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May 28, 2025 02:13
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Jane Street Number Cross 5 solution
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "4bb0677a-7df1-4f6b-82fc-133a766ec495", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "%pip install z3-solver==4.12.4 # not working well with 4.15" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "id": "561f1b0b-2aa9-4e16-b2cd-daf64d5bf6be", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import textwrap\n", | |
| "import time\n", | |
| "from functools import partial\n", | |
| "from itertools import chain, combinations, product\n", | |
| "from sympy import fibonacci, primerange\n", | |
| "from z3 import (\n", | |
| " And,\n", | |
| " Distinct,\n", | |
| " Exists,\n", | |
| " Goal,\n", | |
| " If,\n", | |
| " Implies,\n", | |
| " Int,\n", | |
| " IntVector,\n", | |
| " Not,\n", | |
| " Optimize,\n", | |
| " Or,\n", | |
| " Solver,\n", | |
| " Sum,\n", | |
| " Tactic,\n", | |
| " ToInt,\n", | |
| " get_full_version,\n", | |
| " sat,\n", | |
| " set_param,\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 19, | |
| "id": "e46f4542-fac6-4ff6-91e6-58eefc4abd64", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<img src=\"https://www.janestreet.com/puzzles/may-2025-update.png\" width=\"600\"/>" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.Image object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "from IPython.display import Image, display\n", | |
| "\n", | |
| "url = \"https://www.janestreet.com/puzzles/may-2025-update.png\"\n", | |
| "display(Image(url=url, width=600))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 49, | |
| "id": "3b1eb277-f687-4152-bde0-1e381a9881b7", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# pyplot stuff\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "from matplotlib.patches import Rectangle\n", | |
| "\n", | |
| "def draw_grid(\n", | |
| " rows,\n", | |
| " cols,\n", | |
| " ax,\n", | |
| " *,\n", | |
| " grid,\n", | |
| " grid_groups,\n", | |
| " grid_highlights,\n", | |
| " grid_tiles=None,\n", | |
| " grid_deltas=None,\n", | |
| " labels=[],\n", | |
| "):\n", | |
| " grid = np.array(grid)\n", | |
| " if grid_tiles is None:\n", | |
| " grid_tiles = np.ones((rows, cols), dtype=int)\n", | |
| " if grid_deltas is None:\n", | |
| " grid_deltas = np.zeros((rows, cols), dtype=int)\n", | |
| "\n", | |
| " ax.set_xlim(0, cols)\n", | |
| " ax.set_ylim(0, rows)\n", | |
| " ax.set_aspect(\"equal\")\n", | |
| " ax.axis(\"off\")\n", | |
| " # base grid\n", | |
| " for r in range(rows):\n", | |
| " for c in range(cols):\n", | |
| " x, y = c, rows - 1 - r\n", | |
| " is_tiled = grid_tiles[r][c] == 0\n", | |
| " ax.add_patch(\n", | |
| " Rectangle(\n", | |
| " (x, y),\n", | |
| " 1,\n", | |
| " 1,\n", | |
| " facecolor=\"black\" if is_tiled else \"white\",\n", | |
| " edgecolor=\"black\",\n", | |
| " linewidth=1,\n", | |
| " )\n", | |
| " )\n", | |
| " # highlights\n", | |
| " for r in range(rows):\n", | |
| " for c in range(cols):\n", | |
| " if grid_highlights[r, c]:\n", | |
| " ax.add_patch(\n", | |
| " Rectangle(\n", | |
| " (c, rows - 1 - r),\n", | |
| " 1,\n", | |
| " 1,\n", | |
| " facecolor=\"yellow\",\n", | |
| " edgecolor=\"black\",\n", | |
| " linewidth=1,\n", | |
| " )\n", | |
| " )\n", | |
| " # regions\n", | |
| " for r in range(rows):\n", | |
| " for c in range(cols):\n", | |
| " x, y = c, rows - 1 - r\n", | |
| " if r == 0 or grid_groups[r, c] != grid_groups[r - 1, c]:\n", | |
| " ax.plot([x, x + 1], [y + 1, y + 1], color=\"black\", linewidth=3)\n", | |
| " if r == rows - 1 or grid_groups[r, c] != grid_groups[r + 1, c]:\n", | |
| " ax.plot([x, x + 1], [y, y], color=\"black\", linewidth=3)\n", | |
| " if c == 0 or grid_groups[r, c] != grid_groups[r, c - 1]:\n", | |
| " ax.plot([x, x], [y, y + 1], color=\"black\", linewidth=3)\n", | |
| " if c == cols - 1 or grid_groups[r, c] != grid_groups[r, c + 1]:\n", | |
| " ax.plot([x + 1, x + 1], [y, y + 1], color=\"black\", linewidth=3)\n", | |
| " # frame\n", | |
| " ax.plot(\n", | |
| " [0, cols, cols, 0, 0],\n", | |
| " [0, 0, rows, rows, 0],\n", | |
| " color=\"black\",\n", | |
| " linewidth=6,\n", | |
| " )\n", | |
| " # digits\n", | |
| " for r in range(rows):\n", | |
| " for c in range(cols):\n", | |
| " val = int(grid[r, c])\n", | |
| " if val != 0:\n", | |
| " ax.text(\n", | |
| " c + 0.5,\n", | |
| " rows - 1 - r + 0.5,\n", | |
| " str(val),\n", | |
| " color=\"red\" if grid_deltas[r][c] != 0 else \"black\",\n", | |
| " ha=\"center\",\n", | |
| " va=\"center\",\n", | |
| " fontsize=26,\n", | |
| " )\n", | |
| " # labels\n", | |
| " for i, text in enumerate(labels):\n", | |
| " ax.text(\n", | |
| " -0.3,\n", | |
| " rows - 0.5 - i,\n", | |
| " text,\n", | |
| " ha=\"right\",\n", | |
| " va=\"center\",\n", | |
| " fontsize=16,\n", | |
| " )\n", | |
| "\n", | |
| "\n", | |
| "def draw_footer(ax, nums, total):\n", | |
| " props = {\n", | |
| " \"ha\": \"center\",\n", | |
| " \"va\": \"top\",\n", | |
| " \"transform\": ax.transAxes,\n", | |
| " \"fontweight\": 600,\n", | |
| " \"fontsize\": 10,\n", | |
| " }\n", | |
| " ax.text(\n", | |
| " 0.5,\n", | |
| " -0.02,\n", | |
| " \"Answer:\",\n", | |
| " **props,\n", | |
| " )\n", | |
| " ax.text(\n", | |
| " 0.5,\n", | |
| " -0.10,\n", | |
| " \"\\n\".join(\n", | |
| " textwrap.wrap(\" + \".join(map(str, nums)), width=80),\n", | |
| " ),\n", | |
| " **props,\n", | |
| " )\n", | |
| " text = ax.text(\n", | |
| " 0.45,\n", | |
| " -0.18,\n", | |
| " \"= \",\n", | |
| " **props,\n", | |
| " )\n", | |
| " text = ax.annotate(\n", | |
| " total,\n", | |
| " xycoords=text,\n", | |
| " xy=(1, 0),\n", | |
| " verticalalignment=\"bottom\",\n", | |
| " color=\"red\",\n", | |
| " fontsize=12,\n", | |
| " fontweight=600,\n", | |
| " )\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 44, | |
| "id": "f19c88fe-80f8-4a6c-9786-db29cce39fa8", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "class CrossNumbersSolver:\n", | |
| " DIRECTIONS = [(0, -1), (-1, 0), (0, 1), (1, 0)]\n", | |
| "\n", | |
| " def __init__(self, grid, grid_groups, grid_highlights, clues, tactic=\"default\", labels=[]):\n", | |
| " self.solver = Tactic(tactic).solver()\n", | |
| " self.grid_highlights = grid_highlights\n", | |
| " self.rows = grid.shape[0]\n", | |
| " self.cols = grid.shape[1]\n", | |
| " self.clues = clues\n", | |
| " self.labels = labels\n", | |
| " self.grid_groups = grid_groups\n", | |
| " self.empty_grid = np.zeros((self.rows, self.cols), dtype=object)\n", | |
| "\n", | |
| " r, c = self.rows, self.cols\n", | |
| " size = self.rows * self.cols\n", | |
| " self.grid_tiles = np.array(IntVector(\"t\", size), dtype=object).reshape(r, c)\n", | |
| " self.grid = np.array(IntVector(\"x\", size), dtype=object).reshape(r, c)\n", | |
| " self.grid_deltas = np.empty((r, c, 4), dtype=object)\n", | |
| "\n", | |
| " for i in range(r):\n", | |
| " for j in range(c):\n", | |
| " if self.is_highlighed_cell(i, j):\n", | |
| " continue\n", | |
| " for _, nr, nc, dr, dc in self.walk_neighbors(i, j):\n", | |
| " if self.is_highlighed_cell(nr, nc):\n", | |
| " continue\n", | |
| " if nc == 1 or nc == self.cols - 2:\n", | |
| " continue\n", | |
| " index = self.direction_to_index(dr, dc)\n", | |
| " self.grid_deltas[i][j][index] = Int(\"deltas{}_{}_{}\".format(nr, nc, index))\n", | |
| "\n", | |
| " self.group_ids = np.unique(grid_groups)\n", | |
| " self.groups = [(grid_groups == gid).astype(int) for gid in self.group_ids]\n", | |
| " self.group_ints = [Int(\"group_{}\".format(id)) for id in self.group_ids]\n", | |
| "\n", | |
| " def direction_to_index(self, dir_row, dir_col):\n", | |
| " match [dir_row, dir_col]:\n", | |
| " case [0, -1]:\n", | |
| " return 0\n", | |
| " case [-1, 0]:\n", | |
| " return 1\n", | |
| " case [0, 1]:\n", | |
| " return 2\n", | |
| " case [1, 0]:\n", | |
| " return 3\n", | |
| "\n", | |
| " def direction_to_index_inverted(self, dir_row, dir_col):\n", | |
| " match [dir_row, dir_col]:\n", | |
| " case [0, -1]:\n", | |
| " return 2\n", | |
| " case [-1, 0]:\n", | |
| " return 3\n", | |
| " case [0, 1]:\n", | |
| " return 0\n", | |
| " case [1, 0]:\n", | |
| " return 1\n", | |
| "\n", | |
| " def eval_grid(self, model, grid):\n", | |
| " res = np.ones((self.rows, self.cols), dtype=int)\n", | |
| " for row_index, row in enumerate(grid):\n", | |
| " for col_index, col in enumerate(row):\n", | |
| " if isinstance(col, np.ndarray):\n", | |
| " res[row_index][col_index] = sum(\n", | |
| " [model.eval(x).as_long() for x in col if x is not None]\n", | |
| " )\n", | |
| " else:\n", | |
| " res[row_index][col_index] = model.eval(col).as_long()\n", | |
| " return res\n", | |
| "\n", | |
| " def merge_grids(self, grid, grid_delta, grid_tiles):\n", | |
| " grid = np.array(grid)\n", | |
| " grid_delta = np.array(grid_delta)\n", | |
| " grid_tiles = np.array(grid_tiles)\n", | |
| " merged = grid + grid_delta\n", | |
| " merged[grid == 0] = 0\n", | |
| " merged[grid_tiles == 0] = 0\n", | |
| " return merged\n", | |
| "\n", | |
| " def sum_total(self, grid):\n", | |
| " total = 0\n", | |
| " nums = []\n", | |
| " for row in grid:\n", | |
| " num = 0\n", | |
| " total_row = 0\n", | |
| " for digit in row:\n", | |
| " if digit != 0:\n", | |
| " num = num * 10 + digit\n", | |
| " else:\n", | |
| " if num > 0:\n", | |
| " nums.append(int(num))\n", | |
| " total_row += num\n", | |
| " num = 0\n", | |
| " if num > 0:\n", | |
| " total_row += num\n", | |
| " nums.append(int(num))\n", | |
| " total += total_row\n", | |
| " return total, nums\n", | |
| "\n", | |
| " def generate_fibonacci(self):\n", | |
| " res = []\n", | |
| " for i in range(1, 60):\n", | |
| " fib = fibonacci(i)\n", | |
| " length = len(str(fib))\n", | |
| " if len(res) == length:\n", | |
| " res[length - 1].append(fib)\n", | |
| " else:\n", | |
| " res.append([fib])\n", | |
| " return res\n", | |
| "\n", | |
| " def generate_primes(self, max_digits):\n", | |
| " result = [[] for _ in range(max_digits)]\n", | |
| " for n_digits in range(1, max_digits + 1):\n", | |
| " for p in primerange(10 ** (n_digits - 1), 10**n_digits):\n", | |
| " if \"0\" not in str(p):\n", | |
| " result[n_digits - 1].append(p)\n", | |
| " return result\n", | |
| "\n", | |
| " def walk_group(self, index: int):\n", | |
| " group = self.groups[index]\n", | |
| " for row, col in np.argwhere(group == 1):\n", | |
| " yield self.grid[row][col], row, col\n", | |
| "\n", | |
| " def walk_neighbors(self, row, col, directions=DIRECTIONS):\n", | |
| " for dir_row, dir_col in directions:\n", | |
| " next_row = row + dir_row\n", | |
| " next_col = col + dir_col\n", | |
| " if (\n", | |
| " next_row >= 0\n", | |
| " and next_row <= (self.rows - 1)\n", | |
| " and next_col >= 0\n", | |
| " and next_col <= (self.cols - 1)\n", | |
| " ):\n", | |
| " yield (\n", | |
| " self.grid_tiles[next_row][next_col],\n", | |
| " next_row,\n", | |
| " next_col,\n", | |
| " dir_row,\n", | |
| " dir_col,\n", | |
| " )\n", | |
| "\n", | |
| " def walk_digits(self, row_index, min=2):\n", | |
| " slices = ((l, r) for l, r in combinations(range(self.cols + 1), 2) if r > l + (min - 1))\n", | |
| " for l, r in slices:\n", | |
| " digits = []\n", | |
| " for i, d in enumerate(self.grid[row_index][l:r]):\n", | |
| " col_index = l + i\n", | |
| " sum_delta = self.get_sum_deltas(row_index, col_index)\n", | |
| " digits.append(d + sum_delta)\n", | |
| " yield digits, l, r\n", | |
| "\n", | |
| " def get_deltas(self, row, col):\n", | |
| " return [d for d in self.grid_deltas[row][col] if d is not None]\n", | |
| "\n", | |
| " def get_sum_deltas(self, row, col):\n", | |
| " return Sum(self.get_deltas(row, col))\n", | |
| "\n", | |
| " def is_highlighed_cell(self, row, col):\n", | |
| " return self.grid_highlights[row][col] == 1\n", | |
| "\n", | |
| " def is_digit_match(self, row_index, l, r):\n", | |
| " return And(\n", | |
| " l == 0 or self.grid_tiles[row_index][l - 1] == 0,\n", | |
| " r == self.cols or self.grid_tiles[row_index][r] == 0,\n", | |
| " And([b != 0 for b in self.grid_tiles[row_index][l:r]]),\n", | |
| " )\n", | |
| "\n", | |
| " def sum_digits(self, digits):\n", | |
| " return sum(10**i * digits[-1 - i] for i in range(len(digits)))\n", | |
| "\n", | |
| " def is_square_value(self, value):\n", | |
| " x = Int(f\"sq_{value.hash()}\")\n", | |
| " return And(x >= 0, value == x * x)\n", | |
| "\n", | |
| " def is_square(self, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(\n", | |
| " # Hack to removes duplicates, hardcoded for now\n", | |
| " Implies(len(digits) == 3 and (l == 0 or l == 4), block != 225),\n", | |
| " self.is_square_value(block),\n", | |
| " ),\n", | |
| " # ToInt(block**0.5) == block**0.5, # this crashes z3\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_product_of_20(self, row_index):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " count_2 = Sum([If(d == 2, 1, 0) for d in digits])\n", | |
| " count_4 = Sum([If(d == 4, 1, 0) for d in digits])\n", | |
| " count_5 = Sum([If(d == 5, 1, 0) for d in digits])\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(\n", | |
| " And([Or(d == 1, d == 2, d == 4, d == 5) for d in digits]),\n", | |
| " count_5 == 1,\n", | |
| " count_4 < 2,\n", | |
| " Implies(count_4 == 1, count_2 == 0),\n", | |
| " Implies(count_4 == 0, count_2 == 2),\n", | |
| " ),\n", | |
| " ),\n", | |
| " )\n", | |
| "\n", | |
| " def is_product_of_25(self, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(\n", | |
| " And([Or(d == 1, d == 5) for d in digits]),\n", | |
| " Sum([If(d == 5, 1, 0) for d in digits]) == 2,\n", | |
| " ),\n", | |
| " ),\n", | |
| " )\n", | |
| "\n", | |
| " def is_product_of_2025(self, row_index):\n", | |
| " self.solver.add(\n", | |
| " And(\n", | |
| " self.grid_tiles[row_index][2] == 1,\n", | |
| " self.grid_tiles[row_index][3] == 1,\n", | |
| " self.grid_tiles[row_index][self.cols - 3] == 1,\n", | |
| " self.grid_tiles[row_index][self.cols - 4] == 1,\n", | |
| " )\n", | |
| " )\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.grid_tiles[row_index][0] == 0,\n", | |
| " And(\n", | |
| " self.grid_tiles[row_index][3] != 0,\n", | |
| " self.grid_tiles[row_index][4] != 0,\n", | |
| " ),\n", | |
| " )\n", | |
| " )\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.grid_tiles[row_index][self.cols - 1] == 0,\n", | |
| " And(\n", | |
| " self.grid_tiles[row_index][self.cols - 4] != 0,\n", | |
| " self.grid_tiles[row_index][self.cols - 5] != 0,\n", | |
| " ),\n", | |
| " )\n", | |
| " )\n", | |
| " for digits, l, r in self.walk_digits(row_index, 4):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " count_5 = Sum([If(d == 5, 1, 0) for d in digits])\n", | |
| " count_9 = Sum([If(d == 9, 1, 0) for d in digits])\n", | |
| " count_3 = Sum([If(d == 3, 1, 0) for d in digits])\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(\n", | |
| " block >= 5599, # needed\n", | |
| " And([Or(d == 1, d == 3, d == 5, d == 9) for d in digits]),\n", | |
| " count_5 == 2,\n", | |
| " Or(count_3 == 0, count_3 == 2, count_3 == 3, count_3 == 4),\n", | |
| " Implies(count_3 >= 3, count_9 == 0),\n", | |
| " Implies(count_9 == 1, count_3 >= 2),\n", | |
| " ),\n", | |
| " ),\n", | |
| " )\n", | |
| "\n", | |
| " # only for example\n", | |
| " def is_multiple_of(self, value: int, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " x = Int(f\"mult_{row_index}_{block.hash()}_div_{value}\")\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " block == x * value,\n", | |
| " # block % value == 0,\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_multiple_of_13(self, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " x = Int(f\"mult_{row_index}_{block.hash()}_13\")\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " # block == q * 13,\n", | |
| " If(\n", | |
| " len(digits) == 2,\n", | |
| " Or(\n", | |
| " block == 13,\n", | |
| " block == 26,\n", | |
| " block == 39,\n", | |
| " block == 52,\n", | |
| " block == 65,\n", | |
| " block == 78,\n", | |
| " block == 91,\n", | |
| " ),\n", | |
| " block == x * 13,\n", | |
| " ),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_multiple_of_32(self, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " x = Int(f\"mult_{row_index}_{block.hash()}_32\")\n", | |
| " last_digit = digits[len(digits) - 1]\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(\n", | |
| " Or([last_digit == 2, last_digit == 4, last_digit == 6, last_digit == 8]),\n", | |
| " block == x * 32,\n", | |
| " # block % 32 == 0,\n", | |
| " ),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_divisible(self, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index, 2):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " cons = []\n", | |
| " for d in digits:\n", | |
| " x = Int(\"div_{}{}\".format(row_index, d.hash()))\n", | |
| " cons.append(block == x * d)\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(cons),\n", | |
| " # And([(block % d) == 0 for d in digits]),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_odd_palindrome(self, row_index: int):\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " And(\n", | |
| " block % 2 != 0,\n", | |
| " And([digits[i] == digits[-1 - i] for i in range(len(digits) // 2)]),\n", | |
| " ),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_fibonacci(self, row_index: int):\n", | |
| " fibs = self.generate_fibonacci()\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " Or([block == s for s in fibs[len(digits) - 1]]),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def is_prime(self, row_index: int):\n", | |
| " n = 3\n", | |
| " primes = self.generate_primes(n)\n", | |
| " for digits, l, r in self.walk_digits(row_index):\n", | |
| " block = self.sum_digits(digits)\n", | |
| " if len(digits) <= n:\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " Or([block == x for x in primes[len(digits) - 1]]),\n", | |
| " )\n", | |
| " )\n", | |
| " else:\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " self.is_digit_match(row_index, l, r),\n", | |
| " Or(block % 10 == 1, block % 10 == 3, block % 10 == 7, block % 10 == 9),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def constrain_neighbors(self, cell, row, col):\n", | |
| " neighbors = []\n", | |
| " for neighbor, next_row, next_col, _, dir_col in self.walk_neighbors(row, col):\n", | |
| " neighbors.append(neighbor)\n", | |
| " if dir_col != 0:\n", | |
| " for n in self.walk_neighbors(next_row, next_col, directions=[[0, dir_col]]):\n", | |
| " neighbors.append(n[0])\n", | |
| " self.solver.add(\n", | |
| " Implies(\n", | |
| " cell == 0,\n", | |
| " And([n != 0 for n in neighbors]),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " def walk_neighbors_delta_combinations(self, iterable):\n", | |
| " s = list(iterable)\n", | |
| " n = len(s)\n", | |
| " for r in range(1, n + 1):\n", | |
| " for subset in combinations(s, r):\n", | |
| " subset_set = set(subset)\n", | |
| " rest = [item for item in s if item not in subset_set]\n", | |
| " yield [s for s in subset if s is not None], rest\n", | |
| "\n", | |
| " def solve(self):\n", | |
| " print(f\"Initialized solution for {self.rows} rows and {self.cols} cols\")\n", | |
| " self.solver.add([And(g >= 1, g <= 9) for g in self.group_ints])\n", | |
| "\n", | |
| " for group_index, g in enumerate(self.groups):\n", | |
| " for cell, row, col in self.walk_group(group_index):\n", | |
| " deltas = self.get_deltas(row, col)\n", | |
| " sum_deltas = self.get_sum_deltas(row, col)\n", | |
| " tile = self.grid_tiles[row][col]\n", | |
| " self.constrain_neighbors(tile, row, col)\n", | |
| "\n", | |
| " self.solver.add(And(tile >= 0, tile <= 1), cell == self.group_ints[group_index])\n", | |
| "\n", | |
| " if self.is_highlighed_cell(row, col):\n", | |
| " self.solver.add(tile == 1, sum_deltas == 0)\n", | |
| " else:\n", | |
| " self.solver.add(\n", | |
| " And([d >= 0 for d in deltas]),\n", | |
| " sum_deltas < (10 - self.group_ints[group_index]),\n", | |
| " )\n", | |
| "\n", | |
| " if col == 1 or col == self.cols - 2:\n", | |
| " self.solver.add(tile == 1)\n", | |
| "\n", | |
| " neighbors = []\n", | |
| " neighbor_deltas = []\n", | |
| " for neighbor, nr, nc, dr, dc in self.walk_neighbors(row, col):\n", | |
| " neighbors.append(neighbor)\n", | |
| " delta_index = self.direction_to_index_inverted(dr, dc)\n", | |
| " d = self.grid_deltas[nr][nc][delta_index]\n", | |
| " if d is not None:\n", | |
| " neighbor_deltas.append(d)\n", | |
| "\n", | |
| " neighbor_is_zero = Or([n == 0 for n in neighbors])\n", | |
| " self.solver.add(Implies(Not(neighbor_is_zero), sum_deltas == 0))\n", | |
| "\n", | |
| " possible_sums = []\n", | |
| " for increments, rest in self.walk_neighbors_delta_combinations(neighbor_deltas):\n", | |
| " possible_sums.append(\n", | |
| " And(\n", | |
| " Sum(increments) == self.group_ints[group_index], # force the increments\n", | |
| " And([r == 0 for r in rest]),\n", | |
| " )\n", | |
| " )\n", | |
| "\n", | |
| " self.solver.add(\n", | |
| " If(\n", | |
| " tile == 0,\n", | |
| " Or(possible_sums),\n", | |
| " And([n == 0 for n in neighbor_deltas]),\n", | |
| " ),\n", | |
| " )\n", | |
| "\n", | |
| " for row_index in range(self.rows):\n", | |
| " clue = self.clues[row_index]\n", | |
| " clue(row_index)\n", | |
| "\n", | |
| " print(\"checking...\")\n", | |
| " if self.solver.check() == sat:\n", | |
| " model = self.solver.model()\n", | |
| " groups = [model.eval(g) for g in self.group_ints]\n", | |
| " grid = self.eval_grid(model, self.grid)\n", | |
| " grid_deltas = self.eval_grid(model, self.grid_deltas)\n", | |
| " grid_tiles = self.eval_grid(model, self.grid_tiles)\n", | |
| " grid_placements = self.eval_grid(model, self.grid)\n", | |
| " grid_final = self.merge_grids(grid, grid_deltas, grid_tiles)\n", | |
| " total, nums = self.sum_total(grid_final)\n", | |
| " print(\"Satisfied!\")\n", | |
| " # print(self.solver.statistics())\n", | |
| " print(\"\")\n", | |
| " print(\"Groups\\n\", groups)\n", | |
| " print(\"\")\n", | |
| " print(\"Tiles\\n\", grid_tiles)\n", | |
| " print(\"\")\n", | |
| " print(\"Increments\\n\", grid_deltas)\n", | |
| " print(\"\")\n", | |
| " print(\"Initial Placements\\n\", grid_placements)\n", | |
| " print(\"\")\n", | |
| " print(\"Final Grid\\n\", grid_final)\n", | |
| " print(\"\")\n", | |
| " print(\"numbers:\", nums)\n", | |
| " print(\"total:\", total)\n", | |
| " rows, cols = self.rows, self.cols\n", | |
| " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(cols, rows))\n", | |
| " fig.set_figwidth((cols * 2) + 3)\n", | |
| " fig.set_figheight(rows + 1)\n", | |
| " ax1.set_title(\"(after initial placement)\", fontsize=14)\n", | |
| " title = ax2.set_title(\n", | |
| " \"(after tiles placed; altered values in \",\n", | |
| " fontsize=14,\n", | |
| " loc=\"center\",\n", | |
| " )\n", | |
| " title = ax2.annotate(\n", | |
| " \"red\",\n", | |
| " xycoords=title,\n", | |
| " xy=(1, 0),\n", | |
| " verticalalignment=\"bottom\",\n", | |
| " color=\"red\",\n", | |
| " fontsize=14,\n", | |
| " )\n", | |
| " title = ax2.annotate(\n", | |
| " \")\",\n", | |
| " xycoords=title,\n", | |
| " xy=(1, 0),\n", | |
| " verticalalignment=\"bottom\",\n", | |
| " color=\"black\",\n", | |
| " fontsize=14,\n", | |
| " )\n", | |
| " draw_grid(\n", | |
| " rows,\n", | |
| " cols,\n", | |
| " ax1,\n", | |
| " grid=grid_placements,\n", | |
| " grid_groups=self.grid_groups,\n", | |
| " grid_highlights=self.grid_highlights,\n", | |
| " labels=self.labels,\n", | |
| " )\n", | |
| " draw_grid(\n", | |
| " rows,\n", | |
| " cols,\n", | |
| " ax2,\n", | |
| " grid=grid_final,\n", | |
| " grid_groups=self.grid_groups,\n", | |
| " grid_highlights=self.grid_highlights,\n", | |
| " grid_tiles=grid_tiles,\n", | |
| " grid_deltas=grid_deltas,\n", | |
| " labels=self.labels,\n", | |
| " )\n", | |
| " draw_footer(ax2, nums, total)\n", | |
| " plt.tight_layout(pad=2)\n", | |
| " plt.show()\n", | |
| " else:\n", | |
| " print(\"Not sat\")\n", | |
| " print(\"conflict:\", self.solver.unsat_core())\n", | |
| " print(\"reason:\", self.solver.reason_unknown())\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 45, | |
| "id": "15662e3b-9c7d-4a5b-a74c-6aab4d706048", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Initialized solution for 5 rows and 5 cols\n", | |
| "checking...\n", | |
| "Satisfied!\n", | |
| "\n", | |
| "Groups\n", | |
| " [5, 2, 9]\n", | |
| "\n", | |
| "Tiles\n", | |
| " [[1 1 0 1 1]\n", | |
| " [1 1 1 1 0]\n", | |
| " [1 1 0 1 1]\n", | |
| " [0 1 1 1 1]\n", | |
| " [1 1 1 1 1]]\n", | |
| "\n", | |
| "Increments\n", | |
| " [[0 0 0 3 3]\n", | |
| " [0 0 2 1 0]\n", | |
| " [6 2 0 0 1]\n", | |
| " [0 3 3 0 0]\n", | |
| " [0 0 0 0 0]]\n", | |
| "\n", | |
| "Initial Placements\n", | |
| " [[5 5 5 5 5]\n", | |
| " [2 5 5 5 5]\n", | |
| " [2 2 5 5 5]\n", | |
| " [9 2 2 5 5]\n", | |
| " [9 9 2 2 5]]\n", | |
| "\n", | |
| "Final Grid\n", | |
| " [[5 5 0 8 8]\n", | |
| " [2 5 7 6 0]\n", | |
| " [8 4 0 5 6]\n", | |
| " [0 5 5 5 5]\n", | |
| " [9 9 2 2 5]]\n", | |
| "\n", | |
| "numbers: [55, 88, 2576, 84, 56, 5555, 99225]\n", | |
| "total: 107639\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<Figure size 1300x600 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "\n", | |
| "done in 0.19107985496520996\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "def solve_example():\n", | |
| " example_grid = np.ones((5, 5), dtype=int)\n", | |
| " example_groups = np.array(\n", | |
| " [\n", | |
| " [1, 1, 1, 1, 1],\n", | |
| " [2, 1, 1, 1, 1],\n", | |
| " [2, 2, 1, 1, 1],\n", | |
| " [3, 2, 2, 1, 1],\n", | |
| " [3, 3, 2, 2, 1],\n", | |
| " ]\n", | |
| " )\n", | |
| " example_highligths = np.array(\n", | |
| " [\n", | |
| " [1, 1, 0, 0, 0],\n", | |
| " [1, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 1],\n", | |
| " [0, 0, 0, 1, 1],\n", | |
| " ]\n", | |
| " )\n", | |
| "\n", | |
| " solver = CrossNumbersSolver(\n", | |
| " grid=example_grid,\n", | |
| " grid_groups=example_groups,\n", | |
| " grid_highlights=example_highligths,\n", | |
| " clues=[],\n", | |
| " tactic=\"default\",\n", | |
| " labels=[\n", | |
| " \"multiple of 11\",\n", | |
| " \"multiple of 14\",\n", | |
| " \"multiple of 28\",\n", | |
| " \"multiple of 101\",\n", | |
| " \"multiple of 2025\",\n", | |
| " ],\n", | |
| " )\n", | |
| " solver.clues = [\n", | |
| " partial(solver.is_multiple_of, 11),\n", | |
| " partial(solver.is_multiple_of, 14),\n", | |
| " partial(solver.is_multiple_of, 28),\n", | |
| " partial(solver.is_multiple_of, 101),\n", | |
| " partial(solver.is_multiple_of, 2025),\n", | |
| " ]\n", | |
| " solver.solver.add(\n", | |
| " And(\n", | |
| " solver.group_ints[1] != solver.group_ints[0],\n", | |
| " solver.group_ints[1] != solver.group_ints[2],\n", | |
| " )\n", | |
| " )\n", | |
| " solver.solver.add(\n", | |
| " solver.group_ints[0] == 5,\n", | |
| " solver.group_ints[1] == 2,\n", | |
| " solver.group_ints[2] == 9,\n", | |
| " )\n", | |
| " solver.solve()\n", | |
| "\n", | |
| "start = time.time()\n", | |
| "solve_example()\n", | |
| "end = time.time() - start\n", | |
| "print(\"\")\n", | |
| "print(f\"done in {end}\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 50, | |
| "id": "fa17504a-cc44-465b-b3fe-e75bf1b14362", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Initialized solution for 11 rows and 11 cols\n", | |
| "checking...\n", | |
| "Satisfied!\n", | |
| "\n", | |
| "Groups\n", | |
| " [2, 3, 4, 4, 1, 6, 3, 7, 7]\n", | |
| "\n", | |
| "Tiles\n", | |
| " [[0 1 1 1 1 1 1 0 1 1 1]\n", | |
| " [1 1 0 1 1 1 0 1 1 1 0]\n", | |
| " [0 1 1 1 1 0 1 1 0 1 1]\n", | |
| " [1 1 1 0 1 1 0 1 1 1 0]\n", | |
| " [0 1 1 1 0 1 1 0 1 1 1]\n", | |
| " [1 1 0 1 1 1 0 1 1 1 0]\n", | |
| " [0 1 1 1 1 1 1 1 0 1 1]\n", | |
| " [1 1 1 0 1 1 1 0 1 1 0]\n", | |
| " [1 1 0 1 1 1 1 1 0 1 1]\n", | |
| " [1 1 1 1 1 0 1 1 1 1 0]\n", | |
| " [0 1 1 0 1 1 1 0 1 1 1]]\n", | |
| "\n", | |
| "Increments\n", | |
| " [[0 1 2 0 0 0 3 0 1 0 2]\n", | |
| " [3 0 0 0 0 3 0 0 3 0 0]\n", | |
| " [0 1 0 1 0 0 2 1 0 0 2]\n", | |
| " [3 0 3 0 0 1 0 1 0 0 0]\n", | |
| " [0 2 2 1 0 1 1 0 4 0 2]\n", | |
| " [1 1 0 1 1 0 0 0 4 4 0]\n", | |
| " [0 0 0 1 0 0 0 1 0 0 4]\n", | |
| " [3 0 1 0 3 0 3 0 3 2 0]\n", | |
| " [0 1 0 1 0 0 0 1 0 1 2]\n", | |
| " [2 0 2 6 0 0 2 6 6 2 0]\n", | |
| " [0 1 0 0 1 1 0 0 1 0 0]]\n", | |
| "\n", | |
| "Initial Placements\n", | |
| " [[2 2 2 2 2 2 2 2 2 2 2]\n", | |
| " [2 4 2 2 2 2 2 2 2 2 2]\n", | |
| " [4 4 3 3 3 3 4 4 4 2 4]\n", | |
| " [4 3 3 4 3 1 4 4 4 4 4]\n", | |
| " [4 3 3 4 3 1 1 4 4 1 4]\n", | |
| " [4 4 4 4 4 1 1 1 1 1 4]\n", | |
| " [4 3 6 6 4 4 1 1 6 1 1]\n", | |
| " [4 3 6 6 6 6 6 6 6 7 7]\n", | |
| " [3 3 3 3 6 3 6 7 7 7 7]\n", | |
| " [3 3 3 3 3 3 3 3 3 3 3]\n", | |
| " [3 3 7 7 7 7 7 7 3 3 3]]\n", | |
| "\n", | |
| "Final Grid\n", | |
| " [[0 3 4 2 2 2 5 0 3 2 4]\n", | |
| " [5 4 0 2 2 5 0 2 5 2 0]\n", | |
| " [0 5 3 4 3 0 6 5 0 2 6]\n", | |
| " [7 3 6 0 3 2 0 5 4 4 0]\n", | |
| " [0 5 5 5 0 2 2 0 8 1 6]\n", | |
| " [5 5 0 5 5 1 0 1 5 5 0]\n", | |
| " [0 3 6 7 4 4 1 2 0 1 5]\n", | |
| " [7 3 7 0 9 6 9 0 9 9 0]\n", | |
| " [3 4 0 4 6 3 6 8 0 8 9]\n", | |
| " [5 3 5 9 3 0 5 9 9 5 0]\n", | |
| " [0 4 7 0 8 8 7 0 4 3 3]]\n", | |
| "\n", | |
| "numbers: [342225, 324, 54, 225, 252, 5343, 65, 26, 736, 32, 544, 555, 22, 816, 55, 551, 155, 3674412, 15, 737, 969, 99, 34, 46368, 89, 53593, 5995, 47, 887, 433]\n", | |
| "total: 4135658\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<Figure size 2500x1200 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "\n", | |
| "done in 33.158448934555054\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "def solve_main():\n", | |
| " grid_groups = np.array(\n", | |
| " [\n", | |
| " [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n", | |
| " [1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n", | |
| " [3, 3, 2, 2, 2, 2, 4, 4, 4, 1, 4],\n", | |
| " [3, 2, 2, 3, 2, 5, 4, 4, 4, 4, 4],\n", | |
| " [3, 2, 2, 3, 2, 5, 5, 4, 4, 5, 4],\n", | |
| " [3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 4],\n", | |
| " [3, 7, 6, 6, 3, 3, 5, 5, 6, 5, 5],\n", | |
| " [3, 7, 6, 6, 6, 6, 6, 6, 6, 9, 9],\n", | |
| " [7, 7, 7, 7, 6, 7, 6, 9, 9, 9, 9],\n", | |
| " [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n", | |
| " [7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7],\n", | |
| " ]\n", | |
| " )\n", | |
| "\n", | |
| " grid_highlights = np.array(\n", | |
| " [\n", | |
| " [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0],\n", | |
| " [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0],\n", | |
| " [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n", | |
| " [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0],\n", | |
| " [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n", | |
| " [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", | |
| " ]\n", | |
| " )\n", | |
| "\n", | |
| " grid = np.ones((11, 11), dtype=int)\n", | |
| "\n", | |
| " solver = CrossNumbersSolver(\n", | |
| " grid=grid,\n", | |
| " grid_groups=grid_groups,\n", | |
| " grid_highlights=grid_highlights,\n", | |
| " clues=[],\n", | |
| " tactic=\"default\",\n", | |
| " labels=[\n", | |
| " \"square\",\n", | |
| " \"product digits is 20\",\n", | |
| " \"multiple of 13\",\n", | |
| " \"multiple of 32\",\n", | |
| " \"divisible by each of its digits\",\n", | |
| " \"product of digits is 25\",\n", | |
| " \"divisible by each of its digits\",\n", | |
| " \"odd and a palindrome\",\n", | |
| " \"fibonacci\",\n", | |
| " \"product of digits are 2025\",\n", | |
| " \"prime\",\n", | |
| " ],\n", | |
| " )\n", | |
| " solver.clues = [\n", | |
| " solver.is_square,\n", | |
| " solver.is_product_of_20,\n", | |
| " solver.is_multiple_of_13,\n", | |
| " solver.is_multiple_of_32,\n", | |
| " solver.is_divisible,\n", | |
| " solver.is_product_of_25,\n", | |
| " solver.is_divisible,\n", | |
| " solver.is_odd_palindrome,\n", | |
| " solver.is_fibonacci,\n", | |
| " solver.is_product_of_2025,\n", | |
| " solver.is_prime,\n", | |
| " ]\n", | |
| " solver.solver.add(\n", | |
| " Or(\n", | |
| " solver.group_ints[0] == 1,\n", | |
| " solver.group_ints[0] == 2,\n", | |
| " solver.group_ints[0] == 4,\n", | |
| " solver.group_ints[0] == 5,\n", | |
| " ),\n", | |
| " Or(\n", | |
| " solver.group_ints[4] == 1,\n", | |
| " solver.group_ints[4] == 5,\n", | |
| " ),\n", | |
| " Or(\n", | |
| " solver.group_ints[6] == 1,\n", | |
| " solver.group_ints[6] == 3,\n", | |
| " solver.group_ints[6] == 5,\n", | |
| " solver.group_ints[6] == 9,\n", | |
| " ),\n", | |
| " )\n", | |
| " # group hints, (we are forcing the correct regions here, without this it takes a really long time)\n", | |
| " solver.solver.add(\n", | |
| " solver.group_ints[0] == 2,\n", | |
| " solver.group_ints[1] == 3,\n", | |
| " solver.group_ints[2] == 4,\n", | |
| " solver.group_ints[3] == 4,\n", | |
| " solver.group_ints[4] == 1,\n", | |
| " solver.group_ints[5] == 6,\n", | |
| " solver.group_ints[6] == 3,\n", | |
| " solver.group_ints[7] == 7,\n", | |
| " solver.group_ints[8] == 7,\n", | |
| " )\n", | |
| " solver.solver.add(\n", | |
| " solver.group_ints[0] != solver.group_ints[1],\n", | |
| " solver.group_ints[0] != solver.group_ints[2],\n", | |
| " solver.group_ints[0] != solver.group_ints[3],\n", | |
| " # region 2\n", | |
| " solver.group_ints[1] != solver.group_ints[0],\n", | |
| " solver.group_ints[1] != solver.group_ints[2],\n", | |
| " solver.group_ints[1] != solver.group_ints[3],\n", | |
| " solver.group_ints[1] != solver.group_ints[4],\n", | |
| " # region 3\n", | |
| " solver.group_ints[2] != solver.group_ints[0],\n", | |
| " solver.group_ints[2] != solver.group_ints[1],\n", | |
| " solver.group_ints[2] != solver.group_ints[4],\n", | |
| " solver.group_ints[2] != solver.group_ints[5],\n", | |
| " solver.group_ints[2] != solver.group_ints[6],\n", | |
| " # region 4\n", | |
| " solver.group_ints[3] != solver.group_ints[0],\n", | |
| " solver.group_ints[3] != solver.group_ints[1],\n", | |
| " solver.group_ints[3] != solver.group_ints[4],\n", | |
| " # region 5\n", | |
| " solver.group_ints[4] != solver.group_ints[1],\n", | |
| " solver.group_ints[4] != solver.group_ints[2],\n", | |
| " solver.group_ints[4] != solver.group_ints[3],\n", | |
| " solver.group_ints[4] != solver.group_ints[5],\n", | |
| " solver.group_ints[4] != solver.group_ints[8],\n", | |
| " # region 6\n", | |
| " solver.group_ints[5] != solver.group_ints[2],\n", | |
| " solver.group_ints[5] != solver.group_ints[4],\n", | |
| " solver.group_ints[5] != solver.group_ints[6],\n", | |
| " solver.group_ints[5] != solver.group_ints[8],\n", | |
| " # region 7\n", | |
| " solver.group_ints[6] != solver.group_ints[2],\n", | |
| " solver.group_ints[6] != solver.group_ints[5],\n", | |
| " solver.group_ints[6] != solver.group_ints[7],\n", | |
| " solver.group_ints[6] != solver.group_ints[8],\n", | |
| " # region 8\n", | |
| " solver.group_ints[7] != solver.group_ints[6],\n", | |
| " # region 9\n", | |
| " solver.group_ints[8] != solver.group_ints[4],\n", | |
| " solver.group_ints[8] != solver.group_ints[5],\n", | |
| " solver.group_ints[8] != solver.group_ints[6],\n", | |
| " )\n", | |
| " solver.solve()\n", | |
| "\n", | |
| "start = time.time()\n", | |
| "solve_main()\n", | |
| "end = time.time() - start\n", | |
| "print(\"\")\n", | |
| "print(f\"done in {end}\")\n" | |
| ] | |
| } | |
| ], | |
| "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": "3.12.9" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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