235 lines
7.2 KiB
Plaintext
235 lines
7.2 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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"# photo_problem"
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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/photo_problem.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/photo_problem.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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" Photo problem in Google CP Solver.\n",
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"\n",
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" Problem statement from Mozart/Oz tutorial:\n",
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" http://www.mozart-oz.org/home/doc/fdt/node37.html#section.reified.photo\n",
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" '''\n",
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" Betty, Chris, Donald, Fred, Gary, Mary, and Paul want to align in one\n",
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" row for taking a photo. Some of them have preferences next to whom\n",
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" they want to stand:\n",
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"\n",
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" 1. Betty wants to stand next to Gary and Mary.\n",
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" 2. Chris wants to stand next to Betty and Gary.\n",
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" 3. Fred wants to stand next to Mary and Donald.\n",
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" 4. Paul wants to stand next to Fred and Donald.\n",
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"\n",
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" Obviously, it is impossible to satisfy all preferences. Can you find\n",
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" an alignment that maximizes the number of satisfied preferences?\n",
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" '''\n",
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"\n",
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" Oz solution:\n",
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" 6 # alignment(betty:5 chris:6 donald:1 fred:3 gary:7 mary:4 paul:2)\n",
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" [5, 6, 1, 3, 7, 4, 2]\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/photo_hkj.mzn\n",
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" * Comet: http://hakank.org/comet/photo_problem.co\n",
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" * SICStus: http://hakank.org/sicstus/photo_problem.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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"\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(show_all_max=0):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"Photo problem\")\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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" persons = [\"Betty\", \"Chris\", \"Donald\", \"Fred\", \"Gary\", \"Mary\", \"Paul\"]\n",
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" n = len(persons)\n",
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" preferences = [\n",
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" # 0 1 2 3 4 5 6\n",
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" # B C D F G M P\n",
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" [0, 0, 0, 0, 1, 1, 0], # Betty 0\n",
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" [1, 0, 0, 0, 1, 0, 0], # Chris 1\n",
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" [0, 0, 0, 0, 0, 0, 0], # Donald 2\n",
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" [0, 0, 1, 0, 0, 1, 0], # Fred 3\n",
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" [0, 0, 0, 0, 0, 0, 0], # Gary 4\n",
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" [0, 0, 0, 0, 0, 0, 0], # Mary 5\n",
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" [0, 0, 1, 1, 0, 0, 0] # Paul 6\n",
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" ]\n",
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"\n",
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" print(\"\"\"Preferences:\n",
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" 1. Betty wants to stand next to Gary and Mary.\n",
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" 2. Chris wants to stand next to Betty and Gary.\n",
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" 3. Fred wants to stand next to Mary and Donald.\n",
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" 4. Paul wants to stand next to Fred and Donald.\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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" positions = [solver.IntVar(0, n - 1, \"positions[%i]\" % i) for i in range(n)]\n",
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"\n",
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" # successful preferences\n",
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" z = solver.IntVar(0, n * n, \"z\")\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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" solver.Add(solver.AllDifferent(positions))\n",
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"\n",
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" # calculate all the successful preferences\n",
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" b = [\n",
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" solver.IsEqualCstVar(abs(positions[i] - positions[j]), 1)\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 preferences[i][j] == 1\n",
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" ]\n",
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" solver.Add(z == solver.Sum(b))\n",
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"\n",
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" #\n",
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" # Symmetry breaking (from the Oz page):\n",
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" # Fred is somewhere left of Betty\n",
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" solver.Add(positions[3] < positions[0])\n",
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"\n",
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" # objective\n",
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" objective = solver.Maximize(z, 1)\n",
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" if show_all_max != 0:\n",
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" print(\"Showing all maximum solutions (z == 6).\\n\")\n",
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" solver.Add(z == 6)\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(positions, solver.CHOOSE_FIRST_UNBOUND,\n",
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" solver.ASSIGN_MAX_VALUE)\n",
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"\n",
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" if show_all_max == 0:\n",
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" solver.NewSearch(db, [objective])\n",
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" else:\n",
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" solver.NewSearch(db)\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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" print(\"z:\", z.Value())\n",
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" p = [positions[i].Value() for i in range(n)]\n",
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"\n",
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" print(\" \".join(\n",
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" [persons[j] for i in range(n) for j in range(n) if p[j] == i]))\n",
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" print(\"Successful preferences:\")\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 preferences[i][j] == 1 and abs(p[i] - p[j]) == 1:\n",
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" print(\"\\t\", persons[i], persons[j])\n",
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" print()\n",
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" num_solutions += 1\n",
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"\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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"show_all_max = 0 # show all maximal solutions\n",
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"if len(sys.argv) > 1:\n",
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" show_all_max = 1\n",
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"main(show_all_max)\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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