259 lines
8.1 KiB
Plaintext
259 lines
8.1 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "google",
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"metadata": {},
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"source": [
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"##### Copyright 2025 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "apache",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "basename",
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"metadata": {},
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"source": [
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"# kakuro"
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]
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},
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{
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"cell_type": "markdown",
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"id": "link",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/kakuro.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/kakuro.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "doc",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "install",
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"metadata": {},
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"outputs": [],
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"source": [
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"%pip install ortools"
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]
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},
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{
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"cell_type": "markdown",
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"id": "description",
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"metadata": {},
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"source": [
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"\n",
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"\n",
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" Kakuru puzzle in Google CP Solver.\n",
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"\n",
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" http://en.wikipedia.org/wiki/Kakuro\n",
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" '''\n",
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" The object of the puzzle is to insert a digit from 1 to 9 inclusive\n",
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" into each white cell such that the sum of the numbers in each entry\n",
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" matches the clue associated with it and that no digit is duplicated in\n",
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" any entry. It is that lack of duplication that makes creating Kakuro\n",
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" puzzles with unique solutions possible, and which means solving a Kakuro\n",
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" puzzle involves investigating combinations more, compared to Sudoku in\n",
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" which the focus is on permutations. There is an unwritten rule for\n",
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" making Kakuro puzzles that each clue must have at least two numbers\n",
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" that add up to it. This is because including one number is mathematically\n",
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" trivial when solving Kakuro puzzles; one can simply disregard the\n",
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" number entirely and subtract it from the clue it indicates.\n",
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" '''\n",
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"\n",
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" This model solves the problem at the Wikipedia page.\n",
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" For a larger picture, see\n",
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" http://en.wikipedia.org/wiki/File:Kakuro_black_box.svg\n",
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"\n",
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" The solution:\n",
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" 9 7 0 0 8 7 9\n",
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" 8 9 0 8 9 5 7\n",
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" 6 8 5 9 7 0 0\n",
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" 0 6 1 0 2 6 0\n",
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" 0 0 4 6 1 3 2\n",
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" 8 9 3 1 0 1 4\n",
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" 3 1 2 0 0 2 1\n",
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"\n",
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" Compare with the following models:\n",
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" * Comet : http://www.hakank.org/comet/kakuro.co\n",
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" * MiniZinc: http://www.hakank.org/minizinc/kakuro.mzn\n",
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" * SICStus : http://www.hakank.org/sicstus/kakuro.pl\n",
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" * ECLiPSe: http://www.hakank.org/eclipse/kakuro.ecl\n",
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" * Gecode: http://www.hakank.org/gecode/kenken2.cpp\n",
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"\n",
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" This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
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" Also see my other Google CP Solver models:\n",
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" http://www.hakank.org/google_or_tools/\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "code",
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"metadata": {},
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"outputs": [],
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"source": [
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"import sys\n",
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"\n",
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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"#\n",
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"# Ensure that the sum of the segments\n",
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"# in cc == res\n",
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"#\n",
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"\n",
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"\n",
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"def calc(cc, x, res):\n",
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"\n",
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" solver = list(x.values())[0].solver()\n",
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"\n",
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" # ensure that the values are positive\n",
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" for i in cc:\n",
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" solver.Add(x[i[0] - 1, i[1] - 1] >= 1)\n",
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"\n",
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" # sum the numbers\n",
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" solver.Add(solver.Sum([x[i[0] - 1, i[1] - 1] for i in cc]) == res)\n",
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"\n",
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"\n",
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"def main():\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"Kakuro\")\n",
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"\n",
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" #\n",
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" # data\n",
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" #\n",
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"\n",
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" # size of matrix\n",
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" n = 7\n",
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"\n",
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" # segments\n",
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" # [sum, [segments]]\n",
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" # Note: 1-based\n",
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" problem = [[16, [1, 1], [1, 2]], [24, [1, 5], [1, 6], [1, 7]],\n",
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" [17, [2, 1], [2, 2]], [29, [2, 4], [2, 5], [2, 6], [2, 7]],\n",
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" [35, [3, 1], [3, 2], [3, 3], [3, 4], [3, 5]], [7, [4, 2], [4, 3]],\n",
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" [8, [4, 5], [4, 6]], [16, [5, 3], [5, 4], [5, 5], [5, 6], [5, 7]],\n",
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" [21, [6, 1], [6, 2], [6, 3], [6, 4]], [5, [6, 6], [6, 7]],\n",
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" [6, [7, 1], [7, 2], [7, 3]], [3, [7, 6], [7, 7]],\n",
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" [23, [1, 1], [2, 1], [3, 1]], [30, [1, 2], [2, 2], [3, 2], [4, 2]],\n",
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" [27, [1, 5], [2, 5], [3, 5], [4, 5], [5, 5]], [12, [1, 6], [2, 6]],\n",
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" [16, [1, 7], [2, 7]], [17, [2, 4], [3, 4]],\n",
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" [15, [3, 3], [4, 3], [5, 3], [6, 3], [7, 3]],\n",
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" [12, [4, 6], [5, 6], [6, 6], [7, 6]], [7, [5, 4], [6, 4]],\n",
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" [7, [5, 7], [6, 7], [7, 7]], [11, [6, 1], [7, 1]],\n",
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" [10, [6, 2], [7, 2]]]\n",
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"\n",
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" num_p = len(problem)\n",
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"\n",
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" # The blanks\n",
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" # Note: 1-based\n",
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" blanks = [[1, 3], [1, 4], [2, 3], [3, 6], [3, 7], [4, 1], [4, 4], [4, 7],\n",
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" [5, 1], [5, 2], [6, 5], [7, 4], [7, 5]]\n",
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" num_blanks = len(blanks)\n",
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"\n",
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" #\n",
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" # variables\n",
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" #\n",
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"\n",
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" # the set\n",
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" x = {}\n",
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" for i in range(n):\n",
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" for j in range(n):\n",
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" x[i, j] = solver.IntVar(0, 9, \"x[%i,%i]\" % (i, j))\n",
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"\n",
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" x_flat = [x[i, j] for i in range(n) for j in range(n)]\n",
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"\n",
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" #\n",
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" # constraints\n",
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" #\n",
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"\n",
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" # fill the blanks with 0\n",
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" for i in range(num_blanks):\n",
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" solver.Add(x[blanks[i][0] - 1, blanks[i][1] - 1] == 0)\n",
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"\n",
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" for i in range(num_p):\n",
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" segment = problem[i][1::]\n",
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" res = problem[i][0]\n",
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"\n",
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" # sum this segment\n",
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" calc(segment, x, res)\n",
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"\n",
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" # all numbers in this segment must be distinct\n",
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" segment = [x[p[0] - 1, p[1] - 1] for p in segment]\n",
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" solver.Add(solver.AllDifferent(segment))\n",
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"\n",
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" #\n",
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" # search and solution\n",
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" #\n",
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" db = solver.Phase(x_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)\n",
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"\n",
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" solver.NewSearch(db)\n",
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"\n",
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" num_solutions = 0\n",
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" while solver.NextSolution():\n",
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" for i in range(n):\n",
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" for j in range(n):\n",
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" val = x[i, j].Value()\n",
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" if val > 0:\n",
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" print(val, end=\" \")\n",
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" else:\n",
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" print(\" \", end=\" \")\n",
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" print()\n",
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"\n",
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" print()\n",
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" num_solutions += 1\n",
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"\n",
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" solver.EndSearch()\n",
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"\n",
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" print()\n",
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" print(\"num_solutions:\", num_solutions)\n",
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" print(\"failures:\", solver.Failures())\n",
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" print(\"branches:\", solver.Branches())\n",
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" print(\"WallTime:\", solver.WallTime())\n",
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"\n",
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"\n",
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"main()\n",
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"\n"
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]
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}
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],
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"metadata": {
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"language_info": {
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"name": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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