235 lines
7.4 KiB
Plaintext
235 lines
7.4 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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"# set_covering4"
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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/set_covering4.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/set_covering4.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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" Set partition and set covering in Google CP Solver.\n",
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"\n",
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" Example from the Swedish book\n",
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" Lundgren, Roennqvist, Vaebrand\n",
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" 'Optimeringslaera' (translation: 'Optimization theory'),\n",
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" page 408.\n",
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"\n",
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" * Set partition:\n",
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" We want to minimize the cost of the alternatives which covers all the\n",
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" objects, i.e. all objects must be choosen. The requirement is than an\n",
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" object may be selected _exactly_ once.\n",
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"\n",
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" Note: This is 1-based representation\n",
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"\n",
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" Alternative Cost Object\n",
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" 1 19 1,6\n",
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" 2 16 2,6,8\n",
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" 3 18 1,4,7\n",
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" 4 13 2,3,5\n",
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" 5 15 2,5\n",
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" 6 19 2,3\n",
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" 7 15 2,3,4\n",
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" 8 17 4,5,8\n",
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" 9 16 3,6,8\n",
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" 10 15 1,6,7\n",
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"\n",
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" The problem has a unique solution of z = 49 where alternatives\n",
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" 3, 5, and 9\n",
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" is selected.\n",
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"\n",
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" * Set covering:\n",
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" If we, however, allow that an object is selected _more than one time_,\n",
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" then the solution is z = 45 (i.e. less cost than the first problem),\n",
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" and the alternatives\n",
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" 4, 8, and 10\n",
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" is selected, where object 5 is selected twice (alt. 4 and 8).\n",
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" It's an unique solution as well.\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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" * MiniZinc: http://www.hakank.org/minizinc/set_covering4.mzn\n",
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" * Comet : http://www.hakank.org/comet/set_covering4.co\n",
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" * ECLiPSe : http://www.hakank.org/eclipse/set_covering4.ecl\n",
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" * SICStus : http://www.hakank.org/sicstus/set_covering4.pl\n",
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" * Gecode : http://www.hakank.org/gecode/set_covering4.cpp\n",
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"\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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"\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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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"\n",
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"def main(set_partition=1):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"Set partition and set covering\")\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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" num_alternatives = 10\n",
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" num_objects = 8\n",
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"\n",
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" # costs for the alternatives\n",
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" costs = [19, 16, 18, 13, 15, 19, 15, 17, 16, 15]\n",
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"\n",
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" # the alternatives, and their objects\n",
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" a = [\n",
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" # 1 2 3 4 5 6 7 8 the objects\n",
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" [1, 0, 0, 0, 0, 1, 0, 0], # alternative 1\n",
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" [0, 1, 0, 0, 0, 1, 0, 1], # alternative 2\n",
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" [1, 0, 0, 1, 0, 0, 1, 0], # alternative 3\n",
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" [0, 1, 1, 0, 1, 0, 0, 0], # alternative 4\n",
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" [0, 1, 0, 0, 1, 0, 0, 0], # alternative 5\n",
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" [0, 1, 1, 0, 0, 0, 0, 0], # alternative 6\n",
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" [0, 1, 1, 1, 0, 0, 0, 0], # alternative 7\n",
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" [0, 0, 0, 1, 1, 0, 0, 1], # alternative 8\n",
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" [0, 0, 1, 0, 0, 1, 0, 1], # alternative 9\n",
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" [1, 0, 0, 0, 0, 1, 1, 0] # alternative 10\n",
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" ]\n",
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"\n",
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" #\n",
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" # declare variables\n",
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" #\n",
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" x = [solver.IntVar(0, 1, \"x[%i]\" % i) for i in range(num_alternatives)]\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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" # sum the cost of the choosen alternative,\n",
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" # to be minimized\n",
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" z = solver.ScalProd(x, costs)\n",
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"\n",
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" #\n",
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" for j in range(num_objects):\n",
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" if set_partition == 1:\n",
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" solver.Add(\n",
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" solver.SumEquality([x[i] * a[i][j] for i in range(num_alternatives)],\n",
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" 1))\n",
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" else:\n",
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" solver.Add(\n",
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" solver.SumGreaterOrEqual(\n",
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" [x[i] * a[i][j] for i in range(num_alternatives)], 1))\n",
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"\n",
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" objective = solver.Minimize(z, 1)\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)\n",
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" solution.AddObjective(z)\n",
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"\n",
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" collector = solver.LastSolutionCollector(solution)\n",
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" solver.Solve(\n",
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" solver.Phase([x[i] for i in range(num_alternatives)],\n",
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" solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),\n",
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" [collector, objective])\n",
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"\n",
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" print(\"z:\", collector.ObjectiveValue(0))\n",
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" print(\n",
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" \"selected alternatives:\",\n",
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" [i + 1 for i in range(num_alternatives) if collector.Value(0, x[i]) == 1])\n",
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"\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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"print(\"Set partition:\")\n",
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"main(1)\n",
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"\n",
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"print(\"\\nSet covering:\")\n",
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"main(0)\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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