yoLdwFtlvn8Nasag3YC/Rz0\nBdDNsv8OiZTrWxfjKlS3LPTrI6xRoGaowO245rOIBIVh/8flV5xS8Z+KxEYRDgNKVR9akJvdJjo+\nP/6gytPZzp4oQVOELrg2tjNF6KfKhGz24SLftpoOyxbD7C/g5OFwxLPAIar8nHjrgrk+QqFAlcWK\n5QEXqEvHZ2HKIm/J/zaYIrQDNgdm1nx34Coo2kfkiwm56ccdzvFR5TdgoAhvAs+K8DxwrWboVHYK\ngyXAWcB84APgYlU+q33L/L8+QiXspU36y0zdFL76FAb8FKDPoj6uAVKtjU5AvwFt5//+K5bvvVJu\nSmQj0XHMb58F6FmgI8KQPf4+zl0W5PEBbQU6CnQmaMcs5vkatAPoa6BDUvvuf30FeiuUKizIy+sj\nzBG6AGleAE1BJ4M+mElXtyz3vRq0KMlnvgPd1t/95v8NrpBG5XVz7iy4cH6+HUfQF0H71Xw9GHt6\n1d9VySiY9yPoYQEfAwE9A3Qp6MXJHtISzLHC5anou6CNkn/n6r+xPr9Cp1fy7foIc4QuQBonvxHo\nWNBnMrl4fNh/0o58uO5ZbfzdrzndcnQ+24IuJ412uble4Xkr2OWg29R8L1GXt2Mn5Pg4HQT6PVy3\nf9CrW29lMA1XOrzGMallu3re8fk+ld+j/cZSG3nts6iMeW6zDbRtD2d/CbudqRqKX6DCb/FdvDed\nrBe1hLkviXy7wD97sjndcoEq34nMXgxXvSkiDZL5AAIqV7En8L0qcaqahuZPmCQy+RFY9V8Y1yjX\npTqq7XueCN2Bq4GPRDhflZdT2PQv3t8TVUnh+NhvLCXC1laJtX28peGp88JaFoK+B9otdVn9MRXl\n81NPIftSnOz9lyc6Z6DNQTuDngRa6kxWuT0PoNeA3hP0NVYI1yDoX3Gh6U/VZg4GbeKtzrSQvl8h\njDxeWcRL23+4PawfLsIQYD0uW/qPmH/7+ppqlaZKtRQTTFRiYJ4PzXXKSqH/vlWfaM9fEHbF1CAL\nw+WGjoPgzs1rnrOtpouwAWgJzAXmALNhzZoAnj4PB26P90bVYojttocd9oKfjwnmWIf/5K3K+yLs\nCdwFfCLCaaq8G/sZr5Lsg7gSI2n0nIj3G8vvqsRhkMfKIuEFugNwAi5MtT7uO8T+zea12PfqezeN\nCgWyCXC4CMupoWgO2iq+rCV9ROjjvTAfmOdtk4YCW/UHfDAe7uwAv5fDJs3ghmJ46hSR3CjJ1N7r\nfGvuFGQQJLq+li0GegKLNMbcKfLZtlC+c67MQF5vhb2AdxJ9JjZPQYQXgMNwJTVyTH6ElKqyGjhX\nhKOB/4gwDLhBlXXeR84C9gEuAy5Pfd586eiY3+Sxskh0gU4fr5r7m5H3lFKPSgXyBPAxrgZ+NYXz\n8T1QfnRNWX+cBfyIuwm09wbAN7giZWXALGAdCRXYu63gyYOhLbB2FZz4KrTrA+wELKspi2+KM4ky\n7d487KfN7Eh0fc3+QpWFNT8f7+nz6nKYfZ1PAh0IfKBao0tTIu4GXhThftVc1yOL992v+wMuejO3\n+42PKmNE+B9ePwoR+uJW/TfDrSfDx9fDtrumUzMuPzo65jlh28ES2xHzK2QU9E7Qy7OR1YshPwT0\nUtCnqay18wXo86BXgv4NtLULH0w074dPgt4e7vkpbDtvJtdX1bDS/UfAl++D3uTT9XUf6NVpbjMV\n9LjgjldsqPqIU0CXgF6OT3WdMjhmAtofVLfnbD2CTb89iJYbDmQ7PZB2eiBdtAPbrywkX1o+j9AF\nqP1iCDaXonZZ9DrQQX7L6oUE7wF6mhcX/l9cHf0f4NLF8W/IJaNAfwJtFe65yR9lHsb1Bbol6ALQ\nk3y4vr4A3SvNbY4nhQKXuTt+uh3oDFxuSMY1o7KUoT7owgPppHHiivVAuhTMA0y+jzw2Q+Xd0nAV\nrjRzXDKVVZW1uNIOG8s7eCawNrDiTWjWuuoWzYDmLYGXgYGAX2aQtKi087aeAT98A3NmFZqdN9vr\nS5UfRegJjBNhjiofZTKPCNsCW+LMnOnwKnCnCH9V5f1M9p0NqnwrwgHAQ8B0EY5VZW7AYtwEfFWP\nea1wfsVqLAX2LBDTaH6T18oiz0i1PlTWqKLAIpFZn0H5XxI4Fm8F3hfhLq21OFou5Vy1QIRvgXNV\n+TAMGcJGlZkiDABe9W7a32cwTQkwXtPMH1JlvRcZeAkxhQeDRJXfRfg/oD8wVWTUlXDnYYn6YfiJ\nCMcAfYAuSqMEznbFajv5Q6F3yguSlUBRsLssK3UhfBU+z8qQPlXmA28A5wcrUw0aA2tDliFUVBmJ\nc7aOEqFxBlOUAOMy3P0wXJTethlunzWeleJheGoAvPsYjOsDIw92f3uOd2HW/iLCTsCjwAmqLBXW\nrI/7OVaphcD6gymL1AlsZVGBeyIbfRiUPAe9Jrq/o2PzGAbjqnU2D1KuajQCazmJM4csBoZ6ZsSU\nEKEeLgQ2I2WhykpcV7oLMtneXx7tBTc1SNTS1C+8630UUFphfmvB6lnxPtucn78sJNNoPmNmqNQJ\nXFlA7XZ1VWaJMAFnArgzSLliqPMrCwBVNohwOjAV50u6N8VNOwHLVPk2i90PAWaIcJO6XISQyH3y\nnqeIHwf+BzxW8fqPMKMn8AvNd1YaNxDWrG/B6lnLXM91wwdMWaROLRncoXIL8LYID6rrCxAYXj2s\nLWDucH/rYRUmqpR7Du/pInyhCfo8V+NwMjdBVez3a5GyGXDnBJFfVufaV5CYQJL3BgI7Avt7vj0A\n3lM9x8d9GPEIOxyrUIYXJrk0bDkSyPYq6AXB7rPwQ2dzeD4OcKHPyVvsgk4A/Uf25+LM78I+F7m+\nJmKOa6Dfy4Z3/MMWINQvn0YhPNDGoGvDSkCq/XtoF9BvQRsHt8/CTsoL4JycDToLdNNaPtMM9BfQ\n5lE5F+431e8DuGihn7lRXqLqItAjwj63dXXUWTNUuoXwVFnj1YraBII19yRDlQ9E+Bw4jRg7bm4J\nv7hcPqPKYyLsDjwvQg+NX5KjO/CRZu1nyJ9z4YVTvwC0VuWffswpQiPgP8DDqrztx5xG+tThaKhE\nlWJrjdzIV78FwCDgapGgHgAq7NOxlAPtdhShR3By5DWX4qLFBid4/3BIya+RhETn4vewnN0NcQUn\n/eIOYAXOP2eERB1WFq23yeBpLJSIqFRQZSquQGFAyVnxckAGzIejhgDXAAtEuFGEdsHIk3+osh44\nCeglwmlxPpJNfkUM8c7FP5fBA/uLcLMITbPfR1o0gI2VYLNChN7AUcCpGk7TM8OjTj79uTjtbTvE\nj9zYYXcRzgBeVOXXapuGkJiXFoOAB0UYkcDs4RuJyzo/swC4wzPBnI3rcPY+zjz2mqo/N5FCQZXl\nXoTURBFmqzIdQIRtgNaQfeZ7onMBQ9fh+j98LsKFUFTmVs45z65ugA8rC+8aug84VEOqUmDEELbT\nJOgBuj3op/DxC67zXvXIjVFngr6O67Z1H+guMdv+l4Cb16f53QTXs/jEsGWJkakJ6Kmgk70qpYNB\nO4QtVwjHoYfnoN3G+//poC8FtO8SmDMfLlwdRMQU6C2gpZltWxF0csJkuHoVvHVx2OfOhnduwhYg\n0C+7sfm8XsjGEuDxq46CtgMd5N3gJoGeDPoGAZWEzvw7juwHV65wGd/51eoUdBdcZd2loONBTwRt\nFLZcAX7/q+CrmXDA83DJ93Dq9KDOjyupHkzEFOjtoFemv52FY+fzCF2AwL4oOsCL0U5rZYArIX6C\nt6pQb47tw/4+8WUtjB+bF4Z8spdj8APoHankJBT6cOfngl/C6aPda0JVRVExjp2Qg/N7N+g/098u\nf0KAbdQckXRwixQVi3QbLnLcBJH9nxP5+Flc7Zz9VBmfzlyqrFXlP6ocCrwFbIErrTBWhJ75FfWT\nUYRX4KiyRpUXVDkE2B/YAEwWYZIIfUTilZqOAh0Hwa3Nwzk/iSKmclKRNUOfRf6EABs1iZyyqMyf\nqKh8+XZveLIX9DhJs6+1PwO4AdgWeB64EvhahOs9h2XIFN6PTZU5qlwJbAc8gMsV+U6Ee0XYLVzp\n/CbM81NW6iKkalYwzsHOMgydDVShGWkSOWUR/+l6cFNYfpUPk68ENlXlN1WeUaUb8A9cVEuZCKNE\nKPEqiYZA4f7YvBXcy6ocAewNrMY1FZoqwukhhH/mgPDOj4t6Ov89OPe9BBWM/STD0NmyUrhoUUAK\nzUiTCCqLnD691UjKU2WmKgNwT8Zv4xKIZotwuQhb+LDPNNh0MFy3vtB/bKp8rUop7pjeDpwALBTh\nQRH2CFe6bEjcnySXe60wy8ILh8OyH2H8marT+uaw0GBGZignT+/74ar5ASg0I03yyN7uFzmtfJkw\nKU+VX4BHRHgU+CswAJgjwhvAw8BU1coqmblhbH+YOQpK1lXNfSjMH5u6pLbRwGivuc+ZwOsiLME1\nvnlBQy3JnR6Jc1Nyd37ilLXpCf07Jipr4xNZZHAf+ic49HHVhFnvRliE7WH3e8DF+8Al63MRcQJ6\nBOi4ND6/OejFXkG5MtALaissl6Vs3UAXg24e9jnI7fnV+qB/x1Xa/Qn0EdC9wpYrH4cLDw8uZDZm\nvy+AnpLhtq/me3h6XR2RWlm4xij3/BumD4GSLXPw9JZWBrcqPwH3inAfcBCuSdFNIrwMDFWf+lZ7\nrTwfBwZ6+4ws6jLT3wTeFKENcAbwsggrcFniI1RZ6Z6oA8lW9gUR6uMe/ZvHGYler+097/WD64fg\nVM8mg/vPwGwfZTF8IhLKovLGsHsXaLkFvHKh6uxsI5/ikVFtKFUUmIgr+bA17gY3UoSlwFCcOaW6\n5zMdrsb9wF7OYo6CQ5XFwM0iDMa1Jj0buEVk5v+DE7rBkLapVBROB69TWxNSvlmn/F4jT9DV1Ua8\n11YDSxO8HrtNOYx/Aq7sk+OGRNXJSFl4YejbQ9ZRi0YOELf0K1wSlBqflwvHmBce+4EqrX2Yqz5w\nBG61sR/wHPCIKp+nOc9uwCSgkyqLspWr0BFhKzhzLNzfueYN8pSxMOYOsrvBN8P1HK/tRp7o9dre\n+917qPD5eAT3+6jcJ2/gVs6vpSdnt3thryNg4sh8XwnWRSKwskiUiDZvEAl6V2eBb1Vnq5lTtgPO\nwoWKzsWtNkaqsqa2OTyFMwzXuL7OKwoAVX4QWflzfNNL5yOBpsS/Wf8MLErwXuwNvlxzXKTRT8Jw\nqpNm6GwchdbHr5Wg4R8RUBaBJjqVA41EaKg+Vk9V5VvgehFuAo7GrTbuFeFJ4FFV5iXY9HzcU25A\nDY8KhUQRcWtXAlsBY4BnVFkWhnRB491w/X5wqo00zVCBPvAZGRKBPIvgEp08M8EqfCxTHluaBLo9\nCUUfqlKCM03VB6aL8LYIx8SWFvH6RFwPnKNW578aifIZHuwEnAN0AuaK8LwIB3t+CMM/0gydLbzK\nA3WRCKwsykqh/741bbI5S3SqSMxbnu1ESVq7zgEuE6EUOB64DOY9LHLrUlj9C7QphuOfVO36VbZy\nRI1K08vvw6C4E0wdG2N6WQBMEWEz3FPrEGATER4Dnlblh/AkjwxpZnDnNDfK8IuwY3f9GJWlxo+b\nCNeshieOzd2+dCZoZ3/mSlRl84SJoHuBtgFtUPkdz/i2av7IWYvhT3lZATcfhlcteGSSzwjovqDD\nQFeAvgx6OGi9sOUv1AH6Pug+qX/+9fPg4jX5Xi25ro8IrCyq2mRFOBuXPf1KjnbnY2vVbdrGX35v\ntzvOD9Ea+JMIy2BAY7h+86p23XtbwxafijAIeFKVH/2RKzK0wK0EE6KKAtNx5r5LcW1pbwNaivA4\n7rjaE256pOyzEKEIjroGlveBkmOiUHkgqkTAZ1GDp4EdRdgvR/P7oixE2BTa7Rzf3zLtLVX2VBei\n2xTYG5bqlVJCAAAW6UlEQVTMj69YvpuFS2T6SoQRInQ3G/xGioBfUv2wKitVGQrsiatHtR2uJemr\nIhzlRZ8ZyWlI6maoQcBbqqe97OpVjTokx3WrjAyJnLJQZS1wM66UeC7Iug+3ywVgEvR5O1lhOVXW\nq7II5n4VX7HM/UqVM4H2uCfkobgb3EUitMxGzgiQdGURD2/V/YEq5+LK0b+OCyb4WoR/e3WqjMSk\ntLIQoQtwIq7Uv5HnRE5ZeDwNtBfhgBzMXaPybDqI0B54F3gVOveD0Ye56prJqmzWXrFUlRWqDAF2\nw5nhuuJubsNE2LuOrjbSWlnEQ5XVqjyuyj5AD6AV8IkIb+Rf86u8Iamy8FZpQ4ErVbMPFjFyT8Fn\ncCdChDOBPuo63Pk572BgtSo3Z7DtX3CJeINVeTD97SvKmqRm1xVhS1xpkXOBFbgf5wjNrrRIwSDC\nUGCmKg/7PG9TnJnqHFx5iieAYap87ed+Co3K6/Pg4+DDt2HaxYmuTxEuBI4DDvb8RkaeE2Vl0RCY\nBZyhymQf570K2FyVK5J/NraY3YZ1cNee0P4CVV70S55U8JoxHY5L9usOjMCVYygLUo6gEeE5YKwq\nw3O4j91wNan6Ah/iAhPGeObQOkM6ZUW8ApAzge6qfBm8tEYmRNUMhboM65vw33eRks+iZnvX4YfD\nLWuh6H8+y5MUVTao8pYqxwB74HJE3hbh3Wj3vM7eDJUMVT5X5WKgLfAMrtf7QhFuE2HHXO47X3Cm\nuK731Nb/vWry6cBp8P4LpigKi8iuLGBjFcsvgbNVmeTTnL2BHqqcUvvnug13iqJ6olHJc6rTQi9h\n4K28/oFbbXTG+XkeVWVOqIL5iAiTgBtUmRjwfv+Mq/V1OlCGW22M0iS1voIknRLuIrQA2uGiwyr+\nxv57a7h2A9zcuObWZ38ODfvBLy9UXXUMmA+vHmpRT4VDZFcWsLHT2k3ADT46eFN0cCcqYXBADxHO\n8n6AoaHKOlVeUdfzuhugwFQRxonQy1MmVZ4I3d+i4jDlTpOcryziocpXqlyOi6QaCvwf8J0Id4uw\nS9DyVKfmqndcHzhhisjYC7x2wA+IMEaET7w+Id8D/wEuwj1YrAbeAq7FmTWbwcSX40frNS+CVlNr\nrjoebl+x6jAKhLCzAnM9QBuAzgY9xKf5DgCdmvxzCbOzJ4C+4mULDwPtCiphHyfvuzUG7Q062XXd\nm34fnP51oWbWgs4B3SlsOTxZOoAOBl0COgX0VNAm4ciS6Noc+A3oXaADQY8F3RO0VSrXp6sw0Hdu\nvGvFRfqp1hzHTgj7vNhI47oJW4BAvqT7YU7x46YM+hfQsuSfS/zj8ebZGvRKT5F9DnoJaKuwj1XM\n99wNBswKuiWnP7JXlH+5di0c+nI+KTfQhqC9QMeCLgcdArp7sDL0mpCLm3flcb9ug2vnWnGtJ1JO\n+X0d2ah2fsMWIJAviTaAOfPguPHuh9J1eKY3ENB2oN+m9tmKH8+xCffp1SbqDvoM6M+gL+VLbaJc\n3VRyK3PtSjp3++w6PN1rC7QY9EbQRaDvgZ4J2iz3xyi3N2/QDXg1zcI6Jzb8H3UkoaioLZzcDJ4+\n1Ic2mykn5aXSR0AVBSYDk72M69642kSbifAErjbRwnB6SpevKrxqoIl6IxS9LcJonA/jF5zdvbZ/\n/+qdm1pJUjl4Qe3bVZzPHybBZRPgmGOBO0V4EXhMlY8yOgRJyV2lZi9MW6CyQVRIDZgMn6kjyqLj\nILhnK5+aq6wCmotQT33uI6HKz8BDwEMi7ImLqJkp8sUncNIucO/WfveUToQrafHgnnDpUrh7i4DK\nv/tAosCCP8CFDLfAZWE39/7dotq/K/7fWGRjd7xalMtJh8O9cZTTt4MhfsRcAgWzD5x2GKxaD5wJ\nvOL1aH8MeF41/bIliai8eW82AX7/Hco+8vHm3QBYX13RhtCAyfCZOqIs/GuuosofIvyKu6ms9EO6\nBPv5CDhPhMvglnHwyNZBdRIToTUwATrcDc+/Cp8V0BNhot4In85Q5bZUZ/HCriv6b9eiVBq3iH9t\nHXiiCEfiWrUu9ob377+fkKgznCp9gRtFuBmXSHk2cKsIL+MUx4xUVjzJcAqD73HlNqZkO18MaXbJ\nMwqFOqIsEt1AfsjUnFJReTZnyqICVX4V+W1NUJ3ERNgCGI8zf93r1eEroCdCf0ws6sKuf/ZGQkQ+\n2gPKi2teW+OfhxsvArYB2sSMXaHtrsnOp7o+32OBsZ7y7gc8D/ziNWp6zluJZsMOwNws56hOOhVn\njUIibKdJECO+g+2i3+CzN0Cbpj+ffg7aMTj5g4kmAd0c9BPQm8I+Z9mf79oDC3J7bdXuvM30fILW\nAz0M9EUvGOIp0P0yifID3RS03O+wbdA/gf4U9jVgw/8R6QzuWGoW4Vt7I3xQiqvS2lOV71Kfi/eA\ny1SZmit5q+4v9bo7me+DItyKYjJwuaoVd0uV9As8HrwLdJoJgxpmej69IpGn4YoZrsOZqJ7VFCu4\nej6xJ1XZI5XPp4pXfv8zVbb0c14jfOqMsoiHl9V9BS4ztZcqKdVtEuEtYIgqb+ZSvqr7LCqGgbNg\n9gxY+I2fvgMRmuEycj8FLjBFkVucGWlmSxiwJltfkHcNH4jzbRwFvAE8Ckyu7TyKcCJwkirHZfYt\nEs7bFnhfFd9NpEa41BGfRXy8H9NtInwJvC7CQFVGpLCpj61VU2XVKmAtrlKnbzdzEZoAY4DZwIWm\nKHKLiCvLDXt0Vp2WdSkS73xNAiaJ8CfgVFxEXQPPt/G0KkvjbJoLfwW4e4r5LCJIpGtDpYoqY4BD\ngZtFuNmLFa+NEJQFOwJzfFYUjYGRuNo/56jPocBGVbwOew8BvVX9r1mlynJV7gU64sJvOwJzRHhR\nhMOqXde5VBYWDRVBTFl4qPIp8FdcYbSRIiW71lJAbxVZtlbNgB3Av4qwXqHAF4DfgNNVK5OoDP/x\nOsM9C9ynyvu53Jfnj5yqSj+gGOeHugunOK4WYWu8h48c7N6URUSp02ao6qiyVITDYOYzsNvHcHOj\nBElwYa0sfHkS9G5cz+DCHHup2o87ACqaZaWc6+EH6sJrHxThIWBvnEP8S6AlsKMIU3x+ULDQ2Yhi\nK4tqqLIGBqyrVBRQvZELIZqhsp3EM0U8jstiPl7rWEe3MBDhr8DFwKlhreC81cb7UDQISibAv4Ar\nb4V534hwveeY9gNbWUQUUxZxSZrxHYayyNoM5UXOPAB0AI5R5Xc/BDMS4/UtGQGcr8rCcGWpCMF+\ntZdrIHn95nCzwsc7Ap+J8JoIPbzs9UwxZRFRTFnEpSLjO5YqBfQCUxYVzYegdE849JJMmw95iuIu\nYE/gH6o1vqCRG4YAk1R5OWxB4hdZvL8tnC+4Rk2v4BoaLRDhRhHaZbCThpiyiCSmLOJSVuqSpCru\np+XApT/GlIwIxMFdtaPZoAYw5njoOT5DhXETcDBwpPpYlM5IjAgn4boQXuzPfOl1LRShqQj7itBf\nhKFwQI9EK2ZVVqvyhCr7An8HNgM+EmFsbOfEFLDQ2YhiDu441Cyp/PtqeGA/eKSR95GAVhaJym2n\nV0BQhGuBY4EDVVmRA0GNanhP5ffjlPPq7OervRS6l9HdCdf2tJM32uGc2Z+4MXs6lB+erOS8Fxl4\noQhXAscDl+Cc5E8Bj6syrxZRzQwVUUxZJKB6SWURzgNGiNCNwJRF9tVyRbgUVxbiQFWW+SmdER/P\n5j8cuEOVD/2ZNdGDwxbvekELTdioFBgLDAZmxQYwiPz3Negfp2xM/CKLqvyKi5p7RoRdcSXzp4sw\nE5clPtoFhFTBlEVEMWWROg8DR+I8g3cTiLJIVC03teZDnoK7AKcovs+BgEZ8rgbW4HxEPpHowWHl\nT0AP4NtkCZvZNCFS5QvgUhGuwa1S+wMPiPA0brXxlfvkK9vAlF1FvpkQXJMuIxDCrmRYSAN0S9DF\n8J/T4F8bsm3Rmnx/8SqanrU4lf15LTq/Bd0+7ONWlwZoV9DvQbfxcc7D4Ipl+dbHGnRH0NtAfwB9\nB94aCGcvsfap0RyhC1BoA/5zOlyyLqgfRNVy28dPgDnzQRvVvo2e4vV13ins41WXhlf2ez5oT5/m\n2xt0HOhseOP8fO1jDdoI9Hi4dHG+KTQb/o06XXU2E1wY67g+NU1DJc+pTst5kyAR3gAmqMY3cYjQ\nC3gQKFGlLNfyGJWIMBz4RZUBWc7zZ2AQLpLqBlwp8XXplkIPGpHjJsDIg2u+02ui6qhDgpfI8BPz\nWaSNfy1aM+RSYKoIw1X5IfYNEf6O8638zRRFsIjQF5fD0iW1z1fc+Fu3qbDte/23/wUcA9yBq9n1\na8U2+d/HOjsfm5HfWJ5F2iRN2Msp6hyJT+OePDfialrxFHC0Kh8HIYvhEKE9cA+umuyvyT8fmz8z\n8mD3t+/HMP8zYBmwkyq3pzJXfnHCM07XxeYnpd/S1shPzAyVJkF0rUsuAy1h/my4+ANouAlsWAd3\ndYH2x6gyJQgZDIcXJjsFeEmVe1LbJpEp85hRquN8bUYUJCKMgLld4d4/YPG3+WgqMzLHzFBpkk34\noX8UtYRTFJ4/slJhDVwMLy3EkrOD5nrcQb8v9U0SmTJbbOafWMEiwk5ACexwBzzQXpX+Yctk+Isp\niwwI33bccRDcvWXVBK372sAXaWV2G9khwgG4dqadNa3GUZG07V+FK1L5G5aUF0nMZ1GQhO5kr/M4\nUyDDgbM17YTHeLXHCte275U26Ykrb2IZ3BHFVhYFSSSfTAsGr4LvI8AYVV5Pd/tKU+YW78LK5fDl\nZwVu278CeFSVn7yCg1ZIMIKYsihIykqh/76p1vgxfOd0YFegX6YTeMX/ZgDPqjLKL8GCRoQ2wCnA\nzt5LtrKIKKYsCpD8cLLXTUTYAZcDcYgqv2U53XoK/zf4T+BpVX70/m/KIqIU+oVaZwnfyV738Ews\nI4AbVfnMhykLWlmIsAVwBrB7zMumLCKKObgNI3VuAJbion78oKCVBa6p04uqLIp5zXwWEaWQL1TD\nCAwRDsb5KDqp1l4KPA3WA/V9mitQRNgMV6Z8r2pv2coiotjKwjCSIMLmuBIrZ8bY5v2gkFcWF+Ci\nwRZUe92URUQp1AvVMALBC5N9DBipyls+T1+QykKE5sCFwP5x3jYzVEQpuAvVMALm/4AOQO8czF1Q\nyqKyUm6nfaBhOTy5Nk55GVtZRJSCuVANI2i8vhK3At21Zq9pP/iDgH+D8UqjpxJyHb+A5k/jRYqq\nF9A0ZRFRTFkYRhxEaAw8D5Sq6z+dCwJdWSSomLxvnBt+HDoOqtwO3N+hHVyuT5UQblMWEcWUhWHE\nZxDwLa6sR64I2AyV6Ib/+zARhgEtgc3i/z1o1xTrkZnPIqKYsjCManiNpE7B3zDZavsoKoaTj4KG\nTUU+3i2YDPxEBSiLOwE9gJ+BFbhcktkx/18BH10H5T1TqEdmK4uIYsrCMIi15W/bDnbcE3Y/R/Wk\nZbnbV8/xcE+FOah96uagbEhUgHLqWNXaqwGITLsY+ndMoR6ZKYuIYp3yjDpPbd0PYdU3uBtgQ+9v\nolHb+9Xe6z0QHtu/5k275DnVaTkr4RL/e573NbxySOpO7o611iMTYQwwTJXROfgKRojYysKok3j5\nE9sCXeDkGyqf8qHSlt9hPiC4J+XYsS7Oa2m8t/VOYfQjqVmAsvU2cOE7qk8vSHV7ktcjs5VFRDFl\nYRQ8qYSDeqW0u1QbG4AZ0Kh5/Jv3Z5OAQ/32W4hMHw7lcXpw574fSewNX4TWQJkIN6my0KddmLKI\nKKYsjLwi3TyA+KaV8/cTeeVGOHY7nFLYC2cK+sAbj+DaoS5WRUVmjoDy4po37yWLc+Pgzo9+JKos\nEeER4F/AWT5Na8oiqqiqDRt5MaBFMfSdC6sVVN3fvnOhRXHVz2lT0O1Bu8FJ71R+XmO2u3Qx6C2g\nx4G2A5XE+/3gcbhgdbL9+v9duw6HYye4v7nbV+1yaEvQpaA7+zTfFNDuYV9LNvwftrIw8ohEeQCb\nTxLhG2BrbzQGlgDfQ9sd4puQvp6lyjXJ9ijC32Cvw+Gu/aDk8qCaSeVLPxJVfhbhDlxeyfE+TGkr\ni4hiysLIIxLlAfy6Gmcq+R6nJFapOvOQyLSM7f8ibAk8AfRWHTGTPLh5h8QDwGwR9lZlRpZzmbKI\nKFai3MgjKvIAYikHZn2qyiRVZqmyskJROMpKnb2/PObzye3/XjTUk8BTqkzy7SsUIKr8CtwIDPZh\nOsvgjiimLIw8It6N/+pyeKKzCJ3jbeHMOaMPg5LnoNdE93d0KsltFwBb4FYshlOc23nZ69lgK4uI\nYkl5Rl4RL/ELVu0P3A08CNyimt2Tqwi7AxOArqrMzV7qaCDCicAVwN5VV29pzTELOFaVL30Vzggd\nUxZGQeDlSTwGtAb6qfJphvM0AWYAd6rylH8SFj4i1MMdm8GqvJzhHHOBI1WZ46twRuiYGcooCFRZ\nDPwDuB/4rwjXimQUoHE7UIZrk2rEoMoG4GpgUIbHFsxnEVlMWRgFgxfu/SSwJ9AdeE+EXVPdXoR/\n4Kqr9s/UzFIHGAcsBk7PcHvzWUQUUxZGwaGuNMXfgEeBd0S4QoT6tW3jlbZ4DDhVlZ8DELMg8ZTo\nNcC/PZNdupiyiCjmszAKGhGKgWFAU5wv46s4n6kHjAX+p8r1wUpYmIh8/hbctQWsXJle+1V+AnZU\nZXnupTSCxJLyjIJGlQUilAD9gXdFuAUYosofMR8bCBThcgmMJLiItON3hfu3Tb/9qq0sooqtLIzI\nIEJ7XL5APbipFMaeDR12guK/QP0S1X9PCVvGQkCk23AYFycrPnm/DRF+BbZQrZFdaRQ4trIwIoMq\n80U4GCZfDyv+C+PqxzwZP5n7TnRRIVHZlZT6bTTAoqEiiTm4jUjhwj+v2gFuql+zIGHHQWHKVjgk\nKrtSe70tr4RKQ8wMFUlMWRgRJKsnYyNu2ZWrVqfQb6MeruvBhtzKZ4SBmaGMCFLxZBx8J7ooULP9\n6rIfYFgnuP8QXJXeRJhzO8KYg9uIHPG75/Wfl2KBQSMOXvLjO8ABqsxK8JlmwI+qNZZ1RgQwZWFE\nkngFCU1RZIcI5wDnAfuq8nuc91sC36iyaeDCGTnHlIVhGCnhObBfwvUuHxjn/VbAV6r8KXDhjJxj\nDm7DMFLCKwVyDtBThB5xPmJhsxHGlIVhGCmjygqgD/CYCNtUe9vCZiOMKQvDMNJClam4vt3PVivg\naNFQEcaUhWEYmTAYd/+4KuY1UxYRxpSFYRhp4xVq7AtcKEI372XzWUQYUxaGYWSEKt/hHN7PeWGz\n5rOIMKYsDMPIGFXGAK/jGlGZsogwlmdhGEZWiLAJzPkI7msIzbeCyWMsCTJ6WG0owzCypGhrOK4Z\nPLCdV16lTxrNkowCwcxQhmFkScdBlYoCrCR8NDFlYRhGllhJ+LqAKQvDMLIks2ZJRmFhysIwjCyJ\n1yyp/7wUmiUZBYRFQxmGkTVWEj76mLIwDMMwkmJmKMMwDCMppiwMwzCMpJiyMAzDMJJiysIwDMNI\niikLwzAMIymmLAzDMIykmLIwDMMwkmLKwjAMw0iKKQvDMAwjKaYsDMMwjKSYsjAMwzCSYsrCMAzD\nSIopC8MwDCMppiwMwzCMpJiyMAzDMJJiysIwDMNIiikLwzAMIymmLAzDMIykmLIwDMMwkmLKwjAM\nw0iKKQvDMAwjKaYsDMMwjKSYsjAMwzCSYsrCMAzDSIopC8MwDCMppiwMwzCMpJiyMAzDMJJiysIw\nDMNIiikLwzAMIymmLAzDMIykmLIwDMMwkmLKwjAMw0iKKQvDMAwjKaYsDMMwjKSYsjAMwzCSYsrC\nMAzDSMr/BwzNZAmFc5HQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2eca20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 17924.5 in 0.004 secs for mst_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(mst_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not so great.  Can the alteration strategy help?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def altered_mst_tsp(cities): return alter_tour(mst_tsp(cities))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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adi6wDm6WkSncnfOTveCUiXDRkiwt7lLla1WOBy4C/u3V02pd4Gt/Bp7ErVlJ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\ny0KtgVW7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f72eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80 city tour with length 14105.0 in 0.022 secs for altered_mst_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(altered_mst_tsp, USA_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Better. Let's go to the benchmarks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  mst_tsp |   5953 ± 361 ( 5334 to  7030) |  0.002 secs/map | 30 ⨉ 60-city maps\n",
      "                   nn_tsp |   5668 ± 488 ( 4674 to  6832) |  0.001 secs/map | 30 ⨉ 60-city maps\n",
      "               greedy_tsp |   5392 ± 306 ( 4554 to  5967) |  0.002 secs/map | 30 ⨉ 60-city maps\n",
      "                   dq_tsp |   5268 ± 236 ( 4743 to  5752) |  0.042 secs/map | 30 ⨉ 60-city maps\n"
     ]
    }
   ],
   "source": [
    "benchmarks([mst_tsp, nn_tsp, greedy_tsp, dq_tsp])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not very encouraging: `mst_tsp` is the second slowest and has the longest tours.  I'm sure I could make it faster (at the cost of making the code a bit more complicated), but there is no point if the tours are going to be longer.  \n",
    "\n",
    "What happens when we add the alteration strategy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           altered_dq_tsp |   4953 ± 221 ( 4575 to  5399) |  0.049 secs/map | 30 ⨉ 60-city maps\n",
      "           altered_nn_tsp |   4820 ± 233 ( 4450 to  5346) |  0.008 secs/map | 30 ⨉ 60-city maps\n",
      "          altered_mst_tsp |   4823 ± 227 ( 4354 to  5250) |  0.009 secs/map | 30 ⨉ 60-city maps\n",
      "       altered_greedy_tsp |   4766 ± 207 ( 4320 to  5185) |  0.009 secs/map | 30 ⨉ 60-city maps\n",
      "  repeated_altered_nn_tsp |   4640 ± 194 ( 4298 to  4991) |  0.148 secs/map | 30 ⨉ 60-city maps\n"
     ]
    }
   ],
   "source": [
    "benchmarks([altered_dq_tsp, altered_nn_tsp, altered_mst_tsp, altered_greedy_tsp, repeated_altered_nn_tsp])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now `altered_mst_tsp` is in the middle of the pack, both in tour length and in run time.\n",
    "\n",
    "So why would we want to use the rather complicated minimum spanning tree algorithm, when the greedy algorithm is  simpler to implement, runs faster, and produces shorter tours?\n",
    "\n",
    "Guaranteed Tour Length!\n",
    "---\n",
    "\n",
    "The great thing about the minimum spanning tree algorithm is that it comes with a *guarantee*, which none of the other algorithms offer. You are guaranteed that the tour length it comes up with will be no worse than twice as long as the optimal tour.  (And, with a bit more complication, you can modify it to give a guarantee of 1.5 times longer.)  The guarantee works like this:\n",
    "\n",
    "1. The minimum spanning tree, by definition, connects all the cities with the shortest possible total edge length.\n",
    "2. So if you could follow each edge in the spanning tree just once, and that formed a legal tour, then that would be guaranteed to be\n",
    "a minimal tour.  \n",
    "3. But you can't do that in general; in general there will be places where you skip to the next city without following the spanning tree.  Any such skip, however, is a straight line, and thus will be less than you would take if you went to the next city by following along the spanning tree.\n",
    "4. If you did follow along the spanning tree, you would follow some edges twice, and some edges once.  Hence the total length of the tour would be at most twice the spanning tree, and thus at most twice the minimal tour.\n",
    "\n",
    "A guarantee is great from a theoretical point of view, but in practice the greedy or nearest neighbor algorithms do just better than the minimum spanning tree, on the maps that we actually see. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shoulders of Giants: Held-Karp Algorithm: `hk_tsp`\n",
    "\n",
    "\n",
    "<a href=\"http://www.computerhistory.org/collections/catalog/102650390\"><img src=\"http://archive.computerhistory.org/resources/still-image/IBM/IBM_People/IBM.3_mathematicians_Held_Shareshian_Karp.ca1964.102650390.lg.jpg\">\n",
    "<center>Held, Shareshian, Karp (Computer History Museum)</center></a>\n",
    "\n",
    "<a href=\"http://xkcd.com/399/\">\n",
    "<img src=\"http://imgs.xkcd.com/comics/travelling_salesman_problem.png\">\n",
    "<center>xkcd 399</center></a>\n",
    "\n",
    "Another algorithm that shows up with a literature search is the [Held-Karp Dynamic Programming Algorithm](http://en.wikipedia.org/wiki/Held%E2%80%93Karp_algorithm), named after giants [Michael Held](http://www.computerhistory.org/collections/catalog/102650390) and [Richard Karp](http://en.wikipedia.org/wiki/Richard_M._Karp). It is an algorithm for finding optimal tours, not approximate ones, so it is not appropriate for large *n*.  But even in its simplest form, without any programming tricks, it can go quite a bit further than `alltours_tsp`.  That is because `alltours_tsp` is O(*n*!), while the Held-Karp algorithm is only O(*n*<sup>2</sup> 2<sup>*n*</sup>).  How did Held and Karp achieve this speedup?  They noticed that `alltours_tsp` wastes a lot of time with permutations that can't possibly be optimal tours.  Consider the following 10-city problem, with a 6-city segment shown:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111aba5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_labeled_lines(cross, 'r-', [0, 4, 1, 3, 2, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `alltours_tsp` would consider 4! = 24 different tours that start with those 6 cities. But that seems wasteful: there is no way that this segment could be part of an optimal tour, so why waste time on *any* continuation of it?  The proof that this segment can never be part of an optimal tour comes down to two things.  First, we demonstrate another tour that also starts in city 0 and ends in city 9, and along the way goes through cities 1 through 4, and is shorter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RX46IL0XE+W3XVBpDaoRWOJrwLuA9mfkU4DjwWyMuT+V6Y2ZekJkXZuadbRdTGkNqxOp+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114844588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_labeled_lines(cross, [0, 1, 2, 3, 4, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second, we need this key property:\n",
    "\n",
    ">*Given a start city A, an end city C, and a set of middle cities Bs, then out of all the possible segments that start in A, end in C, and go through all and only the cities in Bs, only the shortest of those segments could ever be part of an optimal tour. \n",
    "\n",
    "Of course, we don't know that the optimal tour goes through exactly those Bs cities before hitting C.  But if it does, then we need only consider the permutation of Bs that leads to the shortest segment.  So we can throw out the red zig-zag segment above, and keep the nice smooth blue segment.\n",
    "\n",
    "So far we have only been talking about segments.  We know that the TSP is defined for tours, not segments. So even if we find the shortest possible segment, it might not be the shortest possible tour.  But here's something we do know: a tour has to end somewhere.  So just find the shortest segment from the start city, `A`, to every possible end city, `C`.  That will give you *n*-2 segments. Out of those, don't choose the shortest *segment*, but rather choose the shortest *tour*.\n",
    "\n",
    "That gives us our algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def hk_tsp(cities):\n",
    "    \"\"\"The H eld-Karpshortest tour of this set of cities.\n",
    "    For each end city C, find the shortest segment from A (the start) to C.\n",
    "    Out of all these shortest segments, pick the one that is the shortest tour.\"\"\"\n",
    "    A = first(cities)\n",
    "    return shortest_tour(shortest_segment(A, cities - {A, C}, C)\n",
    "                         for C in cities if C is not A)\n",
    "\n",
    "# TO DO: function: shortest_segment(A, Bs, C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for `shortest_segment(A, Bs, C)`.  It is defined to produce the shortest segment that starts in city `A`, ends in `C`, and visits some permutation of `Bs` cities in the middle.  If there are no `Bs` cities, then of course the shortest segment is to go directly from `A` to `C`.  If there are `Bs` cities, then one of them has to be the last `B` city visited (just before visiting `C`). So for each `B`, find the shortest segment that first goes from `A`, through all the other `Bs` cities, then to `B`, and finally to `C`.  Out of all these candidate segments, return the one with the minimum segment length.\n",
    "\n",
    "**Note:** the decorator `@functools.lru_cache` makes this a **dynamic programming** algorithm, which is a fancy name meaning that we cache the results of sub-computations because we will re-use them multiple times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@functools.lru_cache(None)\n",
    "def shortest_segment(A, Bs, C):\n",
    "    \"The shortest segment starting at A, going through all Bs, and ending at C.\"\n",
    "    if not Bs:\n",
    "        return [A, C]\n",
    "    else:\n",
    "        segments = [shortest_segment(A, Bs - {B}, B) + [C] \n",
    "                    for B in Bs]\n",
    "        return min(segments, key=segment_length)\n",
    "            \n",
    "def segment_length(segment):\n",
    "    \"The total of distances between each pair of consecutive cities in the segment.\"\n",
    "    # Same as tour_length, but without distance(tour[0], tour[-1])\n",
    "    return sum(distance(segment[i], segment[i-1]) \n",
    "               for i in range(1, len(segment)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's all there is to it.  Let's compare `alltours_tsp` with `hk_tsp` on 10 city tours:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x101815cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2291.8 in 1.650 secs for alltours_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(alltours_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114832da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 city tour with length 2291.8 in 0.037 secs for hk_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(hk_tsp, Cities(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that `hk_tsp` returns the optimal tour, and it is a lot faster.  We can take `hk_tsp` into uncharted territory well beyond the reach of  `alltours_tsp`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IQl9EpEAU+iIiBaLQFxEpEIW+iEiBKPRFRApEoS8iUiD/D6gGX6fvXhHKAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11472fa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14 city tour with length 2886.6 in 1.464 secs for hk_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(hk_tsp, Cities(14))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cIwilnMmEA8RvqEApZy46NxdljETVuDMNcKApdSySncKVd+IDwCuBn7vzr8Th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\nKkRJX0SkQpT0RUQqRElfRKRC/h/0djI4tTI8yAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111aa5cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16 city tour with length 2868.6 in 9.018 secs for hk_tsp\n"
     ]
    }
   ],
   "source": [
    "plot_tsp(hk_tsp, Cities(16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad! In 11 seconds, we did what `alltours_tsp` would have taken an estimated 200 days to complete! Let's repeat the table of expected times, comparing the All Tours algorithm with the Held-Karp algorithm:\n",
    "\n",
    "<table>\n",
    "<tr><th>n <th>`alltours_tsp(Cities(n))`<th>`hk_tsp(Cities(n))`\n",
    "<tr><td>  <td>expected time &approx; O(n!)<td>expected time &approx; O(n<sup>2</sup> 2<sup>n</sup>)\n",
    "<tr><td>10<td> 10! tours = 2 secs                <td>0.1 secs \n",
    "<tr><td>11<td>2 secs &times; 11! / 10! &approx; 22 secs  <td>0.2 secs\n",
    "<tr><td>12<td>2 secs &times; 12! / 10! &approx; 4 mins   <td>0.4 secs\n",
    "<tr><td>14<td>2 secs &times; 14! / 10! &approx; 13 hours <td>3 secs\n",
    "<tr><td>16<td>2 secs &times; 16! / 10! &approx; 200 days <td> 16<sup>2</sup> 2<sup>16</sup> tours = 11 secs\n",
    "<tr><td>18<td>2 secs &times; 18! / 10! &approx; 112 years\n",
    "<td>11 secs &times; (18/16)<sup>2</sup> 2<sup>(18-16)</sup> &approx; 1 min\n",
    "<tr><td>25<td>2 secs &times; 25! / 10! &approx; 270 billion years\n",
    "<td> 11 secs &times; (25/16)<sup>2</sup> 2<sup>(25-16)</sup>  &approx; 4 hours\n",
    "<tr><td>50<td>2 secs &times; 50! / 10! &approx; 5 &times; 10<sup>50</sup> years</a><td>11 secs &times;  (50/16)<sup>2</sup> 2<sup>(50-16)</sup> &approx; 58,000 years\n",
    "</table>\n",
    "\n",
    "So if we had some patience, we could find the optimal tour for a 25 city map, but we still can't handle the 50-city landmarks map.\n",
    "(There are refinements to Held-Karp that can handle 50-city maps, and could do it even with 1960s-era computing power.)\n",
    "\n",
    "We're starting to run out of tricks, but we have one more general strategy to consider."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ensembles of Other Algorithms: `ensemble_tsp`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we have several optimization algorithms and we're not sure which is best, we can always try them all and take the best result.  We will define `ensemble_tsp`, to combine the algorithms we have previously developed. First, if the set of input cities is small enough, it solves the problem optimally with `hk_tsp`.  If the set is too large, it tries a selection of algorithms, and chooses the best resulting tour. The result is guaranteed to be as good or better than any of the component algorithms; but the run time is guaranteed to be longer than any of the component algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ensemble = [altered_dq_tsp, altered_greedy_tsp, altered_mst_tsp, repeated_altered_nn_tsp]\n",
    "\n",
    "def ensemble_tsp(cities, threshold=16, algorithms=ensemble): \n",
    "    \"Apply all algorithms to cities and take the shortest resulting tour.\"\n",
    "    if len(cities) <= threshold:\n",
    "        return hk_tsp(cities)\n",
    "    else:\n",
    "        return shortest_tour(tsp(cities) for tsp in algorithms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's go to the benchmarks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           altered_dq_tsp |   4953 ± 221 ( 4575 to  5399) |  0.049 secs/map | 30 ⨉ 60-city maps\n",
      "       altered_greedy_tsp |   4766 ± 207 ( 4320 to  5185) |  0.009 secs/map | 30 ⨉ 60-city maps\n",
      "          altered_mst_tsp |   4823 ± 227 ( 4354 to  5250) |  0.009 secs/map | 30 ⨉ 60-city maps\n",
      "  repeated_altered_nn_tsp |   4640 ± 194 ( 4298 to  4991) |  0.148 secs/map | 30 ⨉ 60-city maps\n",
      "             ensemble_tsp |   4630 ± 187 ( 4298 to  4991) |  0.213 secs/map | 30 ⨉ 60-city maps\n"
     ]
    }
   ],
   "source": [
    "benchmarks(ensemble + [ensemble_tsp])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           altered_dq_tsp |   6771 ± 220 ( 6273 to  7248) |  0.347 secs/map | 30 ⨉ 120-city maps\n",
      "       altered_greedy_tsp |   6539 ± 240 ( 5994 to  7203) |  0.037 secs/map | 30 ⨉ 120-city maps\n",
      "          altered_mst_tsp |   6616 ± 213 ( 6268 to  7010) |  0.050 secs/map | 30 ⨉ 120-city maps\n",
      "  repeated_altered_nn_tsp |   6402 ± 185 ( 6015 to  6779) |  0.701 secs/map | 30 ⨉ 120-city maps\n",
      "             ensemble_tsp |   6390 ± 184 ( 6015 to  6779) |  1.100 secs/map | 30 ⨉ 120-city maps\n"
     ]
    }
   ],
   "source": [
    "benchmarks(ensemble + [ensemble_tsp], Maps(30, 120))"
   ]
  },
  {
   "cell_type": "code",
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      "           altered_dq_tsp |   9750 ± 288 ( 9187 to 10167) |  3.052 secs/map | 10 ⨉ 250-city maps\n",
      "       altered_greedy_tsp |   9229 ± 261 ( 8723 to  9606) |  0.215 secs/map | 10 ⨉ 250-city maps\n",
      "          altered_mst_tsp |   9484 ± 142 ( 9190 to  9668) |  0.221 secs/map | 10 ⨉ 250-city maps\n",
      "  repeated_altered_nn_tsp |   9187 ± 194 ( 8785 to  9390) |  3.524 secs/map | 10 ⨉ 250-city maps\n",
      "             ensemble_tsp |   9153 ± 216 ( 8723 to  9390) |  6.959 secs/map | 10 ⨉ 250-city maps\n"
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   "source": [
    "benchmarks(ensemble + [ensemble_tsp], Maps(10, 250))"
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    "So the `ensemble_tsp` returns tours that are shortest, but the run time is slowest, as expected. It improves on `repeated_altered_nn_tsp` by less than 1%."
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    "# Further Explorations\n",
    "\n",
    "\n",
    "That's all I'm going to write for now.  But there are still plenty of open questions for you to explore:\n",
    "\n",
    "* **Branch and Cut**: this is a technique to cut off a search early, when a partial solution is obviously not optimal.  We saw how Held-Karp cuts off some permutations of cities when another permutation is better.  A refinement on that is to keep track of, say, the best total length of the segment going through all the Bs cities.  Then, any time you have a partial segment through some of the Bs cities that exceeds the best total, we can stop right there, before even finishing all the Bs.  With this technique, you can find optimal tours for around 50 cities.\n",
    "* **Linear programming**: Lookup the topic \"linear programming\" and see how it applies to TSP.\n",
    "* **Heuristic Algorithms**: There are many approaches for using heurisitic estimates to find good (but not optimal) tours.  For example, *ant colony optimization algorithms* make random choices of which edge to follow, and then the edges that occur in the best tours get reinforced with some virtual pheromones, and other ants tend to follow those pheromones. *Simulated annealing* takes its inspiration from metallurgy.\n",
    "* The **[Lin-Kernighan heuristic](http://akira.ruc.dk/~keld/research/LKH/LKH-1.3/DOC/LKH_REPORT.pdf)**  is one of the best.\n",
    "* The **[Christofides algorithm](https://en.wikipedia.org/wiki/Christofides_algorithm)** gives a guarantee of 3/2 the optimal tour length (improving on the minimum-spanning-tree guarantee).\n",
    "* `altered` as a function: we defined a lot of one-line functions that just called another algorithm, and then calls `alter_tour` on the result.  Can you write a function, `altered(func)`, which takes a TSP algorithm as argument, and returns a TSP algorithm that does the original algorithm and then calls `alter_tour`?\n",
    "* Why does `mst` produce an optimal result, while `greedy_tsp` does not, even though the two algorithms have similar structure in the way they iterate over `shortest_edges_first`?\n",
    "* The code in this notebook was designed for clarity, not efficiency.  Can you make the code faster?\n",
    "* [William Cook](http://www.math.uwaterloo.ca/tsp/) maintains a great page on the TSP.\n",
    "* William Cook also has a [draft chapter](http://www.math.uwaterloo.ca/~bico/papers/comp_chapter1.pdf) on Discrete Optimization featuring TSP. Like my notebook here, Cook goes through a variety of algorithms for TSP, describing each one in prose and in concise, elegant code. The difference is that his code is in C and has an imperative style, while mine is in Python and is largely functional. His code is much more efficient, but if it is 100 times faster, that might only mean two more cities, so the algorithms are more important than the efficiency of the implemenation details. (Also, Cook  chooses a different set of algorithms to explore.) I find his explanation very beautiful and concise, and I think it is very interesting that\n",
    "there can be two quite different approaches, which (in my opinion) both turn out very well. \n",
    "* If you are heavily into math, there's a [taxonomy](http://cstheory.stackexchange.com/questions/9241/approximation-algorithms-for-metric-tsp) of solutions.\n",
    "* What else are you interested in?"
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