Puzzles/Shikaku.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import gurobipy as grb\n",
    "import numpy as np\n",
    "import os\n",
    "from matplotlib.pyplot import MultipleLocator\n",
    "from matplotlib.patches import Rectangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "READING FILE ../assets/data/Shikaku/problems/101_12x12.txt\n",
      "[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0]\n",
      "[0, 0, 0, 0, 12, 4, 0, 3, 0, 0, 0, 3]\n",
      "[0, 12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0]\n",
      "[8, 0, 0, 0, 0, 0, 2, 2, 0, 0, 8, 0]\n",
      "[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "[0, 2, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0]\n",
      "[0, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, 0]\n",
      "[0, 9, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0]\n",
      "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]\n"
     ]
    }
   ],
   "source": [
    "def readInstance(path):\n",
    "    \n",
    "    # 从测试案例中随机选取一个测试案例出来\n",
    "    # file_name = f\"../assets/data/slitherlinkdata/{path}{np.random.randint(1)+1}.txt\"\n",
    "    file_name = f\"../assets/data/Shikaku/problems/{path}.txt\"\n",
    "\n",
    "    m = 0\n",
    "    n = 0\n",
    "    grids = None\n",
    "    print( f\"READING FILE {file_name}\" )\n",
    "    if not os.path.isfile(file_name):\n",
    "        print('File does not exist')\n",
    "    else:\n",
    "\n",
    "        with open(file_name) as file:\n",
    "            firstline = file.readline().strip().split(\" \")\n",
    "            m = int(firstline[0])\n",
    "            n = int(firstline[1])\n",
    "            grids = [[0 for _ in range(n)] for _ in range(m)]\n",
    "\n",
    "            for idx in range(m):\n",
    "                line = file.readline().strip().split(\" \")\n",
    "                assert len(line) == n\n",
    "                \n",
    "                for j in range(n):\n",
    "                    if line[j] not in [ '.', '-']:\n",
    "                        grids[idx][j] = int(line[j])\n",
    "    return m, n, grids\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # data = \"30x25normal1\"\n",
    "    data = \"220_17x17\"\n",
    "    m, n, grids = readInstance(data)\n",
    "    # print(grids)\n",
    "    for g in grids:\n",
    "        print(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x[i, j, k]$: 属于方格  [i, j] 内的第 k 种摆放\n",
    "\n",
    "思路如下：针对每一个包含数字的格，输出所有可行的摆放位置。\n",
    "\n",
    "想象成在一个格子里放入不同的变量\n",
    "\n",
    "-> 子问题：怎么获取一个数字对应的所有可能的Shikaku？\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "READING FILE ../assets/data/Shikaku/problems/362_17x17.txt\n",
      "FOUND OPTIMAL\n"
     ]
    }
   ],
   "source": [
    "from ortools.sat.python import cp_model as cp\n",
    "\n",
    "def getXY(target):\n",
    "    if target == 1:\n",
    "        return [(1,1)]\n",
    "    else:\n",
    "        result = []\n",
    "        for i in range(1, int(math.sqrt(target)) + 1):\n",
    "            if target % i == 0:\n",
    "                result.append((i, target // i))\n",
    "                if i < target // i:\n",
    "                    result.append((target // i, i))\n",
    "        return result\n",
    "    \n",
    "\n",
    "def get_all_pos(i, j, rect, matrix):\n",
    "    x_min, x_max = i - rect[0] + 1, i\n",
    "    y_min, y_max = j - rect[1] + 1, j\n",
    "    tmp_pos =  [(x, y) for x in range(x_min, x_max + 1) for y in range(y_min, y_max + 1)]\n",
    "    new_pos = []\n",
    "    for (x_, y_) in tmp_pos:\n",
    "        if x_ < 0 or y_ < 0:\n",
    "            continue\n",
    "        # 对于位置可行的地方\n",
    "        matrix_np = np.array(matrix)\n",
    "        # 提取子矩阵并求和\n",
    "        submatrix_sum = np.sum(matrix_np[x_: x_ + rect[0] , y_: y_ + rect[1]])\n",
    "        if submatrix_sum != matrix[i][j] or x_ + rect[0] > len(matrix) or y_ + rect[1] > len(matrix[1]):\n",
    "            continue\n",
    "        new_pos.append((x_, y_))\n",
    "    return new_pos\n",
    "\n",
    "def Shikaku_solver(m, n, grids):\n",
    "    model = cp.CpModel()\n",
    "    solver = cp.CpSolver()\n",
    "    cells = dict()\n",
    "    x = dict()\n",
    "    for i in range(len(grids)):\n",
    "        for j in range(len(grids[0])):\n",
    "            cells[i, j] = []\n",
    "    for i in range(len(grids)):\n",
    "        for j in range(len(grids[0])):\n",
    "            \n",
    "            if grids[i][j] != 0:\n",
    "                all_fes_pos = []\n",
    "                tmp_fes_pos = getXY(grids[i][j])\n",
    "                for (x_, y_) in tmp_fes_pos:\n",
    "                    tmp_res = get_all_pos(i, j, (x_, y_), grids)\n",
    "                    if len(tmp_res) > 0:\n",
    "                        for (sub_x, sub_y) in tmp_res:\n",
    "                            all_fes_pos.append([sub_x, sub_y, x_, y_])\n",
    "\n",
    "                for pos in all_fes_pos:\n",
    "\n",
    "                    a, b, c, d = pos[0], pos[1], pos[2], pos[3]\n",
    "                    x[a, b, c, d] = model.NewBoolVar(f\"x_{a}_{b}_{c}_{d}\")\n",
    "\n",
    "                    for k1 in range(c):\n",
    "                        for k2 in range(d):\n",
    "\n",
    "                            cells[a + k1, b + k2].append(x[a, b, c,d])\n",
    "\n",
    "                model.Add(sum([x[a[0], a[1], a[2], a[3]] for a in all_fes_pos]) == 1)\n",
    "\n",
    "\n",
    "    for i in range(len(grids)):\n",
    "        for j in range(len(grids[0])):\n",
    "            model.Add(sum(cells[i, j]) == 1)\n",
    "    status = solver.Solve(model)\n",
    "    result = []\n",
    "    if status == cp.OPTIMAL:\n",
    "        print(\"FOUND OPTIMAL\")\n",
    "        for k, v in x.items():\n",
    "            if solver.Value(x[k]) == 1:\n",
    "                result.append(list(k))\n",
    "    return result\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    data = \"362_17x17\"\n",
    "    m, n, grids = readInstance(data)\n",
    "    result = Shikaku_solver(m, n, grids)\n",
    "    # print(result)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1700x1700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_random_color():\n",
    "    # 生成三个随机的十六进制数字，每个数字的范围是0-255\n",
    "    r = random.randint(0, 255)\n",
    "    g = random.randint(0, 255)\n",
    "    b = random.randint(0, 255)\n",
    "    \n",
    "    # 将RGB值转换为十六进制字符串\n",
    "    hex_color = f'#{r:02x}{g:02x}{b:02x}'\n",
    "    return hex_color\n",
    "\n",
    "def coordinatesParser(m, n, idx):\n",
    "    \"\"\"_summary_\n",
    "        进行坐标转换 \n",
    "    Args:\n",
    "        m (_type_): _description_\n",
    "        n (_type_): _description_\n",
    "        idx (_type_): _description_\n",
    "\n",
    "    Returns:\n",
    "        _type_: _description_\n",
    "    \"\"\"\n",
    "    ori_x , ori_y = idx // n, idx % n \n",
    "    return (0.5 + ori_y, 0.5 + ( m - ori_x - 1) )\n",
    "\n",
    "def coordinatesParserNodes(m, n, idx):\n",
    "    ori_x, ori_y = idx // (n + 1), idx % (n + 1)\n",
    "    return (ori_y, m - ori_x )\n",
    "\n",
    "\n",
    "def vis(m, n, grids, result):\n",
    "    # 可视化\n",
    "    random.seed(123)\n",
    "    grid_color = dict()\n",
    "    for idx, _ in enumerate(result):\n",
    "        grid_color[f\"{idx}\"] = generate_random_color()\n",
    "    plt.figure(figsize = (n, m))\n",
    "    ax = plt.gca()\n",
    "    x_major_locator = MultipleLocator(1)\n",
    "    y_major_locator = MultipleLocator(1)\n",
    "    ax.xaxis.set_major_locator(x_major_locator)\n",
    "    # 把x/y轴的主刻度设置为1的倍数\n",
    "    ax.yaxis.set_major_locator(y_major_locator)\n",
    "    plt.xlim(0,n)\n",
    "    plt.ylim(0,m)\n",
    "    for i in range(m):\n",
    "        for j in range(n):\n",
    "            if grids[i][j] != 0:\n",
    "                new_coor = coordinatesParser(m, n, i * n + j)\n",
    "                ax.text(new_coor[0], new_coor[1], str(grids[i][j]), \n",
    "                        horizontalalignment = \"center\", \n",
    "                        verticalalignment = 'center',\n",
    "                        fontsize = 24)\n",
    "    for idx, rect in enumerate(result):\n",
    "        # [0, 0, 1, 3]\n",
    "        i, j = rect[0] + rect[2] - 1, rect[1] \n",
    "        ax.add_patch(Rectangle((j, m - i - 1), rect[3], rect[2], color = grid_color[f\"{idx}\"], alpha = 0.5))\n",
    "    \n",
    "    plt.grid(linestyle = \"-\")\n",
    "    \n",
    "    plt.show()\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    vis(m, n, grids, result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py310_arm",
   "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": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}