130 lines
3.9 KiB
Plaintext
130 lines
3.9 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 2022 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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"# 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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"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/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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"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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"From Taha 'Introduction to Operations Research', example 6.4-2."
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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.graph.python import max_flow\n",
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"\n",
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"\n",
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"def main():\n",
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" \"\"\"MaxFlow simple interface example.\"\"\"\n",
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" # Instantiate a SimpleMaxFlow solver.\n",
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" smf = max_flow.SimpleMaxFlow()\n",
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"\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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" 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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"\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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" smf.add_arc_with_capacity(arc[0], arc[1], arc[2])\n",
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"\n",
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" # Find the maximum flow between node 0 and node 4.\n",
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" status = smf.solve(0, 4)\n",
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"\n",
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" if status != smf.OPTIMAL:\n",
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" print('There was an issue with the max flow input.')\n",
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" print(f'Status: {status}')\n",
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" exit(1)\n",
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" print('Max flow:', smf.optimal_flow())\n",
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" print('')\n",
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" print(' Arc Flow / Capacity')\n",
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" for i in range(smf.num_arcs()):\n",
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" print('%1s -> %1s %3s / %3s' %\n",
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" (smf.tail(i), smf.head(i), smf.flow(i), smf.capacity(i)))\n",
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" print('Source side min-cut:', smf.get_source_side_min_cut())\n",
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" print('Sink side min-cut:', smf.get_sink_side_min_cut())\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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"nbformat": 4,
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"nbformat_minor": 5
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}
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