203 lines
6.1 KiB
Plaintext
203 lines
6.1 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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"# set_covering3"
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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_covering3.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_covering3.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 covering in Google CP Solver.\n",
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"\n",
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" Problem from\n",
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" Katta G. Murty: 'Optimization Models for Decision Making', page 302f\n",
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" http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf\n",
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"\n",
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" 10 senators making a committee, where there must at least be one\n",
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" representative from each group:\n",
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" group: senators:\n",
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" southern 1 2 3 4 5\n",
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" northern 6 7 8 9 10\n",
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" liberals 2 3 8 9 10\n",
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" conservative 1 5 6 7\n",
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" democrats 3 4 5 6 7 9\n",
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" republicans 1 2 8 10\n",
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"\n",
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" The objective is to minimize the number of senators.\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_covering3_model.mzn (model)\n",
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" http://www.hakank.org/minizinc/set_covering3.mzn (data)\n",
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" * Comet : http://www.hakank.org/comet/set_covering3.co\n",
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" * ECLiPSe : http://www.hakank.org/eclipse/set_covering3.ecl\n",
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" * SICStus : http://hakank.org/sicstus/set_covering3.pl\n",
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" * Gecode : http://hakank.org/gecode/set_covering3.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(unused_argv):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"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_groups = 6\n",
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" num_senators = 10\n",
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"\n",
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" # which group does a senator belong to?\n",
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" belongs = [\n",
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" [1, 1, 1, 1, 1, 0, 0, 0, 0, 0], # 1 southern\n",
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" [0, 0, 0, 0, 0, 1, 1, 1, 1, 1], # 2 northern\n",
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" [0, 1, 1, 0, 0, 0, 0, 1, 1, 1], # 3 liberals\n",
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" [1, 0, 0, 0, 1, 1, 1, 0, 0, 0], # 4 conservative\n",
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" [0, 0, 1, 1, 1, 1, 1, 0, 1, 0], # 5 democrats\n",
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" [1, 1, 0, 0, 0, 0, 0, 1, 0, 1] # 6 republicans\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_senators)]\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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" # number of assigned senators (to minimize)\n",
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" z = solver.Sum(x)\n",
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"\n",
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" # ensure that each group is covered by at least\n",
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" # one senator\n",
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" for i in range(num_groups):\n",
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" solver.Add(\n",
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" solver.SumGreaterOrEqual(\n",
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" [x[j] * belongs[i][j] for j in range(num_senators)], 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, 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(\"x:\", [collector.Value(0, x[i]) for i in range(num_senators)])\n",
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" for j in range(num_senators):\n",
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" if collector.Value(0, x[j]) == 1:\n",
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" print(\"Senator\", j + 1, \"belongs to these groups:\", end=\" \")\n",
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" for i in range(num_groups):\n",
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" if belongs[i][j] == 1:\n",
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" print(i + 1, end=\" \")\n",
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" print()\n",
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"\n",
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" print()\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(\"cp sample\")\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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