A-starMaze.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A${}^*$アルゴリズムで迷路を解く\n",
    "対応する動画：[A*で迷路を解く【研究で使うPython #76】](https://youtu.be/m9dOCHAkX6g)\n",
    "\n",
    "動画のプレイリスト：[研究で使うPython](https://youtube.com/playlist?list=PLw5AEs-T7pLHxLaNvGD9tnhrDxAgH-QIw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## ライブラリの準備\n",
    "import copy\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.animation as animation\n",
    "from IPython import display\n",
    "\n",
    "## 壁を表す定数\n",
    "WALL = 100000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 迷路クラス\n",
    "* フィールド\n",
    "    * `width`, `height`: 迷路の横幅と高さ（四方を囲む壁も含む）\n",
    "    * `data`: 迷路のデータ（2次元リスト形式; 壁がWALLの値，それ以外が0）\n",
    "    * `start`, `goal`: スタート地点とゴール地点の座標（(x,y)のタプル形式）\n",
    "* メソッド\n",
    "    * `__init__`: `'x'`と`' '`で表現されたテキスト形式の迷路データを受け取って初期化する\n",
    "    * `plot_maze`: 迷路をプロットする\n",
    "    * `plot_path`: 経路を渡して迷路とともにプロットする\n",
    "    * `plot_field`: 経路探索に使った値を重ねてプロットする（アニメーションで使う）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Maze:\n",
    "    \n",
    "    def __init__(self, texts):\n",
    "        \"\"\"\n",
    "        初期化用メソッド\n",
    "        \n",
    "        ・texts: 迷路の初期化用テキスト．次のような形式を受け取れる:\n",
    "            maze_texts = [\n",
    "                'xxxxxxxxxxx',\n",
    "                'x       xGx',\n",
    "                'x xxxxx x x',\n",
    "                'x     x   x',\n",
    "                'x xxx xxxxx',\n",
    "                'x x x     x',\n",
    "                'x x xxxxx x',\n",
    "                'x   x     x',\n",
    "                'x xxx xxx x',\n",
    "                'xS    x   x',\n",
    "                'xxxxxxxxxxx',\n",
    "            ]\n",
    "        ただし，xが壁で空白が進めるマス，SとGがそれぞれスタート地点とゴール地点を表す\n",
    "        \"\"\"\n",
    "        \n",
    "        self.height, self.width = len(texts), len(texts[0])  ## 横幅と高さを取得\n",
    "        self.data = [[0 for j in range(self.width)] \n",
    "                     for i in range(self.height)]    ## 迷路のデータを初期化\n",
    "\n",
    "        for y, text in enumerate(texts):\n",
    "            for x, s in enumerate(text):\n",
    "                if s == 'x':\n",
    "                    self.data[y][x] = WALL  ## 壁だったらWALLの値で更新\n",
    "                elif s == 'S':\n",
    "                    self.start = (x, y)     ## スタート地点を記録\n",
    "                elif s == 'G':\n",
    "                    self.goal = (x, y)      ## ゴール地点を記録\n",
    "\n",
    "        \n",
    "\n",
    "\n",
    "    def plot_maze(self, ax=None):\n",
    "        \"\"\"\n",
    "        壁を黒，そうでない場所を白，スタート地点を青丸，ゴール地点を赤丸の形式でプロットする\n",
    "        \n",
    "        ・ax: プロットするaxisを指定する．デフォルトはNone\n",
    "        \"\"\"\n",
    "        \n",
    "        if ax is None:\n",
    "            fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
    "        \n",
    "        ax.axis('off')\n",
    "\n",
    "        im = ax.imshow(self.data, cmap='Greys', origin='lower')\n",
    "        \n",
    "        sc_st = ax.scatter([self.start[0]], [self.start[1]], c='b', s=300)\n",
    "        tx_st = ax.text(self.start[0], self.start[1], 'S', ha='center', va='center', \n",
    "                        fontsize=15, c='w', weight='bold')\n",
    "        \n",
    "        sc_go = ax.scatter([self.goal[0]],  [self.goal[1]],  c='r', s=300)\n",
    "        tx_go = ax.text(self.goal[0],  self.goal[1],  'G', ha='center', va='center', \n",
    "                        fontsize=15, c='w', weight='bold')\n",
    "        \n",
    "        return [im] + [sc_st] + [tx_st] + [sc_go] + [tx_go]\n",
    "    \n",
    "    \n",
    "    \n",
    "    def plot_path(self, path, ax=None):\n",
    "        \"\"\"\n",
    "        迷路と経路をプロットする\n",
    "        \n",
    "        ・path: 表示したい経路．座標のリスト形式を受け付ける（座標は(x,y)のタプル形式を想定）\n",
    "        ・ax: プロットするaxisを指定する．デフォルトはNone\n",
    "        \"\"\"\n",
    "        \n",
    "        if ax is None:\n",
    "            fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
    "        \n",
    "        ax.axis('off')\n",
    "\n",
    "        im = ax.imshow(self.data, cmap='Greys', origin='lower')\n",
    "        \n",
    "        arrows = []\n",
    "        for b, g in zip(path[:-1], path[1:]):\n",
    "            d = (g[0]-b[0], g[1]-b[1])\n",
    "            ar = ax.arrow(*b, *d, length_includes_head=True, head_width=0.2, zorder=1)\n",
    "            arrows.append(ar)\n",
    "        \n",
    "        sc_st = ax.scatter([self.start[0]], [self.start[1]], c='b', s=300)\n",
    "        tx_st = ax.text(self.start[0], self.start[1], 'S', ha='center', va='center', \n",
    "                        fontsize=15, c='w', weight='bold')\n",
    "        \n",
    "        sc_go = ax.scatter([self.goal[0]],  [self.goal[1]],  c='r', s=300)\n",
    "        tx_go = ax.text(self.goal[0],  self.goal[1],  'G', ha='center', va='center', \n",
    "                        fontsize=15, c='w', weight='bold')\n",
    "        \n",
    "        return [im] + arrows + [sc_st] + [tx_st] + [sc_go] + [tx_go]\n",
    "    \n",
    "\n",
    "    \n",
    "    def plot_field(self, field, func, ax=None, cm='Greens'):\n",
    "        \"\"\"\n",
    "        経路探索に使用したフィールドの値を迷路に重ねてプロットする\n",
    "        \n",
    "        ・field: プロットしたいフィールド．迷路と同サイズを想定\n",
    "        ・func: 探索に使用したヒューリスティック関数\n",
    "        ・ax: プロットするaxisを指定する．デフォルトはNone\n",
    "        ・cm: フィールドの値を表示する際のカラーマップの種類．デフォルトはGreen\n",
    "        \"\"\"\n",
    "        \n",
    "        if ax is None:\n",
    "            fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
    "        \n",
    "        ax.axis('off')\n",
    "        \n",
    "        vmx = self.width*self.height - np.sum(np.array(self.data))/WALL \\\n",
    "                + func((0,0), (self.width-2, self.height-2))\n",
    "        fld = ax.imshow(field, cmap=cm, origin='lower', \n",
    "                  vmin=0.,  vmax=vmx)\n",
    "        \n",
    "        wall_arr = np.array([[([0,0,0,1] if self.data[y][x] == WALL else [0,0,0,0]) \n",
    "                              for x in range(self.width)] \n",
    "                             for y in range(self.height)], dtype=float)\n",
    "        wall = ax.imshow(wall_arr, cmap='Greys', origin='lower')\n",
    "        \n",
    "        sc_st = ax.scatter([self.start[0]], [self.start[1]], c='b', s=300)\n",
    "        tx_st = ax.text(self.start[0], self.start[1], 'S', ha='center', va='center', \n",
    "                        fontsize=15, c='w', weight='bold')\n",
    "        \n",
    "        sc_go = ax.scatter([self.goal[0]],  [self.goal[1]],  c='r', s=300)\n",
    "        tx_go = ax.text(self.goal[0],  self.goal[1],  'G', ha='center', va='center', \n",
    "                        fontsize=15, c='w', weight='bold')\n",
    "        \n",
    "        return [fld] + [wall] + [sc_st] + [tx_st] + [sc_go] + [tx_go]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 迷路オブジェクトの作成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 迷路を適当に指定\n",
    "maze_data = [\n",
    "    'xxxxxxxxxxx',\n",
    "    'x       xGx',\n",
    "    'x xxxxx x x',\n",
    "    'x     x   x',\n",
    "    'x xxx xxxxx',\n",
    "    'x x x     x',\n",
    "    'x x xxxxx x',\n",
    "    'x   x     x',\n",
    "    'x xxx xxx x',\n",
    "    'xS    x   x',\n",
    "    'xxxxxxxxxxx',\n",
    "]\n",
    "\n",
    "maze_data = maze_data[::-1] ## 迷路の2次元リストを逆順に"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 迷路の可視化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = Maze(maze_data)\n",
    "m.plot_maze();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A${}^*$アルゴリズムの実行関数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def execute_Astar(maze, func_H, animate=False):\n",
    "    \"\"\"\n",
    "    A*アルゴリズムを実行して最短経路を示す\n",
    "\n",
    "    * maze: 経路探索する迷路\n",
    "    * func_H: ヒューリスティック関数 H\n",
    "    * animate: アニメーション形式で表示するか（デフォルトはFalse，Trueだと最短経路のみ表示）\n",
    "    \"\"\"\n",
    "    \n",
    "    if animate:\n",
    "        ## アニメーション描画用の領域を作成\n",
    "        fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
    "\n",
    "        ims = []  ## 調査するごとのフィールドの図をメモしていくリスト\n",
    "    \n",
    "    \n",
    "    \n",
    "    ## 調査し終えたどうか（および壁かどうか）を表すフィールド\n",
    "    ## （未調査なら0，調査済みあるいは壁なら1以上）\n",
    "    close_field = copy.deepcopy(maze.data)\n",
    "    \n",
    "    ## スタートからの最短距離(関数G)をメモしていくフィールド\n",
    "    G_field = [[WALL for x in range(maze.width)] for y in range(maze.height)]\n",
    "    \n",
    "    ## A*アルゴリズムで使用する関数Fをメモしていくフィールド\n",
    "    F_field = [[WALL for x in range(maze.width)] for y in range(maze.height)]\n",
    "    \n",
    "    ## 調査予定の座標セット\n",
    "    open_set = {maze.start}\n",
    "    \n",
    "    ## スタート地点のGをゼロに，Fの値をG+Hに設定する\n",
    "    G_field[maze.start[1]][maze.start[0]] = 0\n",
    "    F_field[maze.start[1]][maze.start[0]] = func_H(maze.start, maze.goal)\n",
    "    \n",
    "\n",
    "    focal = None    ## 調査中の座標を表す変数\n",
    "    trial = 0       ## 試行回数のカウンタ\n",
    "    \n",
    "    ## 調査予定の座標がなくなるまで繰り返す\n",
    "    while len(open_set) > 0:\n",
    "        \n",
    "        if animate:\n",
    "            ## フィールドの値をプロットしてimsに追加\n",
    "            ims.append(maze.plot_field(F_field, func_H, ax=ax))\n",
    "        \n",
    "        \n",
    "        trial += 1      ## 試行回数を増加\n",
    "        \n",
    "        ## 調査予定の座標セットから，最もFの値が小さいものを見つけてfocalにセットする\n",
    "        F_min = WALL\n",
    "        for x, y in open_set:\n",
    "            if F_field[y][x] < F_min:\n",
    "                focal = (x, y)\n",
    "                F_min = F_field[y][x]\n",
    "        \n",
    "        ## focalにセットした座標は調査予定群から取り除き，調査済みとする\n",
    "        open_set.remove(focal)\n",
    "        close_field[focal[1]][focal[0]] = 1\n",
    "        \n",
    "        \n",
    "        ## もしfocalがゴール地点であれば，探索は終了する\n",
    "        if focal[0] == maze.goal[0] and focal[1] == maze.goal[1]:\n",
    "            break\n",
    "        \n",
    "        \n",
    "        ## focalから上下左右の操作で移動可能な座標を順番に見ていく\n",
    "        for x, y in [[1,0], [0,1], [-1,0], [0,-1]]:\n",
    "            \n",
    "            ## 移動後の座標をneighborと呼ぶ\n",
    "            neighbor = (focal[0]+x, focal[1]+y)\n",
    "            \n",
    "            ## もしneighborが調査済みあるいは壁なら，移動不可能なので次へ\n",
    "            if close_field[neighbor[1]][neighbor[0]] > 0:\n",
    "                continue\n",
    "            \n",
    "            ## neighborにおける最短距離Gをfocalの最短距離+1で更新\n",
    "            G = G_field[focal[1]][focal[0]] + 1\n",
    "            \n",
    "            ## neighborにおけるHの値を計算\n",
    "            H = func_H(neighbor, maze.goal)\n",
    "            \n",
    "            ## もし今計算したF=G+Hの値が，事前にメモされていたFの値より小さければ更新\n",
    "            if F_field[neighbor[1]][neighbor[0]] > G + H:\n",
    "                G_field[neighbor[1]][neighbor[0]] = G\n",
    "                F_field[neighbor[1]][neighbor[0]] = G + H\n",
    "            \n",
    "            ## 調査予定セットにneighborを加える（セットなので既に存在していたら変化なし）\n",
    "            open_set.add(neighbor)\n",
    "    \n",
    "    ## ゴール地点を見つけられないまま繰り返しが終了した場合\n",
    "    else:\n",
    "        print(\"ゴールまでの経路が見つかりませんでした\")\n",
    "        return\n",
    "    \n",
    "    \n",
    "    \n",
    "    ## スタート地点からゴール地点までの最短経路をゴール地点から遡って求める\n",
    "    path = [maze.goal]\n",
    "    \n",
    "    ## 上記の繰り返しを抜けた段階ではfocalがゴール地点を指している．そこから\n",
    "    ## スタート地点に至るまで一歩ずつ戻っていく\n",
    "    while not(focal[0] == maze.start[0] and focal[1] == maze.start[1]):\n",
    "        \n",
    "        ## 移動可能地点を全て探索\n",
    "        for x, y in [[1,0], [0,1], [-1,0], [0,-1]]:\n",
    "            neighbor = (focal[0]+x, focal[1]+y)  ## 移動後座標をneighborと呼ぶ\n",
    "            \n",
    "            ## もしneighborのGの値がfocalのGの値より1だけ小さかったら，\n",
    "            ## neighborは最短経路に含まれるのでfocalを更新．forループを抜ける\n",
    "            if G_field[focal[1]][focal[0]] - G_field[neighbor[1]][neighbor[0]] == 1:\n",
    "                path.append(neighbor)\n",
    "                focal = neighbor\n",
    "                break\n",
    "    \n",
    "    print(trial)         ## 調査した回数を表示\n",
    "    print(path[::-1])    ## 経路を表示（ゴール→スタートの順になっているので逆順にする必要あり）\n",
    "    \n",
    "    \n",
    "    \n",
    "    ## アニメーションを生成する場合\n",
    "    if animate:\n",
    "        ## imsを使ってアニメーションを作成\n",
    "        ani = animation.ArtistAnimation(fig, ims, interval=300, repeat_delay=1000)\n",
    "\n",
    "        ## アニメーションをHTML形式にして表示\n",
    "        html = display.HTML(ani.to_jshtml())\n",
    "        display.display(html)\n",
    "        plt.close()\n",
    "    \n",
    "    \n",
    "    ## いずれにせよ最短経路はプロットする\n",
    "    maze.plot_path(path[::-1])   ## 経路をプロット"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A${}^*$アルゴリズムを実行して最短経路を表示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "41\n",
      "[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 9), (3, 9), (4, 9), (5, 9), (6, 9), (7, 9), (7, 8), (7, 7), (8, 7), (9, 7), (9, 8), (9, 9)]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 関数Hはゴールとの距離の二乗とする\n",
    "func = lambda a,b: (a[0]-b[0])**2+(a[1]-b[1])**2\n",
    "\n",
    "execute_Astar(m, func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A${}^*$アルゴリズムを実行していくときのFの値をプロット\n",
    "\n",
    "* 緑が濃いほどFの値は小さい\n",
    "* 初期段階ではFの値を非常に大きい値にセットしてあるので全部緑になる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "41\n",
      "[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 9), (3, 9), (4, 9), (5, 9), (6, 9), (7, 9), (7, 8), (7, 7), (8, 7), (9, 7), (9, 8), (9, 9)]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img054e4c7248124bd993179bc3408dc946\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider054e4c7248124bd993179bc3408dc946\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim054e4c7248124bd993179bc3408dc946.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim054e4c7248124bd993179bc3408dc946.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim054e4c7248124bd993179bc3408dc946.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim054e4c7248124bd993179bc3408dc946.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim054e4c7248124bd993179bc3408dc946.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim054e4c7248124bd993179bc3408dc946.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim054e4c7248124bd993179bc3408dc946.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim054e4c7248124bd993179bc3408dc946.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim054e4c7248124bd993179bc3408dc946.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim054e4c7248124bd993179bc3408dc946.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select054e4c7248124bd993179bc3408dc946\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_054e4c7248124bd993179bc3408dc946\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_054e4c7248124bd993179bc3408dc946\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_054e4c7248124bd993179bc3408dc946\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_054e4c7248124bd993179bc3408dc946\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_054e4c7248124bd993179bc3408dc946\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_054e4c7248124bd993179bc3408dc946\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img054e4c7248124bd993179bc3408dc946\";\n",
       "    var slider_id = \"_anim_slider054e4c7248124bd993179bc3408dc946\";\n",
       "    var loop_select_id = \"_anim_loop_select054e4c7248124bd993179bc3408dc946\";\n",
       "    var frames = new Array(41);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAYAAAC+ZpjcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "LTdlpqNTnJbpFPXCC/XCnzPWX8cLraI/rL/qjO3QCys/af2D0Fjs4GjtiG0MJXQEfkCalkJIMZCE\\\n",
       "uJuc38VC4bAbmiyvcLLZx2PmXJxzvuf7fW82yT7ns9/zPYPhcDgMAAA1E+MeAADgVCOwAADKBBYA\\\n",
       "QJnAAgAoE1gAAGUCCwCgTGABAJQJLACAMoEFAFAmsAAAygQWAECZwAIAKBNYAABlAgsAoExgAQCU\\\n",
       "CSwAgDKBBQBQJrAAAMoEFgBAmcACACgTWAAAZQILAKBMYAEAlAksAIAygQUAUCawAADKBBYAQJnA\\\n",
       "AgAoE1gAAGUCCwCgTGABAJQJLACAMoEFAFAmsAAAygQWAECZwAIAKBNYAABlAgsAoExgAQCUCSwA\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim054e4c7248124bd993179bc3408dc946 = new Animation(frames, img_id, slider_id, 299.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "execute_Astar(m, func, animate=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A${}^*$ではなくダイクストラ法を実行していくときのFの値をプロット\n",
    "\n",
    "* H関数の値を常にゼロとするとダイクストラ法になる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n",
      "[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 9), (3, 9), (4, 9), (5, 9), (6, 9), (7, 9), (7, 8), (7, 7), (8, 7), (9, 7), (9, 8), (9, 9)]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img5904cbaf1e9a45edaa2285e4e6bd157a\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider5904cbaf1e9a45edaa2285e4e6bd157a\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim5904cbaf1e9a45edaa2285e4e6bd157a.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select5904cbaf1e9a45edaa2285e4e6bd157a\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_5904cbaf1e9a45edaa2285e4e6bd157a\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_5904cbaf1e9a45edaa2285e4e6bd157a\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_5904cbaf1e9a45edaa2285e4e6bd157a\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_5904cbaf1e9a45edaa2285e4e6bd157a\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_5904cbaf1e9a45edaa2285e4e6bd157a\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_5904cbaf1e9a45edaa2285e4e6bd157a\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img5904cbaf1e9a45edaa2285e4e6bd157a\";\n",
       "    var slider_id = \"_anim_slider5904cbaf1e9a45edaa2285e4e6bd157a\";\n",
       "    var loop_select_id = \"_anim_loop_select5904cbaf1e9a45edaa2285e4e6bd157a\";\n",
       "    var frames = new Array(50);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAYAAAC+ZpjcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "3U3OfXAo7XaTNNl+0tPdfb1m9sE553d+v+92z2bf/f5+53sGo9FoFAAAaqYmPQAAgNVGYAEAlAks\\\n",
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     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#func = lambda a,b: (a[0]-b[0])**2+(a[1]-b[1])**2\n",
    "func = lambda a,b: 0.\n",
    "execute_Astar(m, func, animate=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NetworkXの関数で解く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "迷路クラスをグラフに変換する関数\n",
    "\"\"\"\n",
    "\n",
    "def conv_maze_to_graph(maze):\n",
    "    m = maze\n",
    "    Graph = nx.grid_2d_graph(m.width//2, m.height//2, periodic=False)\n",
    "    \n",
    "    for y in range(1, m.height-1, 2):\n",
    "        for x in range(2, m.width-1, 2):\n",
    "            if m.data[y][x] > 0:\n",
    "                l = ((x-2)//2, (y-1)//2)\n",
    "                r = ((x-0)//2, (y-1)//2)\n",
    "                Graph.remove_edge(l, r)\n",
    "                \n",
    "        \n",
    "    for y in range(2, m.height-1, 2):\n",
    "        for x in range(1, m.width-1, 2):\n",
    "            if m.data[y][x] > 0:\n",
    "                b = ((x-1)//2, (y-2)//2)\n",
    "                t = ((x-1)//2, (y-0)//2)\n",
    "                Graph.remove_edge(b, t)\n",
    "    \n",
    "    ## 移動コストを示す属性をリンクに付与する必要がある．今回は一律に1とする．\n",
    "    nx.set_edge_attributes(Graph, {e: 1 for e in Graph.edges()}, \"cost\")\n",
    "    return Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (2, 4), (3, 4), (3, 3), (4, 3), (4, 4)]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 迷路をグラフ形式に変換\n",
    "MG = conv_maze_to_graph(m)\n",
    "\n",
    "## プロット用の領域を確保\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
    "## ノードの座標を指定\n",
    "pos = {(x,y):(x,y) for x,y in MG.nodes()}\n",
    "\n",
    "## 迷路グラフを表示\n",
    "nx.draw(MG, pos, ax=ax)\n",
    "nx.draw_networkx_labels(MG, pos, ax=ax);\n",
    "\n",
    "## 関数Hを定義\n",
    "func = lambda a,b: (a[0]-b[0])**2+(a[1]-b[0])**2\n",
    "\n",
    "## NetworkXの関数に渡すと経路が得られる\n",
    "## （引数：グラフ，スタート地点，ゴール地点，関数H，移動コストのラベル）\n",
    "path = nx.astar_path(MG, (0,0), (4,4), heuristic=func, weight='cost')\n",
    "print(path)\n",
    "\n",
    "## 経路を重ねてプロットする\n",
    "SP = nx.Graph()\n",
    "SP.add_nodes_from(path)\n",
    "SP.add_edges_from([(n1, n2) for n1, n2 in zip(path[:-1], path[1:])])\n",
    "pos = {(x,y):(x,y) for x,y in SP.nodes()}\n",
    "nx.draw(SP, pos, node_color='r', ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}