A solver for the n-queens problem

nqueens.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "72edfc96-2706-4c69-8c1e-8b5654ec4c73",
   "metadata": {},
   "source": [
    "# N-Queens\n",
    "\n",
    "Aswin van Woudenberg (https://www.aswinvanwoudenberg.com | https://github.com/afvanwoudenberg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8027161c-6179-40f4-af84-07bd4d7213a2",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "97e315de",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation\n",
    "\n",
    "from IPython.display import HTML\n",
    "from ipywidgets import widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cc52446-d75e-4408-a145-2569029145c4",
   "metadata": {},
   "source": [
    "## Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c31fa7e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_valid(board, row, col):\n",
    "    for i in range(row):\n",
    "        if board[i] == col or row - i == abs(col - board[i]):\n",
    "            return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "897a92fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_n_queens_(board, row):\n",
    "    if row == len(board):\n",
    "        yield list(board)\n",
    "    else:\n",
    "        for col in range(len(board)):\n",
    "            if is_valid(board, row, col):\n",
    "                board[row] = col\n",
    "                yield from solve_n_queens_(board, row + 1)\n",
    "                board[row] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d033b661",
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_n_queens(n):\n",
    "    board = [-1] * n\n",
    "    yield from solve_n_queens_(board, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63f72258-7f09-4863-a863-f067d1b31102",
   "metadata": {},
   "source": [
    "## Function to display a solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a3ccff26",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_n_queens_solution(solution, ax):\n",
    "    # Define the colors of the squares\n",
    "    light_color = \"#F0D9B5\"\n",
    "    dark_color = \"#B58863\"\n",
    "\n",
    "    board_size = len(solution)\n",
    "    \n",
    "    # Draw the squares\n",
    "    for i in range(board_size):\n",
    "        for j in range(board_size):\n",
    "            if (i + j) % 2 == 0:\n",
    "                color = light_color\n",
    "            else:\n",
    "                color = dark_color\n",
    "            ax.add_patch(plt.Rectangle((i, j), 1, 1, color=color))\n",
    "\n",
    "    # Draw the pieces on the board\n",
    "    for y, x in enumerate(solution):\n",
    "        ax.text(x+0.5, y+0.5, \"♛\", ha=\"center\", va=\"center\", fontsize=240/board_size, color=\"black\")\n",
    "\n",
    "    # Set the aspect ratio to \"equal\"\n",
    "    ax.set_aspect('equal')\n",
    "\n",
    "    # Set the x and y limits to show the whole board\n",
    "    ax.set_xlim(0, board_size)\n",
    "    ax.set_ylim(0, board_size)\n",
    "\n",
    "    # Remove the tick labels\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "\n",
    "    # Flip the y-axis\n",
    "    ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "306c8d99-bb92-4715-8915-f2203b6b191c",
   "metadata": {},
   "source": [
    "## Display all solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6d6da875",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_all_n_queens_solutions(board_size):\n",
    "    for solution in solve_n_queens(board_size):\n",
    "        fig, ax = plt.subplots()\n",
    "        plot_n_queens_solution(solution, ax)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "76d53e01",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all_n_queens_solutions(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d42fd8e0-3656-46cc-a24e-7c430d66afc7",
   "metadata": {},
   "source": [
    "## Show solutions one by one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ec24461b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2bbffe17c417415eb6d1fad7cf272146",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(Dropdown(description='Board size: ', index=7, options=(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d9658a27f8164087bf896a3f5f81b80e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "11e4775f9a684853a8d09fbd0cc541e2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Label(value='')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "board_size_dropdown = widgets.Dropdown(options=list(range(1,21)), value=8, description=\"Board size: \")\n",
    "next_button = widgets.Button(description=\"Next\")\n",
    "hbox = widgets.HBox([board_size_dropdown, next_button])\n",
    "output = widgets.Output()\n",
    "label = widgets.Label()\n",
    "\n",
    "display(hbox, output, label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2a1a9a16",
   "metadata": {},
   "outputs": [],
   "source": [
    "gen = None\n",
    "solution = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e19e56e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def on_board_size_dropdown_change(change):\n",
    "    global gen\n",
    "    global solution\n",
    "    \n",
    "    if change['type'] == 'change' and change['name'] == 'value':\n",
    "        value = change['new']\n",
    "        next_button.layout.display = 'none'\n",
    "        \n",
    "        output.clear_output()\n",
    "        \n",
    "        gen = solve_n_queens(value)\n",
    "        try:\n",
    "            solution = next(gen)            \n",
    "            with output:\n",
    "                fig, ax = plt.subplots()\n",
    "                plot_n_queens_solution(solution, ax)\n",
    "                plt.show()\n",
    "        except StopIteration:\n",
    "            label.value = \"No solutions found.\"\n",
    "            return\n",
    "\n",
    "        try:\n",
    "            solution = next(gen).copy()\n",
    "            label.value = \"\"\n",
    "            next_button.layout.display = 'inline-block'\n",
    "        except StopIteration:\n",
    "            label.value = \"\"\n",
    "\n",
    "board_size_dropdown.observe(on_board_size_dropdown_change)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "98eb75fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def on_next_button_clicked(b):\n",
    "    global gen\n",
    "    global solution\n",
    "    \n",
    "    output.clear_output(wait=True)\n",
    "    with output:\n",
    "        fig, ax = plt.subplots()\n",
    "        plot_n_queens_solution(solution, ax)\n",
    "        plt.show()\n",
    "    \n",
    "    try:\n",
    "        solution = next(gen)\n",
    "    except StopIteration:\n",
    "        label.value = \"\"\n",
    "        next_button.layout.display = 'none'\n",
    "\n",
    "next_button.on_click(on_next_button_clicked)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9fb8c24c",
   "metadata": {},
   "outputs": [],
   "source": [
    "on_board_size_dropdown_change({'type': 'change', 'name': 'value', 'new': board_size_dropdown.value})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e79c450-a9f9-40ef-818b-a6d1a10c76a4",
   "metadata": {},
   "source": [
    "## Create a matplotlib animation that shows all solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d177251c",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "def gen_func(n):\n",
    "    def generator():\n",
    "        yield from solve_n_queens(n)\n",
    "    return generator\n",
    "\n",
    "def animate(solution):\n",
    "    ax.clear()\n",
    "    plot_n_queens_solution(solution, ax)\n",
    "\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b91c5e48",
   "metadata": {},
   "outputs": [
    {
     "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_img45f636622d1b4d439f9f97f8f29b6103\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider45f636622d1b4d439f9f97f8f29b6103\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim45f636622d1b4d439f9f97f8f29b6103.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim45f636622d1b4d439f9f97f8f29b6103.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_select45f636622d1b4d439f9f97f8f29b6103\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_45f636622d1b4d439f9f97f8f29b6103\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_45f636622d1b4d439f9f97f8f29b6103\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_45f636622d1b4d439f9f97f8f29b6103\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_45f636622d1b4d439f9f97f8f29b6103\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_45f636622d1b4d439f9f97f8f29b6103\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_45f636622d1b4d439f9f97f8f29b6103\">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_img45f636622d1b4d439f9f97f8f29b6103\";\n",
       "    var slider_id = \"_anim_slider45f636622d1b4d439f9f97f8f29b6103\";\n",
       "    var loop_select_id = \"_anim_loop_select45f636622d1b4d439f9f97f8f29b6103\";\n",
       "    var frames = new Array(92);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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