133 lines
4.1 KiB
Plaintext
133 lines
4.1 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 2023 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/main/examples/notebook/graph/simple_max_flow_program.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/ortools/graph/samples/simple_max_flow_program.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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"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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"import numpy as np\n",
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"\n",
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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 = np.array([0, 0, 0, 1, 1, 2, 2, 3, 3])\n",
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" end_nodes = np.array([1, 2, 3, 2, 4, 3, 4, 2, 4])\n",
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" capacities = np.array([20, 30, 10, 40, 30, 10, 20, 5, 20])\n",
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"\n",
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" # Add arcs in bulk.\n",
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" # note: we could have used add_arc_with_capacity(start, end, capacity)\n",
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" all_arcs = smf.add_arcs_with_capacity(start_nodes, end_nodes, capacities)\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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" solution_flows = smf.flows(all_arcs)\n",
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" for arc, flow, capacity in zip(all_arcs, solution_flows, capacities):\n",
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" print(f\"{smf.tail(arc)} / {smf.head(arc)} {flow:3} / {capacity:3}\")\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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