218 lines
6.0 KiB
Plaintext
218 lines
6.0 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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"# max_flow_winston1"
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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/max_flow_winston1.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/max_flow_winston1.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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" Max flow problem in Google CP Solver.\n",
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"\n",
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" From Winston 'Operations Research', page 420f, 423f\n",
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" Sunco Oil example.\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/max_flow_winston1.mzn\n",
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" * Comet: http://hakank.org/comet/max_flow_winston1.co\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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]
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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():\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver('Max flow problem, Winston')\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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" n = 5\n",
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" nodes = list(range(n))\n",
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"\n",
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" # the arcs\n",
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" # Note:\n",
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" # This is 1-based to be compatible with other\n",
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" # implementations.\n",
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" arcs1 = [[1, 2], [1, 3], [2, 3], [2, 4], [3, 5], [4, 5], [5, 1]]\n",
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"\n",
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" # convert arcs to 0-based\n",
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" arcs = []\n",
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" for (a_from, a_to) in arcs1:\n",
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" a_from -= 1\n",
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" a_to -= 1\n",
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" arcs.append([a_from, a_to])\n",
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"\n",
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" num_arcs = len(arcs)\n",
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"\n",
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" # capacities\n",
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" cap = [2, 3, 3, 4, 2, 1, 100]\n",
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"\n",
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" # convert arcs to matrix\n",
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" # for sanity checking below\n",
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" mat = {}\n",
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" for i in nodes:\n",
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" for j in nodes:\n",
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" c = 0\n",
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" for k in range(num_arcs):\n",
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" if arcs[k][0] == i and arcs[k][1] == j:\n",
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" c = 1\n",
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" mat[i, j] = c\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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" flow = {}\n",
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" for i in nodes:\n",
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" for j in nodes:\n",
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" flow[i, j] = solver.IntVar(0, 200, 'flow %i %i' % (i, j))\n",
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"\n",
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" flow_flat = [flow[i, j] for i in nodes for j in nodes]\n",
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"\n",
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" z = solver.IntVar(0, 10000, '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(z == flow[n - 1, 0])\n",
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"\n",
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" # capacity of arcs\n",
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" for i in range(num_arcs):\n",
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" solver.Add(flow[arcs[i][0], arcs[i][1]] <= cap[i])\n",
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"\n",
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" # inflows == outflows\n",
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" for i in nodes:\n",
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" s1 = solver.Sum([\n",
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" flow[arcs[k][0], arcs[k][1]] for k in range(num_arcs) if arcs[k][1] == i\n",
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" ])\n",
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" s2 = solver.Sum([\n",
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" flow[arcs[k][0], arcs[k][1]] for k in range(num_arcs) if arcs[k][0] == i\n",
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" ])\n",
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" solver.Add(s1 == s2)\n",
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"\n",
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" # sanity: just arcs with connections can have a flow\n",
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" for i in nodes:\n",
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" for j in nodes:\n",
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" if mat[i, j] == 0:\n",
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" solver.Add(flow[i, j] == 0)\n",
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"\n",
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" # objective: maximize z\n",
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" objective = solver.Maximize(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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" db = solver.Phase(flow_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)\n",
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"\n",
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" solver.NewSearch(db, [objective])\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('z:', z.Value())\n",
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" for i in nodes:\n",
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" for j in nodes:\n",
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" print(flow[i, j].Value(), end=' ')\n",
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" print()\n",
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" print()\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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"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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