288 lines
9.3 KiB
Plaintext
288 lines
9.3 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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"# quasigroup_completion"
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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/quasigroup_completion.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/quasigroup_completion.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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" Quasigroup completion Google CP Solver.\n",
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"\n",
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"\n",
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" See Carla P. Gomes and David Shmoys:\n",
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" \"Completing Quasigroups or Latin Squares: Structured Graph Coloring Problem\"\n",
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"\n",
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" See also\n",
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" Ivars Peterson \"Completing Latin Squares\"\n",
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" http://www.maa.org/mathland/mathtrek_5_8_00.html\n",
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" '''\n",
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" Using only the numbers 1, 2, 3, and 4, arrange four sets of these numbers\n",
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" into\n",
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" a four-by-four array so that no column or row contains the same two numbers.\n",
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" The result is known as a Latin square.\n",
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" ...\n",
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" The so-called quasigroup completion problem concerns a table that is\n",
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" correctly\n",
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" but only partially filled in. The question is whether the remaining blanks\n",
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" in\n",
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" the table can be filled in to obtain a complete Latin square (or a proper\n",
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" quasigroup multiplication table).\n",
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" '''\n",
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"\n",
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" Compare with the following models:\n",
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" * Choco: http://www.hakank.org/choco/QuasigroupCompletion.java\n",
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" * Comet: http://www.hakank.org/comet/quasigroup_completion.co\n",
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" * ECLiPSE: http://www.hakank.org/eclipse/quasigroup_completion.ecl\n",
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" * Gecode: http://www.hakank.org/gecode/quasigroup_completion.cpp\n",
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" * Gecode/R: http://www.hakank.org/gecode_r/quasigroup_completion.rb\n",
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" * JaCoP: http://www.hakank.org/JaCoP/QuasigroupCompletion.java\n",
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" * MiniZinc: http://www.hakank.org/minizinc/quasigroup_completion.mzn\n",
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" * Tailor/Essence': http://www.hakank.org/tailor/quasigroup_completion.eprime\n",
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" * SICStus: http://hakank.org/sicstus/quasigroup_completion.pl\n",
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" * Zinc: http://hakank.org/minizinc/quasigroup_completion.zinc\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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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"default_n = 5\n",
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"X = 0\n",
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"# default problem\n",
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"# (This is the same as quasigroup1.txt)\n",
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"default_puzzle = [[1, X, X, X, 4], [X, 5, X, X, X], [4, X, X, 2, X],\n",
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" [X, 4, X, X, X], [X, X, 5, X, 1]]\n",
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"\n",
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"\n",
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"def main(puzzle=\"\", n=0):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"Quasigroup completion\")\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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" if puzzle == \"\":\n",
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" puzzle = default_puzzle\n",
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" n = default_n\n",
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"\n",
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" print(\"Problem:\")\n",
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" print_game(puzzle, n, n)\n",
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"\n",
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" # declare variables\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(1, n, \"x %i %i\" % (i, j))\n",
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"\n",
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" xflat = [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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" #\n",
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" # set the clues\n",
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" #\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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" if puzzle[i][j] > X:\n",
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" solver.Add(x[i, j] == puzzle[i][j])\n",
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"\n",
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" #\n",
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" # rows and columns must be different\n",
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" #\n",
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" for i in range(n):\n",
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" solver.Add(solver.AllDifferent([x[i, j] for j in range(n)]))\n",
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" solver.Add(solver.AllDifferent([x[j, i] for j in range(n)]))\n",
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"\n",
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" #\n",
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" # solution and search\n",
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" #\n",
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" solution = solver.Assignment()\n",
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" solution.Add(xflat)\n",
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"\n",
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" # This version prints out the solution directly, and\n",
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" # don't collect them as solver.FirstSolutionCollector(solution) do\n",
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" # (db: DecisionBuilder)\n",
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" db = solver.Phase(xflat, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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" solver.NewSearch(db)\n",
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" num_solutions = 0\n",
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" while solver.NextSolution():\n",
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" num_solutions += 1\n",
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" print(\"Solution %i\" % num_solutions)\n",
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" xval = [x[(i, j)].Value() for i in range(n) for j in range(n)]\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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" print(xval[i * n + j], end=\" \")\n",
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" print()\n",
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" print()\n",
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" solver.EndSearch()\n",
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"\n",
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" if num_solutions == 0:\n",
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" print(\"No solutions found\")\n",
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"\n",
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" # # Note: AllSolution may take very much RAM, hence I choose to\n",
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" # # show just the first solution.\n",
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" # # collector = solver.AllSolutionCollector(solution)\n",
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" # collector = solver.FirstSolutionCollector(solution)\n",
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" # solver.Solve(solver.Phase([x[(i,j)] for i in range(n) for j in range(n)],\n",
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" # solver.CHOOSE_FIRST_UNBOUND,\n",
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" # solver.ASSIGN_MIN_VALUE),\n",
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" # [collector])\n",
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" #\n",
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" # num_solutions = collector.SolutionCount()\n",
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" # print \"\\nnum_solutions: \", num_solutions\n",
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" # if num_solutions > 0:\n",
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" # print \"\\nJust showing the first solution...\"\n",
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" # for s in range(num_solutions):\n",
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" # xval = [collector.Value(s, x[(i,j)]) for i in range(n) for j in range(n)]\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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" # print xval[i*n+j],\n",
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" # print\n",
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" # print\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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"#\n",
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"# Read a problem instance from a file\n",
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"#\n",
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"def read_problem(file):\n",
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" f = open(file, \"r\")\n",
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" n = int(f.readline())\n",
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" game = []\n",
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" for i in range(n):\n",
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" x = f.readline()\n",
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" row_x = (x.rstrip()).split(\" \")\n",
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" row = [0] * n\n",
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" for j in range(n):\n",
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" if row_x[j] == \".\":\n",
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" tmp = 0\n",
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" else:\n",
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" tmp = int(row_x[j])\n",
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" row[j] = tmp\n",
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" game.append(row)\n",
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" return [game, n]\n",
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"\n",
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"\n",
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"def print_board(x, rows, cols):\n",
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" for i in range(rows):\n",
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" for j in range(cols):\n",
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" print(\"% 2s\" % x[i, j], end=\" \")\n",
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" print(\"\")\n",
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"\n",
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"\n",
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"def print_game(game, rows, cols):\n",
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" for i in range(rows):\n",
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" for j in range(cols):\n",
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" print(\"% 2s\" % game[i][j], end=\" \")\n",
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" print(\"\")\n",
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"\n",
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"\n",
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"\n",
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"if len(sys.argv) > 1:\n",
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" file = sys.argv[1]\n",
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" print(\"Problem instance from\", file)\n",
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" [game, n] = read_problem(file)\n",
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" main(game, n)\n",
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"else:\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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