attempt_02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9bca7a69",
   "metadata": {},
   "source": [
    "# Jigsaw generation #2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2fe55dd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from tqdm import tqdm\n",
    "\n",
    "from jigsaw import *\n",
    "from jigsaw.default import *\n",
    "from jigsaw.svg import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c3301f54",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_unique(horizontal_edges, vertical_edges, *, constraints=\"border\"):\n",
    "    H, _ = horizontal_edges.shape\n",
    "    _, W = vertical_edges.shape\n",
    "    pieces = grid_to_pieces(horizontal_edges, vertical_edges, opposite)\n",
    "    return has_unique_solution(H, W, pieces, opposite, flip, constraints=constraints)\n",
    "\n",
    "\n",
    "def search(sampler, *validators, max_iterations=None):\n",
    "\n",
    "    # Loop until a grid with a unique solution is found\n",
    "    i = 0\n",
    "    with tqdm(total=max_iterations) as progress:\n",
    "        while max_iterations is None or i < max_iterations:\n",
    "\n",
    "            # Sample grid, according to rules\n",
    "            horizontal_edges, vertical_edges = sampler()\n",
    "            \n",
    "            # Ask validators for compliance\n",
    "            try:\n",
    "                for validator in validators:\n",
    "                    if not validator(horizontal_edges, vertical_edges):\n",
    "                        break\n",
    "                else:\n",
    "                    return horizontal_edges, vertical_edges\n",
    "            finally:\n",
    "                progress.update(1)\n",
    "            \n",
    "            i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "044934e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_solutions(horizontal_edges, vertical_edges, *, constraints=\"border\"):\n",
    "    H, _ = horizontal_edges.shape\n",
    "    _, W = vertical_edges.shape\n",
    "    pieces = grid_to_pieces(horizontal_edges, vertical_edges, opposite)\n",
    "    iterator = iterate_unique_solutions(H, W, pieces, opposite, flip, constraints=constraints)\n",
    "    count = sum(1 for _ in iterator)\n",
    "    return count\n",
    "\n",
    "def display_solutions(horizontal_edges, vertical_edges, *, constraints=\"border\"):\n",
    "    H, _ = horizontal_edges.shape\n",
    "    _, W = vertical_edges.shape\n",
    "    pieces = grid_to_pieces(horizontal_edges, vertical_edges, opposite)\n",
    "    for h, v in iterate_unique_solutions(H, W, pieces, opposite, flip, constraints=constraints):\n",
    "        display_grid(h, v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e0bbf145",
   "metadata": {},
   "outputs": [],
   "source": [
    "def has_unique_pieces(horizontal_edges, vertical_edges):\n",
    "    pieces = grid_to_pieces(horizontal_edges, vertical_edges, opposite)\n",
    "    pieces = canonize_piece(pieces, flip)\n",
    "    pieces = pieces.reshape(-1, 4)\n",
    "    unique_pieces = np.unique(pieces, axis=0)\n",
    "    return pieces.shape[0] == unique_pieces.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2002ba1",
   "metadata": {},
   "source": [
    "## 1. 4x4 with 8 corners (no constraint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "99af4f3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CENTERED_SMALL_MALE', 'CENTERED_SMALL_FEMALE', 'RIGHT_SMALL_MALE',\n",
       "       'RIGHT_SMALL_FEMALE', 'LEFT_SMALL_MALE', 'LEFT_SMALL_FEMALE'],\n",
       "      dtype='<U22')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Choose edge types\n",
    "edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    LEFT_SMALL_MALE,\n",
    "])\n",
    "\n",
    "# Automatically expand types to match combinations\n",
    "edge_types = expand_edge_types(edge_types, opposite, flip)\n",
    "\n",
    "# Show actual types\n",
    "edge_names[edge_types]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dba07a32",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "30it [00:06,  4.49it/s]\n"
     ]
    }
   ],
   "source": [
    "# Generate grid\n",
    "H, W = 4, 4\n",
    "generator = np.random.default_rng(42)\n",
    "def sampler():\n",
    "    horizontal_edges, vertical_edges = sample_random_grid(H, W, edge_types, generator=generator)\n",
    "    horizontal_edges[1:-1, 2] = FLAT\n",
    "    vertical_edges[2, 1:-1] = FLAT\n",
    "    return horizontal_edges, vertical_edges\n",
    "horizontal_edges, vertical_edges = search(sampler, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "05a8554e",
   "metadata": {},
   "outputs": [
    {
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0b234f9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_4x4_cross = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "013661e0",
   "metadata": {},
   "source": [
    "## 2. 5x5 with nested corners"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "daf3a667",
   "metadata": {},
   "outputs": [
    {
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    }
   ],
   "source": [
    "# This will be a 5x5 grid, with 4 additional corned inside\n",
    "H, W = 5, 5\n",
    "horizontal_edges, vertical_edges = sample_random_grid(H, W, np.array([FLAT_ALTERNATIVE]))\n",
    "horizontal_edges[[1, 1, 3, 3], [1, 4, 1, 4]] = FLAT\n",
    "vertical_edges[[1, 1, 4, 4], [1, 3, 1, 3]] = FLAT\n",
    "\n",
    "# First, make sure that the overall layout can only be solved one way\n",
    "assert is_unique(horizontal_edges, vertical_edges)\n",
    "\n",
    "# Show it, to illustrate the purpose\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6c357d40",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "234it [00:06, 34.65it/s]\n"
     ]
    }
   ],
   "source": [
    "# Outer perimeter cannot contain any centered small pin\n",
    "# This makes it easier to identify which corners are inside\n",
    "outer_edge_types = np.array([\n",
    "    LEFT_SMALL_MALE,\n",
    "    LEFT_SMALL_FEMALE,\n",
    "    RIGHT_SMALL_MALE,\n",
    "    RIGHT_SMALL_FEMALE,\n",
    "] * 2 + [\n",
    "    DOUBLE_SMALL_MALE,\n",
    "    DOUBLE_SMALL_FEMALE,\n",
    "    TWISTED_SMALL_MALE,\n",
    "    TWISTED_SMALL_FEMALE,\n",
    "])\n",
    "\n",
    "generator = np.random.default_rng(13746)\n",
    "\n",
    "def sampler():\n",
    "    \n",
    "    # Start with empty (i.e. flat-only) 5x5 grid\n",
    "    H = W = 5\n",
    "    horizontal_edges = np.zeros((H, W + 1), dtype=np.uint8)\n",
    "    vertical_edges = np.zeros((H + 1, W), dtype=np.uint8)\n",
    "    \n",
    "    # Sample outer perimeter\n",
    "    horizontal_edges[[0, 0, 0, 0, 4, 4, 4, 4], [1, 2, 3, 4, 1, 2, 3, 4]] = generator.choice(outer_edge_types, size=8)\n",
    "    vertical_edges[[1, 2, 3, 4, 1, 2, 3, 4], [0, 0, 0, 0, 4, 4, 4, 4]] = generator.choice(outer_edge_types, size=8)\n",
    "    \n",
    "    # Inner area is set to wildcard, for the moment\n",
    "    horizontal_edges[[1, 1, 2, 2, 2, 2, 3, 3], [2, 3, 1, 2, 3, 4, 2, 3]] = FLAT_ALTERNATIVE\n",
    "    vertical_edges[[2, 3, 1, 2, 3, 4, 2, 3], [1, 1, 2, 2, 2, 2, 3, 3]] = FLAT_ALTERNATIVE\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "\n",
    "outer_horizontal_edges, outer_vertical_edges = search(sampler, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e75c78b2",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(outer_horizontal_edges, outer_vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "507c2f77",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "8it [00:08,  1.03s/it]\n"
     ]
    }
   ],
   "source": [
    "inner_edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    CENTERED_SMALL_FEMALE,\n",
    "    LEFT_SMALL_MALE,\n",
    "    LEFT_SMALL_FEMALE,\n",
    "    RIGHT_SMALL_MALE,\n",
    "    RIGHT_SMALL_FEMALE,\n",
    "] * 4 + [\n",
    "    DOUBLE_SMALL_MALE,\n",
    "    DOUBLE_SMALL_FEMALE,\n",
    "    #TWISTED_SMALL_MALE,\n",
    "    #TWISTED_SMALL_FEMALE,\n",
    "])\n",
    "\n",
    "generator = np.random.default_rng(123)\n",
    "\n",
    "def sampler():\n",
    "    \n",
    "    # Start with selected solution\n",
    "    horizontal_edges = outer_horizontal_edges.copy()\n",
    "    vertical_edges = outer_vertical_edges.copy()\n",
    "    \n",
    "    # Inner can contain twisted pins as well\n",
    "    horizontal_edges[[1, 1, 2, 2, 2, 2, 3, 3], [2, 3, 1, 2, 3, 4, 2, 3]] = generator.choice(inner_edge_types, size=8)\n",
    "    vertical_edges[[2, 3, 1, 2, 3, 4, 2, 3], [1, 1, 2, 2, 2, 2, 3, 3]] = generator.choice(inner_edge_types, size=8)\n",
    "    \n",
    "    # Place centered ones manually, to ensure diversity\n",
    "    horizontal_edges[1, 2] = CENTERED_SMALL_MALE\n",
    "    horizontal_edges[3, 2] = CENTERED_SMALL_MALE\n",
    "    horizontal_edges[3, 3] = CENTERED_SMALL_MALE\n",
    "    vertical_edges[2, 3] = CENTERED_SMALL_FEMALE\n",
    "    vertical_edges[3, 1] = CENTERED_SMALL_FEMALE\n",
    "    vertical_edges[1, 2] = CENTERED_SMALL_FEMALE\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "\n",
    "horizontal_edges, vertical_edges = search(sampler, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "976c1f75",
   "metadata": {},
   "outputs": [
    {
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193.87451660040608 A 6.4 6.4 0 1 0 26.9254833995939 193.87451660040608 A 3.2 3.2 0 0 1 28.799999999999997 188.8 C 46.400000000000006 188.8, 46.400000000000006 192.0, 64.0 192.0 C 76.8 192.0, 76.8 195.2, 89.6 195.2 A 3.2 3.2 0 0 0 91.4745166004061 190.12548339959392 A 6.4 6.4 0 1 1 100.5254833995939 190.12548339959392 A 3.2 3.2 0 0 0 102.4 195.2 C 115.2 195.2, 115.2 192.0, 128.0 192.0 C 136.0 192.0, 136.0 188.8, 144.0 188.8 A 3.2 3.2 0 0 1 145.87451660040608 193.87451660040608 A 6.4 6.4 0 1 0 154.9254833995939 193.87451660040608 A 3.2 3.2 0 0 1 156.8 188.8 C 174.4 188.8, 174.4 192.0, 192.0 192.0 C 200.0 192.0, 200.0 195.2, 208.0 195.2 A 3.2 3.2 0 0 0 209.87451660040608 190.12548339959392 A 6.4 6.4 0 1 1 218.9254833995939 190.12548339959392 A 3.2 3.2 0 0 0 220.8 195.2 C 238.4 195.2, 238.4 192.0, 256.0 192.0 C 264.0 192.0, 264.0 188.8, 272.0 188.8 A 3.2 3.2 0 0 1 273.8745166004061 193.87451660040608 A 6.4 6.4 0 1 0 282.9254833995939 193.87451660040608 A 3.2 3.2 0 0 1 284.8 188.8 L 291.2 188.8 A 3.2 3.2 0 0 1 293.0745166004061 193.87451660040608 A 6.4 6.4 0 1 0 302.1254833995939 193.87451660040608 A 3.2 3.2 0 0 1 304.0 188.8 C 312.0 188.8, 312.0 192.0, 320.0 192.0 L 336.0 192.0 M -16.0 256.0 L 0.0 256.0 C 7.999999999999999 256.0, 7.999999999999999 252.8, 15.999999999999998 252.8 A 3.2 3.2 0 0 1 17.874516600406096 257.8745166004061 A 6.4 6.4 0 1 0 26.9254833995939 257.8745166004061 A 3.2 3.2 0 0 1 28.799999999999997 252.8 C 46.400000000000006 252.8, 46.400000000000006 256.0, 64.0 256.0 L 128.0 256.0 C 145.6 256.0, 145.6 252.8, 163.2 252.8 A 3.2 3.2 0 0 1 165.0745166004061 257.8745166004061 A 6.4 6.4 0 1 0 174.12548339959392 257.8745166004061 A 3.2 3.2 0 0 1 176.0 252.8 C 184.0 252.8, 184.0 256.0, 192.0 256.0 L 256.0 256.0 C 264.0 256.0, 264.0 252.8, 272.0 252.8 A 3.2 3.2 0 0 1 273.8745166004061 257.8745166004061 A 6.4 6.4 0 1 0 282.9254833995939 257.8745166004061 A 3.2 3.2 0 0 1 284.8 252.8 C 302.4 252.8, 302.4 256.0, 320.0 256.0 L 336.0 256.0 M -16.0 320.0 L 0.0 320.0 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b3bce62e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Focus on the inner part\n",
    "inner_horizontal_edges = horizontal_edges[1:-1, 1:-1]\n",
    "inner_vertical_edges = vertical_edges[1:-1, 1:-1]\n",
    "\n",
    "# Show it\n",
    "display_grid(inner_horizontal_edges, inner_vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7c388c49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking unicity on this subset is a bit more tricky\n",
    "# We need to allow any pins on the central edges\n",
    "horizontal_constraints = np.full((3, 3 + 1), -1)\n",
    "vertical_constraints = np.full((3 + 1, 3), -1)\n",
    "horizontal_constraints[0, [0, -1]] = FLAT\n",
    "horizontal_constraints[2, [0, -1]] = FLAT\n",
    "vertical_constraints[[0, -1], 0] = FLAT\n",
    "vertical_constraints[[0, -1], 2] = FLAT\n",
    "constraints = horizontal_constraints, vertical_constraints\n",
    "\n",
    "# Hopefully there is only a unique solution\n",
    "count_solutions(inner_horizontal_edges, inner_vertical_edges, constraints=constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c0211154",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_5x5_nested = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddafa5bf",
   "metadata": {},
   "source": [
    "## 3. 4x4 with pure square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "94b34305",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"padding:1em\"><svg width=\"320\" height=\"320\" xmlns=\"http://www.w3.org/2000/svg\"><g transform=\"translate(32.0 32.0)\"><path fill=\"none\" stroke=\"black\" d=\"M 0.0 -16.0 L 0.0 0.0 L 0.0 64.0 L 0.0 128.0 L 0.0 192.0 L 0.0 256.0 L 0.0 272.0 M 64.0 -16.0 L 64.0 0.0 L 64.0 64.0 L 64.0 76.8 M 64.0 89.6 L 64.0 102.4 M 64.0 115.2 L 64.0 128.0 L 64.0 140.8 M 64.0 153.6 L 64.0 166.4 M 64.0 179.2 L 64.0 192.0 L 64.0 204.8 M 64.0 217.6 L 64.0 230.4 M 64.0 243.2 L 64.0 256.0 L 64.0 272.0 M 128.0 -16.0 L 128.0 0.0 L 128.0 12.8 M 128.0 25.6 L 128.0 38.4 M 128.0 51.2 L 128.0 64.0 L 128.0 76.8 M 128.0 89.6 L 128.0 102.4 M 128.0 115.2 L 128.0 128.0 L 128.0 140.8 M 128.0 153.6 L 128.0 166.4 M 128.0 179.2 L 128.0 192.0 L 128.0 204.8 M 128.0 217.6 L 128.0 230.4 M 128.0 243.2 L 128.0 256.0 L 128.0 272.0 M 192.0 -16.0 L 192.0 0.0 L 192.0 12.8 M 192.0 25.6 L 192.0 38.4 M 192.0 51.2 L 192.0 64.0 L 192.0 76.8 M 192.0 89.6 L 192.0 102.4 M 192.0 115.2 L 192.0 128.0 L 192.0 140.8 M 192.0 153.6 L 192.0 166.4 M 192.0 179.2 L 192.0 192.0 L 192.0 204.8 M 192.0 217.6 L 192.0 230.4 M 192.0 243.2 L 192.0 256.0 L 192.0 272.0 M 256.0 -16.0 L 256.0 0.0 L 256.0 64.0 L 256.0 128.0 L 256.0 192.0 L 256.0 256.0 L 256.0 272.0 M -16.0 0.0 L 0.0 0.0 L 64.0 0.0 L 128.0 0.0 L 192.0 0.0 L 256.0 0.0 L 272.0 0.0 M -16.0 64.0 L 0.0 64.0 L 64.0 64.0 L 76.8 64.0 M 89.6 64.0 L 102.4 64.0 M 115.2 64.0 L 128.0 64.0 L 140.8 64.0 M 153.6 64.0 L 166.4 64.0 M 179.2 64.0 L 192.0 64.0 L 204.8 64.0 M 217.6 64.0 L 230.4 64.0 M 243.2 64.0 L 256.0 64.0 L 272.0 64.0 M -16.0 128.0 L 0.0 128.0 L 12.8 128.0 M 25.6 128.0 L 38.4 128.0 M 51.2 128.0 L 64.0 128.0 L 76.8 128.0 M 89.6 128.0 L 102.4 128.0 M 115.2 128.0 L 128.0 128.0 L 140.8 128.0 M 153.6 128.0 L 166.4 128.0 M 179.2 128.0 L 192.0 128.0 L 204.8 128.0 M 217.6 128.0 L 230.4 128.0 M 243.2 128.0 L 256.0 128.0 L 272.0 128.0 M -16.0 192.0 L 0.0 192.0 L 12.8 192.0 M 25.6 192.0 L 38.4 192.0 M 51.2 192.0 L 64.0 192.0 L 76.8 192.0 M 89.6 192.0 L 102.4 192.0 M 115.2 192.0 L 128.0 192.0 L 140.8 192.0 M 153.6 192.0 L 166.4 192.0 M 179.2 192.0 L 192.0 192.0 L 204.8 192.0 M 217.6 192.0 L 230.4 192.0 M 243.2 192.0 L 256.0 192.0 L 272.0 192.0 M -16.0 256.0 L 0.0 256.0 L 64.0 256.0 L 128.0 256.0 L 192.0 256.0 L 256.0 256.0 L 272.0 256.0\"/></g></svg></div>"
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       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This will be a 4x4 grid\n",
    "H, W = 4, 4\n",
    "horizontal_edges, vertical_edges = sample_random_grid(H, W, np.array([FLAT_ALTERNATIVE]))\n",
    "horizontal_edges[0, 1] = FLAT\n",
    "vertical_edges[1, 0] = FLAT\n",
    "\n",
    "# First, make sure that the overall layout can only be solved one way only\n",
    "assert is_unique(horizontal_edges, vertical_edges)\n",
    "\n",
    "# Show it, to illustrate the purpose\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7613dc43",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "4850it [00:07, 620.60it/s]\n"
     ]
    }
   ],
   "source": [
    "# Choose edge types\n",
    "edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    #LEFT_SMALL_MALE,\n",
    "    CENTERED_MEDIUM_MALE,\n",
    "])\n",
    "edge_types = expand_edge_types(edge_types, opposite, flip)\n",
    "\n",
    "# Generate grid\n",
    "generator = np.random.default_rng(123123)\n",
    "def sampler():\n",
    "    horizontal_edges, vertical_edges = sample_random_grid(H, W, edge_types, generator=generator)\n",
    "    \n",
    "    # Add square in upper-left corner\n",
    "    horizontal_edges[0, 1] = FLAT\n",
    "    vertical_edges[1, 0] = FLAT\n",
    "    \n",
    "    # Central pieces have male pins \"radiating\" outside\n",
    "    horizontal_edges[1:3, 1] = generator.choice([CENTERED_SMALL_MALE, CENTERED_MEDIUM_MALE], size=2)\n",
    "    horizontal_edges[1:3, 3] = generator.choice([CENTERED_SMALL_FEMALE, CENTERED_MEDIUM_FEMALE], size=2)\n",
    "    vertical_edges[1, 1:3] = generator.choice([CENTERED_SMALL_FEMALE, CENTERED_MEDIUM_FEMALE], size=2)\n",
    "    vertical_edges[3, 1:3] = generator.choice([CENTERED_SMALL_MALE, CENTERED_MEDIUM_MALE], size=2)\n",
    "\n",
    "    # Corners that are not next to the square are male only (i.e. they cannot connect with the radiating center)\n",
    "    horizontal_edges[[0, 3], 3] = generator.choice([CENTERED_SMALL_MALE, CENTERED_MEDIUM_MALE], size=2)\n",
    "    horizontal_edges[3, 1] = generator.choice([CENTERED_SMALL_FEMALE, CENTERED_MEDIUM_FEMALE])\n",
    "    vertical_edges[3, [0, 3]] = generator.choice([CENTERED_SMALL_FEMALE, CENTERED_MEDIUM_FEMALE], size=2)\n",
    "    vertical_edges[1, 3] = generator.choice([CENTERED_SMALL_MALE, CENTERED_MEDIUM_MALE])\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "horizontal_edges, vertical_edges = search(sampler, has_unique_pieces, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7c421aaa",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f6d8d66d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_4x4_pure = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfd8fcb0",
   "metadata": {},
   "source": [
    "## 4. 4x4 with more edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ca0a93ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This will be a 4x4 grid\n",
    "H, W = 4, 4\n",
    "horizontal_edges, vertical_edges = sample_random_grid(H, W, np.array([FLAT_ALTERNATIVE]))\n",
    "vertical_edges[2, 1:-1] = FLAT\n",
    "\n",
    "# First, make sure that the overall layout can only be solved one way\n",
    "assert is_unique(horizontal_edges, vertical_edges)\n",
    "\n",
    "# Show it, to illustrate the purpose\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "de190120",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CENTERED_SMALL_MALE', 'CENTERED_SMALL_FEMALE', 'RIGHT_SMALL_MALE',\n",
       "       'RIGHT_SMALL_FEMALE', 'LEFT_SMALL_MALE', 'LEFT_SMALL_FEMALE'],\n",
       "      dtype='<U22')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Choose edge types\n",
    "edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    LEFT_SMALL_MALE,\n",
    "])\n",
    "\n",
    "# Automatically expand types to match combinations\n",
    "edge_types = expand_edge_types(edge_types, opposite, flip)\n",
    "\n",
    "# Show actual types\n",
    "edge_names[edge_types]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "64072a40",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "6it [00:00, 166.68it/s]\n"
     ]
    }
   ],
   "source": [
    "# Generate grid\n",
    "H, W = 4, 4\n",
    "generator = np.random.default_rng(78125)\n",
    "def sampler():\n",
    "    horizontal_edges, vertical_edges = sample_random_grid(H, W, edge_types, generator=generator)\n",
    "    \n",
    "    # Add an horizontal split, so that the inner pieces are also edge pieces\n",
    "    vertical_edges[2, 1:-1] = FLAT\n",
    "    \n",
    "    # Force the two \"internal\" edge pairs to have double pins\n",
    "    horizontal_edges[1:-1, 2] = DOUBLE_SMALL_MALE\n",
    "    \n",
    "    # Force one end of these \"pairs\" to have female centered pins\n",
    "    horizontal_edges[1:-1, 1] = CENTERED_SMALL_FEMALE\n",
    "    \n",
    "    # And then force corners to not provide any male centered pins\n",
    "    # Therefore, these \"pairs\" cannot be connected to a corner\n",
    "    horizontal_edges[[0, 3], 1] = generator.choice([CENTERED_SMALL_MALE, LEFT_SMALL_MALE, LEFT_SMALL_FEMALE, RIGHT_SMALL_MALE, RIGHT_SMALL_FEMALE], size=2)\n",
    "    horizontal_edges[[0, 3], 3] = generator.choice([CENTERED_SMALL_FEMALE, LEFT_SMALL_MALE, LEFT_SMALL_FEMALE, RIGHT_SMALL_MALE, RIGHT_SMALL_FEMALE], size=2)\n",
    "    vertical_edges[1, [0, 3]] = generator.choice([CENTERED_SMALL_FEMALE, LEFT_SMALL_MALE, LEFT_SMALL_FEMALE, RIGHT_SMALL_MALE, RIGHT_SMALL_FEMALE], size=2)\n",
    "    vertical_edges[3, [0, 3]] = generator.choice([CENTERED_SMALL_MALE, LEFT_SMALL_MALE, LEFT_SMALL_FEMALE, RIGHT_SMALL_MALE, RIGHT_SMALL_FEMALE], size=2)\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "horizontal_edges, vertical_edges = search(sampler, has_unique_pieces, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e40e9533",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "01d1fe55",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_4x4_edge = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "983675dd",
   "metadata": {},
   "source": [
    "## 5. 4x4 with 6 corners"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e6f8fca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This will be a 4x4 grid\n",
    "H, W = 4, 4\n",
    "horizontal_edges, vertical_edges = sample_random_grid(H, W, np.array([FLAT_ALTERNATIVE]))\n",
    "horizontal_edges[0, 2] = FLAT\n",
    "\n",
    "# First, make sure that the overall layout can only be solved one way\n",
    "assert is_unique(horizontal_edges, vertical_edges)\n",
    "\n",
    "# Show it, to illustrate the purpose\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2485621e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CENTERED_SMALL_MALE', 'CENTERED_SMALL_FEMALE', 'RIGHT_SMALL_MALE',\n",
       "       'RIGHT_SMALL_FEMALE', 'LEFT_SMALL_MALE', 'LEFT_SMALL_FEMALE'],\n",
       "      dtype='<U22')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Choose edge types\n",
    "edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    LEFT_SMALL_MALE,\n",
    "])\n",
    "\n",
    "# Automatically expand types to match combinations\n",
    "edge_types = expand_edge_types(edge_types, opposite, flip)\n",
    "\n",
    "# Show actual types\n",
    "edge_names[edge_types]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2343e585",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "3it [00:00, 142.89it/s]\n"
     ]
    }
   ],
   "source": [
    "# Generate grid\n",
    "H, W = 4, 4\n",
    "generator = np.random.default_rng(78125)\n",
    "def sampler():\n",
    "    horizontal_edges, vertical_edges = sample_random_grid(H, W, edge_types, generator=generator)\n",
    "    \n",
    "    # Add a single flat edge, so that the top edge pieces become corners\n",
    "    horizontal_edges[0, 2] = FLAT\n",
    "    \n",
    "    # Add some double pins, in such a way that there cannot be ambiguity\n",
    "    # Pairs can be easily identified (but not necessarily orientation)\n",
    "    horizontal_edges[3, 1] = DOUBLE_SMALL_MALE\n",
    "    vertical_edges[1, 1] = DOUBLE_SMALL_MALE\n",
    "    vertical_edges[3, 2] = DOUBLE_SMALL_MALE\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "horizontal_edges, vertical_edges = search(sampler, has_unique_pieces, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "50ea09fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ef6608ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_4x4_6_corners = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97b3f18e",
   "metadata": {},
   "source": [
    "## 6. 4x4 corners-only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9817f3d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This will be a 4x4 grid\n",
    "H, W = 4, 4\n",
    "horizontal_edges, vertical_edges = sample_random_grid(H, W, np.array([FLAT_ALTERNATIVE]))\n",
    "horizontal_edges[:, 2] = FLAT\n",
    "vertical_edges[2, :] = FLAT\n",
    "\n",
    "# First, make sure that the overall layout can only be solved one way\n",
    "assert is_unique(horizontal_edges, vertical_edges)\n",
    "\n",
    "# Show it, to illustrate the purpose\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "4080daf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CENTERED_MEDIUM_MALE', 'CENTERED_MEDIUM_FEMALE',\n",
       "       'CENTERED_SMALL_MALE', 'CENTERED_SMALL_FEMALE', 'RIGHT_SMALL_MALE',\n",
       "       'RIGHT_SMALL_FEMALE', 'LEFT_SMALL_MALE', 'LEFT_SMALL_FEMALE'],\n",
       "      dtype='<U22')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Choose edge types\n",
    "edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    LEFT_SMALL_MALE,\n",
    "    #DOUBLE_SMALL_MALE,\n",
    "    CENTERED_MEDIUM_MALE,\n",
    "])\n",
    "\n",
    "# Automatically expand types to match combinations\n",
    "edge_types = expand_edge_types(edge_types, opposite, flip)\n",
    "\n",
    "# Show actual types\n",
    "edge_names[edge_types]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8e165163",
   "metadata": {},
   "outputs": [],
   "source": [
    "# `is_unique` will not work here, as sub-puzzles may be arranged in too many ways\n",
    "# We will exploit the fact that we need to make exactly 4 unique sub-puzzles\n",
    "\n",
    "from collections import Counter\n",
    "\n",
    "def is_okay(horizontal_edges, vertical_edges):\n",
    "    pieces = grid_to_pieces(horizontal_edges, vertical_edges, opposite)\n",
    "    iterator = iterate_unique_solutions(2, 2, pieces, opposite, flip, constraints=\"border\")\n",
    "    grids = []\n",
    "    for grid in iterator:\n",
    "        grids.append(grid)\n",
    "        if len(grids) > 4:\n",
    "            return False\n",
    "    if len(grids) < 4:\n",
    "        return False\n",
    "    \n",
    "    # Take original set of pieces\n",
    "    available = Counter(map(tuple, canonize_piece(pieces.reshape(-1, 4), flip)))\n",
    "    \n",
    "    # Take generated sub-jigsaws\n",
    "    used = Counter()\n",
    "    for h, v in grids:\n",
    "        ps = canonize_piece(grid_to_pieces(h, v, opposite), flip)\n",
    "        for p in ps.reshape(-1, 4):\n",
    "            used[tuple(p)] += 1\n",
    "    \n",
    "    # This must match\n",
    "    return available == used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "52af0c96",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "9539it [00:16, 594.66it/s]\n"
     ]
    }
   ],
   "source": [
    "# Generate grid\n",
    "H, W = 4, 4\n",
    "generator = np.random.default_rng(123456789)\n",
    "def sampler():\n",
    "    horizontal_edges, vertical_edges = sample_random_grid(H, W, edge_types, generator=generator)\n",
    "    \n",
    "    # Add a single flat edge, so that the top edge pieces become corners\n",
    "    horizontal_edges[:, 2] = FLAT\n",
    "    vertical_edges[2, :] = FLAT\n",
    "    \n",
    "    horizontal_edges[0, 1] = TWISTED_SMALL_MALE\n",
    "    horizontal_edges[0, 3] = TWISTED_SMALL_FEMALE\n",
    "    vertical_edges[1, 1] = TWISTED_SMALL_MALE\n",
    "    \n",
    "    horizontal_edges[3, 1] = LEFT_SMALL_MALE\n",
    "    horizontal_edges[3, 3] = RIGHT_SMALL_MALE\n",
    "    \n",
    "    #vertical_edges[3, 0] = LEFT_SMALL_MALE\n",
    "    #vertical_edges[3, 2] = LEFT_SMALL_FEMALE\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "horizontal_edges, vertical_edges = search(sampler, has_unique_pieces, is_okay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d0a6813b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d31de733",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_4x4_only_corners = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08653700",
   "metadata": {},
   "source": [
    "## 7. 4x4 cycle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "157725bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This will be a 4x4 grid\n",
    "H, W = 4, 4\n",
    "horizontal_edges, vertical_edges = sample_random_grid(H, W, np.array([FLAT_ALTERNATIVE]))\n",
    "vertical_edges[1, 1:-1] = FLAT\n",
    "vertical_edges[2, 2:] = FLAT\n",
    "vertical_edges[3, 1:-1] = FLAT\n",
    "horizontal_edges[1:-1, 1] = FLAT\n",
    "\n",
    "# Show it, to illustrate the purpose\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "48bcdbd3",
   "metadata": {},
   "outputs": [
    {
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      ],
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This design has actually 3 possible layouts\n",
    "display_solutions(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "55328f1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CENTERED_SMALL_MALE', 'CENTERED_SMALL_FEMALE', 'RIGHT_SMALL_MALE',\n",
       "       'RIGHT_SMALL_FEMALE', 'LEFT_SMALL_MALE', 'LEFT_SMALL_FEMALE'],\n",
       "      dtype='<U22')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Choose edge types\n",
    "edge_types = np.array([\n",
    "    CENTERED_SMALL_MALE,\n",
    "    LEFT_SMALL_MALE,\n",
    "    #DOUBLE_SMALL_MALE,\n",
    "])\n",
    "\n",
    "# Automatically expand types to match combinations\n",
    "edge_types = expand_edge_types(edge_types, opposite, flip)\n",
    "\n",
    "# Show actual types\n",
    "edge_names[edge_types]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "be2d06c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "1569it [00:03, 500.87it/s]\n"
     ]
    }
   ],
   "source": [
    "# Generate grid\n",
    "H, W = 4, 4\n",
    "generator = np.random.default_rng(42)\n",
    "def sampler():\n",
    "    horizontal_edges, vertical_edges = sample_random_grid(H, W, edge_types, generator=generator)\n",
    "    \n",
    "    # Add walls\n",
    "    vertical_edges[1, 1:-1] = FLAT\n",
    "    vertical_edges[2, 2:] = FLAT\n",
    "    vertical_edges[3, 1:-1] = FLAT\n",
    "    horizontal_edges[1:-1, 1] = FLAT\n",
    "    \n",
    "    # Add some specific constraints, to force the desired pattern\n",
    "    horizontal_edges[2, 2] = TWISTED_SMALL_MALE\n",
    "    vertical_edges[2, 1] = TWISTED_SMALL_FEMALE\n",
    "    vertical_edges[3, 3] = TWISTED_SMALL_MALE\n",
    "    horizontal_edges[2, 3] = DOUBLE_SMALL_FEMALE\n",
    "    horizontal_edges[3, 3] = DOUBLE_SMALL_MALE\n",
    "    \n",
    "    return horizontal_edges, vertical_edges\n",
    "horizontal_edges, vertical_edges = search(sampler, has_unique_pieces, is_unique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "cdf8f38b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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188.8, 248.0 192.0, 256.0 192.0 L 272.0 192.0 M -16.0 256.0 L 0.0 256.0 L 64.0 256.0 L 128.0 256.0 L 192.0 256.0 L 256.0 256.0 L 272.0 256.0\"/></g></svg></div>"
      ],
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       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show it\n",
    "display_grid(horizontal_edges, vertical_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "f8d3e03b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep it for later\n",
    "pieces_4x4_cycle = grid_to_pieces(horizontal_edges, vertical_edges, opposite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a885b0e2",
   "metadata": {},
   "source": [
    "## Export as SVG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "3ec4f478",
   "metadata": {},
   "outputs": [
    {
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       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Export jigsaw puzzles separately\n",
    "for name, pieces in {\n",
    "    \"01_4x4_cross\": pieces_4x4_cross,\n",
    "    \"02_5x5_nested\": pieces_5x5_nested,\n",
    "    \"03_4x4_pure\": pieces_4x4_pure,\n",
    "    \"04_4x4_edge\": pieces_4x4_edge,\n",
    "    \"05_4x4_6_corners\": pieces_4x4_6_corners,\n",
    "    \"06_4x4_only_corners\": pieces_4x4_only_corners,\n",
    "    \"07_4x4_cycle\": pieces_4x4_cycle,\n",
    "}.items():\n",
    "    horizontal_edges, vertical_edges = pieces_to_grid(pieces, opposite)\n",
    "    display_grid(horizontal_edges, vertical_edges)\n",
    "    with open(f\"image/02_{name}.svg\", \"w\") as file:\n",
    "        file.write(grid_to_svg(horizontal_edges, vertical_edges, margin=1 / 25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "37f9953a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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   ],
   "source": [
    "# Or pack jigsaw puzzles as a single grid\n",
    "pieces = np.zeros((8, 8, 4), dtype=np.uint8)\n",
    "pieces[:4, :4] = pieces_4x4_cycle\n",
    "pieces[4:, :4] = pieces_4x4_6_corners\n",
    "pieces[:4, 4:] = pieces_4x4_edge\n",
    "pieces[4:, 4:] = pieces_4x4_pure\n",
    "horizontal_edges, vertical_edges = pieces_to_grid(pieces, opposite)\n",
    "display_grid(horizontal_edges, vertical_edges)\n",
    "with open(\"image/02.svg\", \"w\") as file:\n",
    "    file.write(grid_to_svg(horizontal_edges, vertical_edges, margin=1 / 25))"
   ]
  }
 ],
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