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   "source": [
    "# Copyright 2010-2018 Google LLC\n",
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "#     http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License.\n",
    "# [START program]\n",
    "\"\"\"From Taha 'Introduction to Operations Research', example 6.4-2.\"\"\"\n",
    "# [START import]\n",
    "from __future__ import print_function\n",
    "from ortools.graph import pywrapgraph\n",
    "# [END import]\n",
    "\n",
    "\n",
    "\"\"\"MaxFlow simple interface example.\"\"\"\n",
    "\n",
    "# [START data]\n",
    "# Define three parallel arrays: start_nodes, end_nodes, and the capacities\n",
    "# between each pair. For instance, the arc from node 0 to node 1 has a\n",
    "# capacity of 20.\n",
    "\n",
    "start_nodes = [0, 0, 0, 1, 1, 2, 2, 3, 3]\n",
    "end_nodes = [1, 2, 3, 2, 4, 3, 4, 2, 4]\n",
    "capacities = [20, 30, 10, 40, 30, 10, 20, 5, 20]\n",
    "# [END data]\n",
    "\n",
    "# Instantiate a SimpleMaxFlow solver.\n",
    "# [START constraints]\n",
    "max_flow = pywrapgraph.SimpleMaxFlow()\n",
    "# Add each arc.\n",
    "for arc in zip(start_nodes, end_nodes, capacities):\n",
    "    max_flow.AddArcWithCapacity(arc[0], arc[1], arc[2])\n",
    "# [END constraints]\n",
    "\n",
    "# [START solve]\n",
    "# Find the maximum flow between node 0 and node 4.\n",
    "if max_flow.Solve(0, 4) == max_flow.OPTIMAL:\n",
    "    print('Max flow:', max_flow.OptimalFlow())\n",
    "    print('')\n",
    "    print('  Arc    Flow / Capacity')\n",
    "    for i in range(max_flow.NumArcs()):\n",
    "        print('%1s -> %1s   %3s  / %3s' %\n",
    "              (max_flow.Tail(i), max_flow.Head(i), max_flow.Flow(i),\n",
    "               max_flow.Capacity(i)))\n",
    "    print('Source side min-cut:', max_flow.GetSourceSideMinCut())\n",
    "    print('Sink side min-cut:', max_flow.GetSinkSideMinCut())\n",
    "else:\n",
    "    print('There was an issue with the max flow input.')\n",
    "# [END solve]\n",
    "\n"
   ]
  }
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