245 lines
7.1 KiB
Plaintext
245 lines
7.1 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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"# discrete_tomography"
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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/discrete_tomography.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/discrete_tomography.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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" Discrete tomography in Google CP Solver.\n",
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"\n",
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" Problem from http://eclipse.crosscoreop.com/examples/tomo.ecl.txt\n",
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" '''\n",
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" This is a little 'tomography' problem, taken from an old issue\n",
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" of Scientific American.\n",
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"\n",
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" A matrix which contains zeroes and ones gets \"x-rayed\" vertically and\n",
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" horizontally, giving the total number of ones in each row and column.\n",
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" The problem is to reconstruct the contents of the matrix from this\n",
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" information. Sample run:\n",
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"\n",
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" ?- go.\n",
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" 0 0 7 1 6 3 4 5 2 7 0 0\n",
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" 0\n",
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" 0\n",
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" 8 * * * * * * * *\n",
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" 2 * *\n",
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" 6 * * * * * *\n",
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" 4 * * * *\n",
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" 5 * * * * *\n",
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" 3 * * *\n",
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" 7 * * * * * * *\n",
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" 0\n",
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" 0\n",
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"\n",
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" Eclipse solution by Joachim Schimpf, IC-Parc\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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" * Comet: http://www.hakank.org/comet/discrete_tomography.co\n",
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" * Gecode: http://www.hakank.org/gecode/discrete_tomography.cpp\n",
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" * MiniZinc: http://www.hakank.org/minizinc/tomography.mzn\n",
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" * Tailor/Essence': http://www.hakank.org/tailor/tomography.eprime\n",
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" * SICStus: http://hakank.org/sicstus/discrete_tomography.pl\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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"\n",
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"def main(row_sums=\"\", col_sums=\"\"):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"n-queens\")\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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" if row_sums == \"\":\n",
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" print(\"Using default problem instance\")\n",
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" row_sums = [0, 0, 8, 2, 6, 4, 5, 3, 7, 0, 0]\n",
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" col_sums = [0, 0, 7, 1, 6, 3, 4, 5, 2, 7, 0, 0]\n",
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"\n",
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" r = len(row_sums)\n",
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" c = len(col_sums)\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(r):\n",
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" t = []\n",
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" for j in range(c):\n",
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" t.append(solver.IntVar(0, 1, \"x[%i,%i]\" % (i, j)))\n",
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" x.append(t)\n",
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" x_flat = [x[i][j] for i in range(r) for j in range(c)]\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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" solver.Add(solver.Sum([x[i][j]\n",
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" for j in range(c)]) == row_sums[i])\n",
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" for i in range(r)\n",
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" ]\n",
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" [\n",
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" solver.Add(solver.Sum([x[i][j]\n",
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" for i in range(r)]) == col_sums[j])\n",
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" for j in range(c)\n",
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" ]\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(x_flat)\n",
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"\n",
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" # db: DecisionBuilder\n",
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" db = solver.Phase(x_flat, 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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" print_solution(x, r, c, row_sums, col_sums)\n",
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" print()\n",
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"\n",
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" num_solutions += 1\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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"#\n",
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"# Print solution\n",
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"#\n",
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"\n",
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"\n",
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"def print_solution(x, rows, cols, row_sums, col_sums):\n",
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" print(\" \", end=\" \")\n",
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" for j in range(cols):\n",
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" print(col_sums[j], end=\" \")\n",
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" print()\n",
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" for i in range(rows):\n",
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" print(row_sums[i], end=\" \")\n",
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" for j in range(cols):\n",
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" if x[i][j].Value() == 1:\n",
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" print(\"#\", 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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"\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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" row_sums = f.readline()\n",
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" col_sums = f.readline()\n",
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" row_sums = [int(r) for r in (row_sums.rstrip()).split(\",\")]\n",
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" col_sums = [int(c) for c in (col_sums.rstrip()).split(\",\")]\n",
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"\n",
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" return [row_sums, col_sums]\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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" [row_sums, col_sums] = read_problem(file)\n",
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" main(row_sums, col_sums)\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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