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"\n",
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"\n",
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"From 538's [The Riddler](https://fivethirtyeight.com/features/can-you-zoom-around-the-race-track/) on 6 August 2021 (slightly edited):\n",
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"From 538's [The Riddler](https://fivethirtyeight.com/features/can-you-zoom-around-the-race-track/) on 6 August 2021 (slightly edited):\n",
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"\n",
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"\n",
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"> The game of [RaceTrack](https://link.springer.com/chapter/10.1007/978-3-642-13122-6_26) was published by recreational mathematician [Martin Gardner](http://www.martin-gardner.org/) in [1973](https://www.scientificamerican.com/article/mathematical-games-1973-01/). There have been some neat [digital versions](https://harmmade.com/vectorracer/#) since then, and it’s high time we had a race here on The Riddler: the Riddler-opolis 500!\n",
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"> The game of [RaceTrack](https://link.springer.com/chapter/10.1007/978-3-642-13122-6_26) was published by recreational mathematician [Martin Gardner](http://www.martin-gardner.org/) in [1973](https://www.scientificamerican.com/article/mathematical-games-1973-01/). There have been some neat [digital versions](https://harmmade.com/vectorracer/#) since then, and it’s high time we had a race here: the Riddler-opolis 500!\n",
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">\n",
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">\n",
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"> You begin at the blue point on the starting line below the circle (diagram shown below) with a velocity vector of zero, and your goal is to circumnavigate the track in a counterclockwise loop. You’ll be moving from point to point on the grid, without ever venturing into the outer wall or the central circle. (Moving tangent to the circle is allowed, as is being on a grid point along a wall.)\n",
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"> You begin at the blue point on the starting line below the circle (diagram shown below) with a velocity vector of zero, and your goal is to circumnavigate the track in a counterclockwise loop. You’ll be moving from point to point on the grid, without ever crashing into the outer wall or the central circle. (Moving tangent to the circle is allowed, as is being on a grid point along a wall.)\n",
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">\n",
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">\n",
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"> For each move you have a choice of nine possible destinations, corresponding to the 3x3 grid that surrounds the point formed by adding your current velocity vector to your current position. That is, you can maintain your current velocity, or you can alter your velocity (and hence your destination) by one grid point in any direction (horizontally, vertically or diagonally). For example, if your first move was up and to the right, then your possible second moves are shown below, although two of them will cause you to crash into the central circle.\n",
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"> For each move you have a choice of nine possible destinations, corresponding to the 3x3 grid that surrounds the point formed by adding your current velocity vector to your current position. That is, you can maintain your current velocity, or you can alter your velocity (and hence your destination) by accelerating one grid point in any direction (horizontally, vertically or diagonally). For example, if your first move was up and to the right, then your nine possible second moves are shown below, although two of them will cause you to crash into the central circle.\n",
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">\n",
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">\n",
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"> \n",
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"> \n",
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">\n",
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">\n",
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@@ -24,17 +24,16 @@
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"\n",
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"\n",
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"# Defining Points and the Track\n",
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"# Defining Points and the Track\n",
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"\n",
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"\n",
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"I will define the following:\n",
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"I will start by defining the following:\n",
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"- `Point`: a point in the 2-D plane, implemented as a complex number. `X(p)` and `Y(p)` give coordinates\n",
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"- `Point(x, y)`: a point in the 2-D plane, implemented as a complex number.\n",
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"- `Path`: a list of points representing the car's moves\n",
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"- `Path`: a list of points representing the car's positions as it moves.\n",
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"- `track`: all the legal grid points\n",
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"- `track`: all the legal grid points on the race track.\n",
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"- `start`: the single starting point\n",
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"- `start`: the single starting point.\n",
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"- `finish`: a Path defining the finish line\n",
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"- `zero`: a zero vector (your starting velocity vector).\n",
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"- `zero`: a vector (your starting velocity vector)\n",
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"- `radius`: the radius of the central circle (whose center is defined as the origin).\n",
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"- `radius`: the radius of the central circle, whose center is defined as the origin\n",
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"- `accelerations`: the nine possible acceleration vectors, to changes the car's velocity.\n",
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"- `deltas`: the nine possible changes to the car's velocity on each move\n",
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"- `X(point)`, `Y(point)`: the x- and y-coordinates of a point, respectively.\n",
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"- `X(point)`, `Y(point)`: the x- and y-coordinates of a point, respectively\n",
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"- `velocity(path)`: the car's current velocity when it has just made the last move in a path."
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"- `velocity(path)`: the car's velocity when it has just made the last move in a path"
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]
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]
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},
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},
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{
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{
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@@ -50,10 +49,9 @@
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"Path = List[Point]\n",
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"Path = List[Point]\n",
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"track = {Point(x, y) for x in range(-7, 8) for y in range(-7, 8) if abs(Point(x, y)) >= 3}\n",
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"track = {Point(x, y) for x in range(-7, 8) for y in range(-7, 8) if abs(Point(x, y)) >= 3}\n",
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"start = Point(0, -5)\n",
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"start = Point(0, -5)\n",
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"finish = [Point(0, -3), Point(0, -7)]\n",
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"zero = Vector(0, 0)\n",
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"zero = Vector(0, 0)\n",
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"radius = 3\n",
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"radius = 3\n",
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"deltas = [Vector(x, y) for y in (1, 0, -1) for x in (-1, 0, 1)]\n",
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"accelerations = [Vector(x, y) for y in (1, 0, -1) for x in (-1, 0, 1)]\n",
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"\n",
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"\n",
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"def X(point) -> float: return point.real\n",
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"def X(point) -> float: return point.real\n",
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"def Y(point) -> float: return point.imag\n",
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"def Y(point) -> float: return point.imag\n",
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@@ -78,17 +76,17 @@
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"def plot(paths=()):\n",
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"def plot(paths=(), finish=[Point(0, -3), Point(0, -7)]):\n",
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" \"\"\"Plot the track and any paths, along with the start and finish line.\"\"\"\n",
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" \"\"\"Plot the track and any paths, along with the start and finish line.\"\"\"\n",
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" fig, ax = plt.subplots()\n",
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" fig, ax = plt.subplots()\n",
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" plt.xticks([]); plt.yticks([])\n",
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" plt.xticks([]); plt.yticks([])\n",
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" ax.set_aspect('equal');\n",
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" ax.set_aspect('equal');\n",
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" ax.add_artist(plt.Circle((0, 0), 3, alpha=0.1, color='k', ec='w'))\n",
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" ax.add_artist(plt.Circle((0, 0), 3, alpha=0.1, color='k', ec='w'))\n",
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" ax.plot(*XY(track), 'k,' ) # grid points\n",
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" ax.plot(*XY(track), 'k,' ) # grid points\n",
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" for path in paths:\n",
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" ax.plot(*XY([start]), 'ks', ms=10) # start point\n",
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" ax.plot(*XY(path), 'o-') # paths\n",
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" ax.plot(*XY(finish), 'k:') # finish line\n",
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" ax.plot(*XY([start]), 'bD') # start point\n",
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" for path in paths: # paths\n",
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" ax.plot(*XY(finish), 'b:') # finish line\n",
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" ax.plot(*XY(path), 'o-') \n",
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" plt.title(f'{len(paths)} paths of {set(len(path) - 1 for path in paths)} moves')\n",
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" plt.title(f'{len(paths)} paths of {set(len(path) - 1 for path in paths)} moves')\n",
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" \n",
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" \n",
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"def XY(points) -> Tuple[List[float], List[float]]: \n",
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"def XY(points) -> Tuple[List[float], List[float]]: \n",
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@@ -100,7 +98,7 @@
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"cell_type": "markdown",
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"cell_type": "markdown",
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"metadata": {},
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"metadata": {},
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"source": [
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"source": [
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"Below is my replication of the diagram above: nine paths for the second move (two of which crash)."
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"Below is my replication of The Riddler's diagram above: the first move goes up and to the right, and there are nine paths for the second move (two of which crash into the central circle)."
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]
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]
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},
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},
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{
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{
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@@ -110,7 +108,7 @@
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"outputs": [
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"outputs": [
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{
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{
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"data": {
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"data": {
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"image/png": 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truncated
|
"image/png": "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 truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
]
|
]
|
||||||
@@ -120,9 +118,9 @@
|
|||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"path = [start, Point(1, -4)]\n",
|
"path1 = [start, Point(1, -4)]\n",
|
||||||
"paths = [path + [Point(path[-1] + velocity(path) + d)] \n",
|
"paths = [path1 + [Point(path1[-1] + velocity(path1) + a)] \n",
|
||||||
" for d in deltas]\n",
|
" for a in accelerations]\n",
|
||||||
"plot(paths)"
|
"plot(paths)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
@@ -130,9 +128,11 @@
|
|||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"# Navigating Regions\n",
|
"# Circumnavigating the Track\n",
|
||||||
"\n",
|
"\n",
|
||||||
"The goal of the race is to circumnavigate the center circle. I can describe that in a way that's generalizable to different tracks by saying that `is_complete(path)` is true if the path enters *regions* of points in a prescribed order. For our track a path is complete if it travels from the fourth [quadrant](https://mathworld.wolfram.com/Quadrant.html) to the first, second, third, and back to the fourth. A *region* is defined by a predicate that is true of any point in the region."
|
"The goal of the race is to circumnavigate the center circle. I can test for that by seeing if the path goes from the fourth [quadrant](https://mathworld.wolfram.com/Quadrant.html) to the first, second, third, and back to the fourth. The function `is_complete(path)` does that.\n",
|
||||||
|
"\n",
|
||||||
|
"If you want to generalize this to other race tracks, you can change the definition of `quadrant` (there could be more than 4 quadrants/regions, and they could have any shape), and change the `regions` in the parameter list of `is_complete`."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@@ -141,33 +141,38 @@
|
|||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
"def Q1(p: Point) -> bool: \"upper right quadrant\"; return X(p) >= 0 and Y(p) >= 0\n",
|
"def is_complete(path, regions=(4, 1, 2, 3, 4)) -> bool:\n",
|
||||||
"def Q2(p: Point) -> bool: \"upper left quadrant\"; return X(p) < 0 and Y(p) >= 0\n",
|
|
||||||
"def Q3(p: Point) -> bool: \"lower left quadrant\"; return X(p) < 0 and Y(p) < 0 \n",
|
|
||||||
"def Q4(p: Point) -> bool: \"lower right quadrant\"; return X(p) >= 0 and Y(p) < 0\n",
|
|
||||||
"\n",
|
|
||||||
"circumnavigate = (Q4, Q1, Q2, Q3, Q4)\n",
|
|
||||||
" \n",
|
|
||||||
"def is_complete(path, regions=circumnavigate) -> bool:\n",
|
|
||||||
" \"\"\"Does the path go through all the regions in the prescribed order?\"\"\"\n",
|
" \"\"\"Does the path go through all the regions in the prescribed order?\"\"\"\n",
|
||||||
" current = 0\n",
|
" i = 0\n",
|
||||||
" for p in path:\n",
|
" for p in path:\n",
|
||||||
" if regions[current](p):\n",
|
" if quadrant(p) == regions[i]:\n",
|
||||||
" current += 1\n",
|
" i += 1\n",
|
||||||
" if current == len(regions):\n",
|
" if i == len(regions):\n",
|
||||||
" return True\n",
|
" return True\n",
|
||||||
" return False"
|
" return False\n",
|
||||||
|
"\n",
|
||||||
|
"def quadrant(p: Point) -> int: \n",
|
||||||
|
" \"\"\"What quadrant of the 2-D plane is this point in?\"\"\"\n",
|
||||||
|
" if X(p) >= 0:\n",
|
||||||
|
" return 1 if Y(p) >= 0 else 4\n",
|
||||||
|
" else:\n",
|
||||||
|
" return 2 if Y(p) >= 0 else 3"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"# Possible and Legal Moves\n",
|
"# Legal Moves\n",
|
||||||
"\n",
|
"\n",
|
||||||
"I'm thinking about how to solve for our specific track, and also how to make the code general enough that it could handle other tracks. I'll do that by splitting up responsibility:\n",
|
"I'm considering how to solve for our specific central-circle-track, and also make the code general enough that it can handle other tracks. I'll do that by splitting up responsibility for determining legal moves:\n",
|
||||||
"- `possible_moves(path)` is general; it returns up to 9 points that are on the track and have the right velocity. \n",
|
"- `all_moves(path)` is general; it considers points with all 9 accelerations and returns the points that are on the track.\n",
|
||||||
"- `legal_moves(path)` is specific; it won't cross into the center circle, and it won't pass from the fourth quadrant backwards into the third (while that is not technically illegal, it was causing problems, and no fast path should do that)."
|
"- `circle_track_moves(path)` is specific; it limits moves in the following ways:\n",
|
||||||
|
" - It won't let a move intersect the center circle (even if the start and end points of a move are outside the circle).\n",
|
||||||
|
" - It won't make moves that stay in one place (they are legal, but wasteful and not needed on this track).\n",
|
||||||
|
" - It won't pass from the fourth quadrant backwards into the third (such moves are legal, but wasteful).\n",
|
||||||
|
" \n",
|
||||||
|
"In the code below `p` is the previous point on a path, `p1` is where the next point would be if the velocity remained constant, and `p2` is the point we arrive at when acceleration is applied."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@@ -176,22 +181,27 @@
|
|||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
"def possible_moves(path) -> List[Point]:\n",
|
"def all_moves(path) -> List[Point]:\n",
|
||||||
" \"\"\"All moves with the right velocity that end up on the track.\"\"\"\n",
|
" \"\"\"Moves with any allowable acceleration that end up on the track.\"\"\"\n",
|
||||||
" p, v = path[-1], velocity(path)\n",
|
" p1: Point = path[-1] + velocity(path)\n",
|
||||||
" return {(p + v + Δ) for Δ in deltas} & track\n",
|
" return {(p1 + a) for a in accelerations} & track\n",
|
||||||
" \n",
|
" \n",
|
||||||
"def legal_moves(path) -> List[Point]:\n",
|
"def circle_track_moves(path) -> List[Point]:\n",
|
||||||
" \"\"\"What points can be reached in one step from this path?\"\"\"\n",
|
" \"\"\"Reasonable moves on the circle track.\"\"\"\n",
|
||||||
" p = path[-1]\n",
|
" p = path[-1]\n",
|
||||||
" return [p2 for p2 in possible_moves(path)\n",
|
" return [p2 for p2 in all_moves(path)\n",
|
||||||
" if not (Q4(p) and Q3(p2)) # Don't go backwards over the finish line\n",
|
" if p2 != p\n",
|
||||||
|
" and not (quadrant(p) == 4 and quadrant(p2) == 3) # Don't go backwards over finish line\n",
|
||||||
" and not intersects_circle(p, p2)]\n",
|
" and not intersects_circle(p, p2)]\n",
|
||||||
"\n",
|
"\n",
|
||||||
"def intersects_circle(p: Point, p2: Point, radius=radius, N=20):\n",
|
"def intersects_circle(p: Point, p2: Point, center=zero, radius=radius, N=20) -> bool:\n",
|
||||||
" \"\"\"Are any of N+1 points on the line segment [p, p2] inside the circle's radius?\"\"\"\n",
|
" \"\"\"Does a line from p to p2 intersect a circle with given center and radius?\"\"\"\n",
|
||||||
" linepoints = (p + (i / N) * (p2 - p) for i in range(N + 1))\n",
|
" return any(abs(q - center) < radius for q in waypoints(p, p2, N))\n",
|
||||||
" return any(abs(q) < radius for q in linepoints)"
|
"\n",
|
||||||
|
"def waypoints(p, p2, N) -> List[Point]:\n",
|
||||||
|
" \"\"\"All the points that are i/N of the way from p to p2\"\"\"\n",
|
||||||
|
" return [p + (i / N) * (p2 - p)\n",
|
||||||
|
" for i in range(N + 1)]"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@@ -209,7 +219,9 @@
|
|||||||
"\n",
|
"\n",
|
||||||
"Now I want to expand paths by adding legal moves to the end until I find complete path(s). I could keep all my paths in a `list`, but there will be an exponential number of them (up to 9<sup><i>n<i/></sup> paths of length *n* and it looks like *n* will be around 10 to 13).\n",
|
"Now I want to expand paths by adding legal moves to the end until I find complete path(s). I could keep all my paths in a `list`, but there will be an exponential number of them (up to 9<sup><i>n<i/></sup> paths of length *n* and it looks like *n* will be around 10 to 13).\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Instead I will keep track of a `frontier`, which I define as a mapping of `{(endpoint, velocity): path}`. The idea is that there may be many paths that arrive at the some endpoint with the same velocity in the same number of moves, but if so, the best continuation of all of them will be the same, so I only need to keep one of them. "
|
"Instead I will keep track of a `frontier`, which I define as a mapping of `{(endpoint, velocity): path}`. The idea is that there may be many paths that arrive at the some endpoint with the same velocity in the same number of moves, but if so, the best continuation of all of them will be the same, so I only need to keep one of them. \n",
|
||||||
|
" \n",
|
||||||
|
"*Note:* Before I added the limitation that moves can't pass backwards from the fourth quadrant to the third, I had a bug: sometimes the frontier would capture a `(endpoint, velocity)` pair for a path that was in the third quadrant but hadn't circumnavigated and was replacing a path to the same point that had circumnavigated. This meant that I was discarding some valid paths."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@@ -218,8 +230,8 @@
|
|||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
"def expand(frontier) -> dict:\n",
|
"def expand(frontier, legal_moves=circle_track_moves) -> dict:\n",
|
||||||
" \"\"\"The {(endpoint, velocity): path} mapping extended one move in all legal ways.\"\"\"\n",
|
" \"\"\"The {(endpoint, velocity): path} frontier extended one move in all legal ways.\"\"\"\n",
|
||||||
" return {(p, velocity([path[-1], p])): path + [p] \n",
|
" return {(p, velocity([path[-1], p])): path + [p] \n",
|
||||||
" for path in frontier.values() \n",
|
" for path in frontier.values() \n",
|
||||||
" for p in legal_moves(path)}"
|
" for p in legal_moves(path)}"
|
||||||
@@ -229,119 +241,42 @@
|
|||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"I will show how the frontier expands over the first few steps:"
|
"# Searching for Fastest Complete Paths\n",
|
||||||
|
"\n",
|
||||||
|
"Now all I have to do to solve the problem is repeatedly expand the frontier until some path(s) are complete. The first completed paths found are guaranteed to be the fastest (i.e., have the fewest moves), because we are expanding one move at a time. In the end, I return a list of all the completed paths in the frontier, but there may be many other paths that are not returned, because the frontier only keeps one path for each `(endpoint, velocity)` pair along the way. "
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 7,
|
"execution_count": 7,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [],
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAOsAAAD7CAYAAACL3GNOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAfxElEQVR4nO2deXgcxZ2w35pTM9Lo9A3G4vIVTMIR+AyxwZgjhNtkCQFCYLkDZGEJfECyBLJkYSEJJhwJEC/mZg0xhwLETmITG3DABoMBHxiDicGnbo0099T+0SN5JM2l0YxmevR7n0ePZqr7N11d3W9XdXVXt9JaIwhC8WMpdAYEQcgMkVUQTILIKggmQWQVBJMgsgqCSRBZBcEkiKxDhFJqs1Lq2DwvY7RSaplSqkMp9esU87mUUq8qpVqUUjcM4Pc/UEptU0pdm5scCwOhpGRVSj0Z25nalVKfKKUu7jPdrZR6UCnVqJRqU0oty1M+5iulbs/Hb6fhUqARqNRaX5divmOBA4HxWuu7AJRSTqXUPKXUFzHZVyulTowP0lp/HbgE+Hme8i+kwFboDOSYO4CLtNYBpdRk4HWl1Gqt9bux6Q9jrPMUoBn4RoHymS8mAGt1+jtdaoHNWmtvXJoN2AIcBfwT+A6wQCk1TWu9OW6+j4AqpZRVax3JXdaFtGitS/IPmARsA86K+96OUetkEv86hvzvAG3AS0Bt3PTngO2xacuAr8XSLwVCQBDwAg2x9M3AT4A1sZj/Bcpi00YAfwJaMQ4iywFLknwdAayM/cZK4IhY+vw+yz02xbpdBCzLoAzWAGf2SdsL0IAzTex84EHgtVh+3gTGAHOBFmA9cFDc/FNiZd4KfAycGkv/f7FytsbNewawJvbZAtwIbAKagAXd2wkoA56MpbfGymt0offNrPfpQmcg5ytk7CBdsR3qPaAiln4+8CFwD0ZT8cO+O2Kf33kd+Ao4ACgH/gg8GTf9XwEP4IztgO/32VFv7/N7m2Pij8Oo2dYBl8em3QH8HrDH/mYAKkGeamM7+g8wasLvx77XJVtugt+wA0/Er0uS+UYDfmByn3RXLP3kNPHzY+V8SEyaJcDnse1gBW4Hlsbl6VPgZsABHAN0AJNi0zcBx8X99nPAjbHP1wD/APaMbYuHgGdi0y4DGgB3bJmHkOHBuhj/Cp6BvKyUsWG+BfwMsMfSbo4JfGtshzgK44g/JclvvA7cGfd9KkatZU0wb3Xst6vidtREsp4X9/0u4Pexz7/AqLn3S7NePwDe6ZO2Argg2XL7zPsNjNp3R6plxeT5K/BQkulXA1HiDlAJ5pkPPNInZl3c92lAa+zzDIza0xI3/Rng1tjn24H/iX32AJ3AhNj3dcDsuLixsXW0YRxQ3wIOLPQ+mYu/kupg6kZrHdFav4FxtL0iluzD2Ii3a62DWuu/A0uB41P81Ja4z19g7MQjlFJWpdSdSqlNSql2DBHBaM6mYnvc5y6gIvb5boyaZbFS6jOl1I1J4sfF8hHPF8AeaZYLgNb6fYydfQVGjdQPpZQFo+YNAlclmG4DbsM4cByUZpE74j77EnzvXv9xwBatdTRuevx6PQ3MUUo5gTnAe1rr7nKYALyglGpVSrViyBvBaBk8ASwCnlVKbVVK3aWUsqfJc9FSkrLGYQP2jX1ek0X8+LjPe2HI3gicA5yG0ataBdTH5lGx/wMayqS17tBaX6e13gc4Bfh3pdTsBLNuxdg549kLo7me6bL8GOeRU/tOU0opYB7Gjn6m1jqU4CdGAzXAizpWleWArcD42IGim5710lqvxZD3RIyyfzpuvi3AiVrr6ri/Mq31V1rrkNb6Nq31VIxz/ZMxmuGmpGRkVUqNUkqdrZSqiNV8J2Cc0y2JzbIMo5fzJqWUTSl1JHA0xpE3GecppaYqpdwYTdXntdED6gECGB0XbuC/+sTtAPYZQN5PVkrtF5OlHaNmSNTT+iowUSl1Tmwdvoch3Z8yXVaMAMapQF9+h9HRc4rW2pcktrtmCgxwmal4G6Npe4NSyq6UOhrjoPVs3DxPAz8GZmKcs3bze+CXSqkJAEqpkUqp02KfZymlpimlrBjlGiJxuZqCkpEVoza7AvgSo9PlV8A1WuuXAGK1xGkYlyTagEeA87XW61P85hMY517bMTpJfhxLfxzjSP8VsBajgyOeecDUWNPsxQzyvj/GOaIXo4n6oNb69X4rqHUTRu1wHcaB4gaMjp7GDJYRT5Q+2z62s1+GcV67XSnljf2d2yfWGvcbOUFrHQROxag5GzE6Cftum2cwDq5L+qzvvcDLGKcQHRjb4vDYtDHA8xiirgP+jtE7bEpU7loypYVS6nWMHtM/FDovuUYpdTzGgWiK1rp5gLFnAfdrrUflJXNCUkqpZhUy53WMmvxjpdRPMg1SSr2L0eT//3nKl5CCUruDSciAWLOzb/M2k7hD8pAdIUOkGSwIJkGawYJgEkRWQTAJAzpnHTFihK6vr89TVgRBePfddxu11iMTTRuQrPX19axatSo3uRIEoR9Kqb63k/YgzWBBMAkiqyCYBJFVEEyCyCoIJkFkFQSTILIKgkkQWQXBJORFVmMMtcSZNa4Qy5S49ORF1mwHB0hcccQVYpkSlx5pBguCSRBZBcEkiKyCYBJEVkEwCSKrIJgEkVUQTILIKggmQWQVBJMgsgqCSRBZBcEkiKyCYBJEVkEwCTLqRuKKYpkSlx4ZdSNxRbFMiUuPNIMFwSSIrIJgEkRWQTAJIqsgmASRVRBMgsgqCCZBZBUEkyCyCoJJEFkFwSSIrIJgEkRWQTAJIqsgmAQZdSNxRbFMiUuPjLqRuKJYpsSlR5rBgmASRFZBMAkiqyCYBJFVEEyCyCoIJkFkFQSTILIKgkkQWQXBJIisgmASRFZBMAkiqyCYBJFVEEyCjLqRuKJYpsSlR0bdSFxRLFPi0iPNYEEwCSKrIJgEkVUQTILIKggmQWQVBJMgsgqCSRBZBcEkiKyCYBJEVkEwCSKrIJgEkVUQTILIKggmQUbdSFxRLFPi0mMb9C8kwCwjGswep7UmHA4TDoeJRqNEIhGi0SjRaBStNY2NjTQ1NaGUwmKxYLVasVgsWCwW7HY7NlvyzV8s6zjc4+LJi6xCftBa4/f7CQaDhEKhHkmzpVtau92Ow+HA6XTmpAYQ8oPIWuREo1H8fn+PpIORM9FvBwIBAoEAYMjrdDpxOp24XC4Rt8gQWYuUYDBIV1cXfr8/p4KmIhqN4vP58Pl8dHR04HK5cLvdKZvLwtAhW6HI8Pv9eL1egsFgQfMRiUTwer10dnbidDqpqKjA4XAUNE/DHZG1SAgGg3R0dPQ0SYuF7vNkv9+Py+XC4/FITVsgpNQLTDQapb29na6urkJnJS0+nw+/3095eTkej0fOaYcYkbWA+Hw+2tvbiUQihc5Kxmit8Xq9BAIBqqqqpGk8hMgdTAUgGo3S2tpKS0uLqUSNJxQK0dTUREdHR6GzMmyQmnWICYfDtLS0EAqFCp2VQaO1pqOjg1AoRHV1NRaLHPvziZTuEBIIBGhqaioJUePx+/00NjaW3HoVGyLrENHV1UVzc7Npm73pCIfDNDU1FV1vdikhsg4BXV1dtLa25uT+0GImGo3S0tIiwuYJGXWT57huUYcL2QpbzNuwkHHxyLtu8hjn9/tpa2vLahlmplvYgZzDFus2LHRcPNIMzhPhcHhYNH2T0S3sUN3XPBwQWfOA7KgG3QcsITeIrHmgtbVVLmPE8Pv9cuNEjhBZc0z3sDZhN8UwiqgUEFlzSCQSob29vdDZKDq01rS1tQ3b8/dcIbLmkLa2tmF/npqMUCgkzeFBIrLmiO4xn0JyOjs7CYfDhc6GaRFZc4TUGunpvvFfyA6RNQd0dXVJ72+G+Hw+6WzKEpE1B3i93kJnwVRIeWWHyDpI/H6/nIcNkEAgIGWWBSLrIDHDs5OKDa21lFsWyKibQcSFw2EZDpYlPp+v13VXs237oYqLR0bdDCKu7w4nZE4kEsHn8/V8N9u2H6q4eKQZPAjkuurgkFbJwBBZs6T77W1C9gQCAWmZDACRNUtkRxs80WhUrrkOAJE1S6QJlxukHDNHZM0SuWMpN0g5Zo7ImgXdbxgXBo/ImjkiaxYEg0E5X80R0WhUOuoyRGTNglJ9UHehkNo1M0TWLBBZc4ucUmSGyJoFsnPlFinPzBBZs0Bq1twi5ZkZImsWSE2QW6Q8M0NkzQLpCc4tUp6ZIUPksmDMmDFZxQnJMcu2lyFyJovbvn17VnFCcsyy7WWInMnIxVFS2I2UZ2aIrFkgO1dusVhkN8wEKaUssFqthc5CSSGyZoaUUhaIrLlFyjMzRNYskJogt0h5ZoaUUhbYbLZCZ6GkkPLMDJE1C+x2e6GzUDJYLBaRNUNE1iyw2WzSdMsRNptNetczRPa4LJHaNTc4HI5CZ8E0iKxZ4nQ6C52FkkAOepkjsmaJyDp4LBYLZWVlhc6GaRBZs8Rut0vHyCBxOBxyvjoAZNTNIOKkVhgc8eVntm0/VHHxyKibQcSJrNnTtwlstm0/VHHxSDN4EDgcDunNzJKysjK5/DVApLQGidvtLnQWTImU28ARWQeJy+WSG9EHiLRIskNkHSRKKSoqKgqdDVMh5ZUdImsOcLvdchknQ5xOp3TMZYnImgOkds0cj8dT6CyYFpE1R7jdbjkPS4OU0eAQWXNIVVWVXI5IgtVqpbKystDZMDWyZ+UQu90uzeEkVFZWyoFskEjp5Zjy8nJp6vXB7XbjcrkKnQ3TI12YOUYpRU1NDY2NjfLCJYzWRlVVVdLp65YvZfmzj9PR1IinbgQzzj6fKTNmDWEOzYPUrHnAarVSXV097EeUWK1WampqkpbDuuVLWfzw/XQ07gKt6WjcxeKH72fd8qVDnFNzIKNu8hTndDpT1iiljlKK6urqlNeflz/7OOFgoFdaOBhg+bOPD2g52ebPDHHxyKiLine truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
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||||||
{
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||||||
"data": {
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|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
"source": [
|
||||||
"frontier = {(start, zero): [start]}\n",
|
"def search(path=[start], legal_moves=circle_track_moves) -> List[Path]:\n",
|
||||||
"\n",
|
" \"\"\"Find the shortest possible complete path(s).\"\"\"\n",
|
||||||
"for i in range(6):\n",
|
" frontier = {(path[-1], velocity(path)): path}\n",
|
||||||
" frontier = expand(frontier)\n",
|
" complete_paths = []\n",
|
||||||
" plot(frontier.values())\n",
|
" while not complete_paths:\n",
|
||||||
" plt.show()"
|
" frontier = expand(frontier, legal_moves)\n",
|
||||||
|
" complete_paths = list(filter(is_complete, frontier.values()))\n",
|
||||||
|
" return complete_paths"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"(Note that the growth is much slower then 9<sup><i>n</i></sup>.)\n",
|
"# Solutions"
|
||||||
"\n",
|
|
||||||
"# Searching for Fastest Complete Paths\n",
|
|
||||||
"\n",
|
|
||||||
"Now all I have to do to solve the problem is repeatedly expand the frontier until some path(s) are complete. The first completed paths are guaranteed to be the fastest (i.e., have the fewest moves), because we are expanding one move at a time. In the end, I return a list of all the completed paths in the frontier, but there may be many other paths that are not returned, because I only kept one path for each `(endpoint, velocity)` pair along the way. "
|
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 8,
|
"execution_count": 8,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
|
||||||
"source": [
|
|
||||||
"def search(path=[start]) -> Path:\n",
|
|
||||||
" \"\"\"Find the shortest possible complete path(s).\"\"\"\n",
|
|
||||||
" frontier = {(path[-1], velocity(path)): path}\n",
|
|
||||||
" completed = []\n",
|
|
||||||
" while not completed:\n",
|
|
||||||
" frontier = expand(frontier)\n",
|
|
||||||
" completed = list(filter(is_complete, frontier.values()))\n",
|
|
||||||
" return completed"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 9,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
]
|
]
|
||||||
@@ -351,14 +286,16 @@
|
|||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"plot(search([start]))"
|
"solutions = search([start])\n",
|
||||||
|
"\n",
|
||||||
|
"plot(solutions)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"We see that the fastest path takes 12 moves, and there are several ways to get there.\n",
|
"We see that the fastest path takes 12 moves, and there are 7 ways to get there (with other ways discarded).\n",
|
||||||
"\n",
|
"\n",
|
||||||
"# Submitting your Answer\n",
|
"# Submitting your Answer\n",
|
||||||
"\n",
|
"\n",
|
||||||
@@ -370,30 +307,65 @@
|
|||||||
"> 4 5 6\n",
|
"> 4 5 6\n",
|
||||||
"> 7 8 9\n",
|
"> 7 8 9\n",
|
||||||
"\n",
|
"\n",
|
||||||
"I will define two functions to translate back and forth between my path and The Riddler's list of digits: "
|
"I will define two functions to translate back and forth between my `Path` and The Riddler's list of `Digits`: "
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 9,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"Digits = List[int] # each int is 1-9\n",
|
||||||
|
"\n",
|
||||||
|
"def digits_from_path(path) -> Digits:\n",
|
||||||
|
" \"\"\"The digits that the path represents.\"\"\"\n",
|
||||||
|
" return [1 + accelerations.index(velocity(path[:i + 1]) - velocity(path[:i]))\n",
|
||||||
|
" for i in range(1, len(path))]\n",
|
||||||
|
"\n",
|
||||||
|
"def path_from_digits(digits, start=start) -> Path:\n",
|
||||||
|
" \"\"\"The path that the digits represent.\"\"\"\n",
|
||||||
|
" v = zero # Velocity\n",
|
||||||
|
" path = [start]\n",
|
||||||
|
" for d in digits:\n",
|
||||||
|
" v += accelerations[d - 1]\n",
|
||||||
|
" path.append(v + path[-1])\n",
|
||||||
|
" return path"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 10,
|
"execution_count": 10,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"[[3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 6, 3],\n",
|
||||||
|
" [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 6],\n",
|
||||||
|
" [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 3],\n",
|
||||||
|
" [3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 3, 3],\n",
|
||||||
|
" [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 9],\n",
|
||||||
|
" [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 6],\n",
|
||||||
|
" [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 3]]"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 10,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"Digits = List[int]\n",
|
"[digits_from_path(path) for path in solutions]"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"# Alternative Solutions\n",
|
||||||
"\n",
|
"\n",
|
||||||
"def digits_from_path(path) -> Digits:\n",
|
"We can search from five different two-move opening sequences and one five-move sequence, and get different solution paths. Every solution is 12 moves. I don't understand why every plot has exactly 7 solution paths; I suppose it is because the finish line is crowded and there are only so many ways to get there."
|
||||||
" \"\"\"The digits that the path represents.\"\"\"\n",
|
|
||||||
" return [deltas.index(velocity(path[:i + 1]) - velocity(path[:i])) + 1\n",
|
|
||||||
" for i in range(1, len(path))]\n",
|
|
||||||
"\n",
|
|
||||||
"def path_from_digits(digits, start=start) -> Path:\n",
|
|
||||||
" \"\"\"The path that the digits represent.\"\"\"\n",
|
|
||||||
" velo = zero # Velocity\n",
|
|
||||||
" path = [start]\n",
|
|
||||||
" for d in digits:\n",
|
|
||||||
" velo += deltas[d - 1]\n",
|
|
||||||
" path.append(velo + path[-1])\n",
|
|
||||||
" return path"
|
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@@ -402,127 +374,104 @@
|
|||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"data": {
|
||||||
"output_type": "stream",
|
"image/png": 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truncated
|
||||||
"text": [
|
"text/plain": [
|
||||||
"[3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 6, 3]\n",
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
"[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 6]\n",
|
]
|
||||||
"[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 3]\n",
|
},
|
||||||
"[3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 3, 3]\n",
|
"metadata": {},
|
||||||
"[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 9]\n",
|
"output_type": "display_data"
|
||||||
"[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 6]\n",
|
},
|
||||||
"[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 3]\n"
|
{
|
||||||
]
|
"data": {
|
||||||
|
"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
|
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"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
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"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"image/png": "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 truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"for path in search([start]):\n",
|
"openings = [3, 3], [3, 5], [3, 6], [6, 2], [6, 3], [3, 5, 2, 4, 4]\n",
|
||||||
" digits = digits_from_path(path)\n",
|
"for digits in openings:\n",
|
||||||
" assert path == path_from_digits(digits_from_path(path)) # Inverses\n",
|
" plot(search(path_from_digits(digits)))"
|
||||||
" assert digits == digits_from_path(path_from_digits(digits)) # Inverses\n",
|
|
||||||
" print(digits)"
|
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "markdown",
|
"cell_type": "markdown",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"# Alternative Paths\n",
|
"# Tests and Visualizations\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Here we search from several different opening move sequences and get different results, but all of 12 moves:"
|
"Below are a few unit tests; there should be more.\n",
|
||||||
|
"\n",
|
||||||
|
"Here are three tests/visualizations for `intersects_circle`:"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 12,
|
"execution_count": 12,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
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|
||||||
{
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|
||||||
"data": {
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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
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|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
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|
||||||
"image/png": 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truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"data": {
|
|
||||||
"image/png": "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 truncated
|
|
||||||
"text/plain": [
|
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
"metadata": {},
|
|
||||||
"output_type": "display_data"
|
|
||||||
}
|
|
||||||
],
|
|
||||||
"source": [
|
|
||||||
"for opening in ([3, 3], [3, 5], [3, 6], [6, 2], [6, 3]):\n",
|
|
||||||
" plot(search(path_from_digits(opening)))"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "markdown",
|
|
||||||
"metadata": {},
|
|
||||||
"source": [
|
|
||||||
"# Tests\n",
|
|
||||||
"\n",
|
|
||||||
"The code that I have the least confidence in is `intersects_circle`. Here are some tests and visualizations for it:"
|
|
||||||
]
|
|
||||||
},
|
|
||||||
{
|
|
||||||
"cell_type": "code",
|
|
||||||
"execution_count": 13,
|
|
||||||
"metadata": {},
|
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
"def test_intersects(expected: bool, segments: List[Path]):\n",
|
"def test_intersects(expected: bool, segments: List[Path]):\n",
|
||||||
" \"\"\"Test if segments do the expected thing with `intersects_circle`.\"\"\"\n",
|
" \"\"\"Test if segments do the expected thing with `intersects_circle`.\"\"\"\n",
|
||||||
" plot(segments)\n",
|
" plot(segments, finish=[])\n",
|
||||||
" for p, q in segments:\n",
|
" for p, q in segments:\n",
|
||||||
" assert intersects_circle(p, q) is expected"
|
" assert intersects_circle(p, q) is expected"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 14,
|
"execution_count": 13,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
]
|
]
|
||||||
@@ -542,12 +491,12 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 15,
|
"execution_count": 14,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": "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 truncated
|
"image/png": "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 truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<Figure size 432x288 with 1 Axes>"
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
]
|
]
|
||||||
@@ -564,6 +513,154 @@
|
|||||||
" [Point(-3, -2),Point(1, -4)],\n",
|
" [Point(-3, -2),Point(1, -4)],\n",
|
||||||
" [Point(-7, 0), Point(7, 7)]])"
|
" [Point(-7, 0), Point(7, 7)]])"
|
||||||
]
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 15,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"image/png": "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 truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"# The waypoints that are checked to see if they are outside the circle\n",
|
||||||
|
"p, q = Point(-7, 0), Point(5, -6)\n",
|
||||||
|
"plot([waypoints(p, q, 20)], finish=[])\n",
|
||||||
|
"assert not intersects_circle(p, q)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"Here's a visualization for `expand(frontier)` showing the first few expansions.\n",
|
||||||
|
"Note that the growth in number of paths is much slower then 9<sup><i>n</i></sup>."
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 16,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"image/png": "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 truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
|
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"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"image/png": "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 truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "display_data"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"frontier = {(start, zero): [start]}\n",
|
||||||
|
"\n",
|
||||||
|
"for i in range(4):\n",
|
||||||
|
" frontier = expand(frontier)\n",
|
||||||
|
" plot(frontier.values())"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"Additional tests:"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 17,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"'tests pass'"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 17,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"assert start == Point(0, -5) == 0-5j\n",
|
||||||
|
"assert path1 == [start, Point(1, -4)] == [0-5j, 1-4j]\n",
|
||||||
|
"\n",
|
||||||
|
"assert X(start) == 0 and Y(start) == -5 \n",
|
||||||
|
"assert velocity([start]) == 0\n",
|
||||||
|
"assert velocity(path1) == Vector(1, 1)\n",
|
||||||
|
"assert XY(path1) == ([0, 1], [-5, -4])\n",
|
||||||
|
"\n",
|
||||||
|
"assert quadrant(start) == 4\n",
|
||||||
|
"assert quadrant(Point(1, 2)) == 1\n",
|
||||||
|
"assert quadrant(Point(-5, 4)) == 2\n",
|
||||||
|
"assert quadrant(Point(-1, -1)) == 3\n",
|
||||||
|
"\n",
|
||||||
|
"assert waypoints(0, 10, 10) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
|
||||||
|
"assert waypoints(zero, Point(10, 20), 10) == [\n",
|
||||||
|
" 0j,1+2j,2+4j,3+6j,4+8j,5+10j,6+12j,7+14j,8+16j,9+18j,10+20j]\n",
|
||||||
|
"\n",
|
||||||
|
"# There are 9 moves from the start point\n",
|
||||||
|
"assert all_moves([start]) == {-1-4j, -1-5j, -1-6j, \n",
|
||||||
|
" 0-4j, 0-5j, 0-6j, \n",
|
||||||
|
" 1-4j, 1-5j, 1-6j}\n",
|
||||||
|
"\n",
|
||||||
|
"# But 3 moves are backwards and 1 stays in the same place; those are disallowed\n",
|
||||||
|
"assert circle_track_moves([start]) == [0-6j, 1-6j, 1-5j, 0-4j, 1-4j]\n",
|
||||||
|
"assert expand({(start, zero): [start]}) == {\n",
|
||||||
|
" (0-6j, 0-1j): [0-5j, 0-6j],\n",
|
||||||
|
" (1-6j, 1-1j): [0-5j, 1-6j],\n",
|
||||||
|
" (1-5j, 1+0j): [0-5j, 1-5j],\n",
|
||||||
|
" (0-4j, 0+1j): [0-5j, 0-4j],\n",
|
||||||
|
" (1-4j, 1+1j): [0-5j, 1-4j]}\n",
|
||||||
|
"\n",
|
||||||
|
"for path in solutions:\n",
|
||||||
|
" digits = digits_from_path(path)\n",
|
||||||
|
" assert path == path_from_digits(digits_from_path(path)) # Inverses\n",
|
||||||
|
" assert digits == digits_from_path(path_from_digits(digits)) # Inverses\n",
|
||||||
|
"\n",
|
||||||
|
"'tests pass'"
|
||||||
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"metadata": {
|
"metadata": {
|
||||||
|
|||||||
Reference in new issue
Block a user