mazes.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 183,
      "id": "727cef1f-590b-48da-9a8e-e4ea68f255de",
      "metadata": {},
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from enum import Enum\n",
        "from functools import cache\n",
        "from random import choice"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "id": "9113b0ba-d8f0-43f0-bf4d-44d70f6cec93",
      "metadata": {},
      "outputs": [],
      "source": [
        "class Dir(Enum):\n",
        "    U = 0\n",
        "    R = 1\n",
        "    D = 2\n",
        "    L = 3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 188,
      "id": "7a9695dd-6e56-4003-9cff-52c95c43bf2b",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<Dir.U: 0>, <Dir.R: 1>, <Dir.D: 2>, <Dir.L: 3>]"
            ]
          },
          "execution_count": 188,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "list(Dir)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "id": "c5100eee-8962-4019-b086-a8654a3b6b48",
      "metadata": {},
      "outputs": [],
      "source": [
        "def valid_coords(coords: tuple[int, int], size: int) -> bool:\n",
        "    i, j = coords\n",
        "    return i >= 0 and i < size and j >= 0 and j < size"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 260,
      "id": "ebb00aaa-a24b-4fe3-a61b-8c41c796d072",
      "metadata": {},
      "outputs": [],
      "source": [
        "class Node:\n",
        "    i: int\n",
        "    j: int\n",
        "    size: int\n",
        "\n",
        "    children: list[Node]\n",
        "\n",
        "    def __init__(self, i, j, size):\n",
        "        self.i, self.j = i, j\n",
        "        self.size = size\n",
        "        self.children = []\n",
        "\n",
        "    def __repr__(self):\n",
        "        return f\"Node({self.i}, {self.j}, {self.size})\"\n",
        "\n",
        "    def __eq__(self, o) -> bool:\n",
        "        if isinstance(o, tuple):\n",
        "            return (self.i, self.j) == o\n",
        "        elif isinstance(o, type(self)):\n",
        "            return self.i == o.i and self.j == o.j\n",
        "        return False\n",
        "\n",
        "    def __hash__(self) -> int:\n",
        "        return hash((self.i, self.j))\n",
        "\n",
        "    @property\n",
        "    @cache\n",
        "    def walls(self) -> list[bool]:\n",
        "        walls = []\n",
        "        for dirn in Dir:\n",
        "            neighbor = self.get_neighbor_coords(dirn)\n",
        "            walls.append(neighbor not in self.children)\n",
        "        if self.i == 0:\n",
        "            walls[Dir.U.value] = True\n",
        "        if self.i == self.size - 1:\n",
        "            walls[Dir.D.value] = True\n",
        "        if self.j == 0:\n",
        "            walls[Dir.L.value] = True\n",
        "        if self.j == self.size - 1:\n",
        "            walls[Dir.R.value] = True\n",
        "        return walls\n",
        "\n",
        "    def to_xy(self) -> tuple[i, j]:\n",
        "        return self.j, self.size - self.i\n",
        "\n",
        "    def get_neighbor_coords(self, dirn: Dir) -> tuple[int, int]:\n",
        "        match dirn:\n",
        "            case Dir.U:\n",
        "                return self.i - 1, self.j\n",
        "            case Dir.R:\n",
        "                return self.i, self.j + 1\n",
        "            case Dir.D:\n",
        "                return self.i + 1, self.j\n",
        "            case Dir.L:\n",
        "                return self.i, self.j - 1\n",
        "\n",
        "    def choose_neighbor(self, existing_nodes: dict[Node, Node]) -> Node | None:\n",
        "        possible_dirs = []\n",
        "        for dirn in Dir:\n",
        "            coords = self.get_neighbor_coords(dirn)\n",
        "            if valid_coords(coords, self.size) and coords not in existing_nodes:\n",
        "                possible_dirs.append(coords)\n",
        "        if len(possible_dirs) == 0:\n",
        "            return None\n",
        "        neighbor_coords = choice(possible_dirs)\n",
        "        return Node(*neighbor_coords, self.size)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 309,
      "id": "ceb2da26-98dd-4879-ad6b-308c3809bd1d",
      "metadata": {},
      "outputs": [],
      "source": [
        "class Maze:\n",
        "    size: int\n",
        "    dfs_start: Node\n",
        "    nodes: dict[Node, Node]\n",
        "    start: Node\n",
        "    end: Node\n",
        "\n",
        "    def __init__(self, size: int):\n",
        "        self.size = size\n",
        "        self.nodes = {}\n",
        "        self._create()\n",
        "\n",
        "    def _create(self):\n",
        "        opts = list(range(self.size))\n",
        "        node = Node(choice(opts), choice(opts), self.size)\n",
        "        self.dfs_start = node\n",
        "        self.nodes[node] = node\n",
        "\n",
        "        path = []\n",
        "        while len(self.nodes) < self.size ** 2:\n",
        "            neighbor = node.choose_neighbor(self.nodes)\n",
        "            if neighbor is None:\n",
        "                # go back up the path to find a new node with untraversed neighbors\n",
        "                node = path[-1]\n",
        "                path = path[:-1]\n",
        "            else:\n",
        "                path.append(node)\n",
        "                node.children.append(neighbor)\n",
        "                neighbor.children.append(node)\n",
        "                self.nodes[neighbor] = neighbor\n",
        "                node = neighbor\n",
        "\n",
        "        self.start, self.end = self._choose_endpoints()\n",
        "\n",
        "    def _choose_endpoints(self) -> tuple[Node, Node]:\n",
        "        opts = list(range(self.size))\n",
        "        s_edge, e_edge = choice(list(Dir)), choice(list(Dir))\n",
        "        s_other, e_other = choice(opts), choice(opts)\n",
        "        nodes = []\n",
        "        for edge, other in [(s_edge, s_other), (e_edge, e_other)]:\n",
        "            match edge:\n",
        "                case Dir.U:\n",
        "                    coords = [0, other]\n",
        "                case Dir.R:\n",
        "                    coords = [other, self.size - 1]\n",
        "                case Dir.D:\n",
        "                    coords = [self.size - 1, other]\n",
        "                case Dir.L:\n",
        "                    coords = [other, 0]\n",
        "            nodes.append(self.nodes[tuple(coords)])\n",
        "        return tuple(nodes)\n",
        "\n",
        "    def show(self, show_dfs_start = True):\n",
        "        ratio = self.size / 20\n",
        "        w, h = ratio * 6.4, ratio * 4.8\n",
        "\n",
        "        fig, ax = plt.subplots(dpi=200)\n",
        "        fig.set_figwidth(w)\n",
        "        fig.set_figheight(h)\n",
        "\n",
        "        if show_dfs_start:\n",
        "            x, y = self.dfs_start.to_xy()\n",
        "            ax.scatter([x + 0.5], [y + 0.5], color=\"red\")\n",
        "\n",
        "        for n, c in [(self.start, \"blue\"), (self.end, \"green\")]:\n",
        "            x, y = n.to_xy()\n",
        "            ax.scatter([x + 0.5], [y + 0.5], color=c)\n",
        "\n",
        "        for i in range(self.size):\n",
        "            for j in range(self.size):\n",
        "                node = self.nodes[(i, j)]\n",
        "                x, y = node.to_xy()\n",
        "                for dirn in Dir:\n",
        "                    if node.walls[dirn.value]:\n",
        "                        match dirn:\n",
        "                            case Dir.U:\n",
        "                                ax.plot([x, x + 1], [y + 1, y + 1], color=\"black\")\n",
        "                            case Dir.R:\n",
        "                                ax.plot([x + 1, x + 1], [y, y + 1], color=\"black\")\n",
        "                            case Dir.D:\n",
        "                                ax.plot([x, x + 1], [y, y], color=\"black\")\n",
        "                            case Dir.L:\n",
        "                                ax.plot([x, x], [y, y + 1], color=\"black\")\n",
        "\n",
        "        ax.set_axis_off()\n",
        "\n",
        "        plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 310,
      "id": "6f5e69fc-7484-484c-9102-52cc1b1cdc4d",
      "metadata": {},
      "outputs": [],
      "source": [
        "m = Maze(46)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 311,
      "id": "5b5ac2ac-a77c-45e7-8f27-3295709f5d5f",
      "metadata": {},
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "<Figure size 2944x2208 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "m.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "dbefd5a5-2b2c-46ba-9a1d-8805d76d73cd",
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "778f7ab5-0cbd-4047-8f7d-810b5c14b0cd",
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3e80e276-455d-41e9-add9-a4db47cfba75",
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "47101485-ed0f-41fe-b67d-0c0022a3a0d2",
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1e0b2204-184d-4658-92ee-e072e284236f",
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.13"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}