220 lines
6.8 KiB
Plaintext
220 lines
6.8 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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"# broken_weights"
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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/broken_weights.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/broken_weights.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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" Broken weights problem in Google CP Solver.\n",
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"\n",
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" From http://www.mathlesstraveled.com/?p=701\n",
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" '''\n",
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" Here's a fantastic problem I recently heard. Apparently it was first\n",
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" posed by Claude Gaspard Bachet de Meziriac in a book of arithmetic problems\n",
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" published in 1612, and can also be found in Heinrich Dorrie's 100\n",
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" Great Problems of Elementary Mathematics.\n",
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"\n",
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" A merchant had a forty pound measuring weight that broke\n",
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" into four pieces as the result of a fall. When the pieces were\n",
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" subsequently weighed, it was found that the weight of each piece\n",
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" was a whole number of pounds and that the four pieces could be\n",
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" used to weigh every integral weight between 1 and 40 pounds. What\n",
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" were the weights of the pieces?\n",
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"\n",
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" Note that since this was a 17th-century merchant, he of course used a\n",
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" balance scale to weigh things. So, for example, he could use a 1-pound\n",
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" weight and a 4-pound weight to weigh a 3-pound object, by placing the\n",
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" 3-pound object and 1-pound weight on one side of the scale, and\n",
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" the 4-pound weight on the other side.\n",
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" '''\n",
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"\n",
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" Compare with the following problems:\n",
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" * MiniZinc: http://www.hakank.org/minizinc/broken_weights.mzn\n",
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" * ECLiPSE: http://www.hakank.org/eclipse/broken_weights.ecl\n",
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" * Gecode: http://www.hakank.org/gecode/broken_weights.cpp\n",
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" * Comet: http://hakank.org/comet/broken_weights.co\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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"def main(m=40, n=4):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver('Broken weights')\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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" print('total weight (m):', m)\n",
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" print('number of pieces (n):', n)\n",
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" print()\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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" weights = [solver.IntVar(1, m, 'weights[%i]' % j) for j in range(n)]\n",
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" x = {}\n",
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" for i in range(m):\n",
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" for j in range(n):\n",
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" x[i, j] = solver.IntVar(-1, 1, 'x[%i,%i]' % (i, j))\n",
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" x_flat = [x[i, j] for i in range(m) 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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" # symmetry breaking\n",
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" for j in range(1, n):\n",
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" solver.Add(weights[j - 1] < weights[j])\n",
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"\n",
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" solver.Add(solver.SumEquality(weights, m))\n",
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"\n",
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" # Check that all weights from 1 to 40 can be made.\n",
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" #\n",
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" # Since all weights can be on either side\n",
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" # of the side of the scale we allow either\n",
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" # -1, 0, or 1 or the weights, assuming that\n",
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" # -1 is the weights on the left and 1 is on the right.\n",
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" #\n",
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" for i in range(m):\n",
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" solver.Add(i + 1 == solver.Sum([weights[j] * x[i, j] for j in range(n)]))\n",
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"\n",
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" # objective\n",
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" objective = solver.Minimize(weights[n - 1], 1)\n",
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"\n",
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" #\n",
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" # search and result\n",
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" #\n",
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" db = solver.Phase(weights + x_flat, solver.CHOOSE_FIRST_UNBOUND,\n",
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" solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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" search_log = solver.SearchLog(1)\n",
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"\n",
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" solver.NewSearch(db, [objective])\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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" num_solutions += 1\n",
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" print('weights: ', end=' ')\n",
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" for w in [weights[j].Value() for j in range(n)]:\n",
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" print('%3i ' % w, end=' ')\n",
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" print()\n",
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" print('-' * 30)\n",
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" for i in range(m):\n",
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" print('weight %2i:' % (i + 1), end=' ')\n",
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" for j in range(n):\n",
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" print('%3i ' % x[i, j].Value(), end=' ')\n",
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" print()\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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" 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(), 'ms')\n",
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"\n",
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"\n",
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"m = 40\n",
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"n = 4\n",
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"if len(sys.argv) > 1:\n",
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" m = int(sys.argv[1])\n",
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"if len(sys.argv) > 2:\n",
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" n = int(sys.argv[2])\n",
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"main(m, n)\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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