csflow.cs

// Copyright 2010-2022 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

using System;
using Google.OrTools.Graph;

public class CsFlow
{
    private static void SolveMaxFlow()
    {
        Console.WriteLine("Max Flow Problem");
        int numNodes = 6;
        int numArcs = 9;
        int[] tails = { 0, 0, 0, 0, 1, 2, 3, 3, 4 };
        int[] heads = { 1, 2, 3, 4, 3, 4, 4, 5, 5 };
        int[] capacities = { 5, 8, 5, 3, 4, 5, 6, 6, 4 };
        int[] expectedFlows = { 4, 4, 2, 0, 4, 4, 0, 6, 4 };
        int expectedTotalFlow = 10;
        MaxFlow maxFlow = new MaxFlow();
        for (int i = 0; i < numArcs; ++i)
        {
            int arc = maxFlow.AddArcWithCapacity(tails[i], heads[i], capacities[i]);
            if (arc != i)
                throw new Exception("Internal error");
        }
        int source = 0;
        int sink = numNodes - 1;
        Console.WriteLine("Solving max flow with " + numNodes + " nodes, and " + numArcs + " arcs, source=" + source +
                          ", sink=" + sink);
        MaxFlow.Status solveStatus = maxFlow.Solve(source, sink);
        if (solveStatus == MaxFlow.Status.OPTIMAL)
        {
            long totalFlow = maxFlow.OptimalFlow();
            Console.WriteLine("total computed flow " + totalFlow + ", expected = " + expectedTotalFlow);
            for (int i = 0; i < numArcs; ++i)
            {
                Console.WriteLine("Arc " + i + " (" + maxFlow.Head(i) + " -> " + maxFlow.Tail(i) +
                                  "), capacity = " + maxFlow.Capacity(i) + ") computed = " + maxFlow.Flow(i) +
                                  ", expected = " + expectedFlows[i]);
            }
        }
        else
        {
            Console.WriteLine("Solving the max flow problem failed. Solver status: " + solveStatus);
        }
    }

    private static void SolveMinCostFlow()
    {
        Console.WriteLine("Min Cost Flow Problem");
        int numSources = 4;
        int numTargets = 4;
        int[,] costs = { { 90, 75, 75, 80 }, { 35, 85, 55, 65 }, { 125, 95, 90, 105 }, { 45, 110, 95, 115 } };
        int expectedCost = 275;
        MinCostFlow minCostFlow = new MinCostFlow();
        for (int source = 0; source < numSources; ++source)
        {
            for (int target = 0; target < numTargets; ++target)
            {
                minCostFlow.AddArcWithCapacityAndUnitCost(source, /*target=*/numSources + target,
                                                          /*capacity=*/1,
                                                          /*flow unit cost=*/costs[source, target]);
            }
        }
        for (int source = 0; source < numSources; ++source)
        {
            minCostFlow.SetNodeSupply(source, 1);
        }
        for (int target = 0; target < numTargets; ++target)
        {
            minCostFlow.SetNodeSupply(numSources + target, -1);
        }
        Console.WriteLine("Solving min cost flow with " + numSources + " sources, and " + numTargets + " targets.");
        MinCostFlow.Status solveStatus = minCostFlow.Solve();
        if (solveStatus == MinCostFlow.Status.OPTIMAL)
        {
            Console.WriteLine("total computed flow cost = " + minCostFlow.OptimalCost() +
                              ", expected = " + expectedCost);
        }
        else
        {
            Console.WriteLine("Solving the min cost flow problem failed." + " Solver status: " + solveStatus);
        }
    }

    static void Main()
    {
        SolveMaxFlow();
        SolveMinCostFlow();
    }
}