133 lines
4.5 KiB
Plaintext
133 lines
4.5 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"##### Copyright 2021 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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"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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"metadata": {},
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"source": [
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"# simple_max_flow_program"
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]
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},
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{
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"cell_type": "markdown",
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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/master/examples/notebook/graph/simple_max_flow_program.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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/master/ortools/graph/samples/simple_max_flow_program.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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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"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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"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": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#!/usr/bin/env python3\n",
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"# Copyright 2010-2021 Google LLC\n",
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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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"# [START program]\n",
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"\"\"\"From Taha 'Introduction to Operations Research', example 6.4-2.\"\"\"\n",
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"# [START import]\n",
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"from ortools.graph import pywrapgraph\n",
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"# [END import]\n",
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"\n",
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"\n",
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"\"\"\"MaxFlow simple interface example.\"\"\"\n",
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"\n",
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"# [START data]\n",
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"# Define three parallel arrays: start_nodes, end_nodes, and the capacities\n",
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"# between each pair. For instance, the arc from node 0 to node 1 has a\n",
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"# capacity of 20.\n",
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"\n",
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"start_nodes = [0, 0, 0, 1, 1, 2, 2, 3, 3]\n",
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"end_nodes = [1, 2, 3, 2, 4, 3, 4, 2, 4]\n",
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"capacities = [20, 30, 10, 40, 30, 10, 20, 5, 20]\n",
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"# [END data]\n",
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"\n",
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"# Instantiate a SimpleMaxFlow solver.\n",
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"# [START constraints]\n",
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"max_flow = pywrapgraph.SimpleMaxFlow()\n",
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"# Add each arc.\n",
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"for arc in zip(start_nodes, end_nodes, capacities):\n",
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" max_flow.AddArcWithCapacity(arc[0], arc[1], arc[2])\n",
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"# [END constraints]\n",
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"\n",
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"# [START solve]\n",
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"# Find the maximum flow between node 0 and node 4.\n",
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"if max_flow.Solve(0, 4) == max_flow.OPTIMAL:\n",
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" print('Max flow:', max_flow.OptimalFlow())\n",
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" print('')\n",
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" print(' Arc Flow / Capacity')\n",
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" for i in range(max_flow.NumArcs()):\n",
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" print('%1s -> %1s %3s / %3s' %\n",
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" (max_flow.Tail(i), max_flow.Head(i), max_flow.Flow(i),\n",
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" max_flow.Capacity(i)))\n",
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" print('Source side min-cut:', max_flow.GetSourceSideMinCut())\n",
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" print('Sink side min-cut:', max_flow.GetSinkSideMinCut())\n",
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"else:\n",
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" print('There was an issue with the max flow input.')\n",
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"# [END solve]\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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"nbformat": 4,
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"nbformat_minor": 4
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}
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