Ford-Fulkerson 最大流算法

1 FORD-FULKERSON-METHOD(G, s, t)
2   initialize flow f to 0
3   while there exists an augmenting path p
4     do augment flow f along p
5   return f

  1 using System;
  2 using System.Collections.Generic;
  3 using System.Linq;
  4 
  5 namespace GraphAlgorithmTesting
  6 {
  7   class Program
  8   {
  9     static void Main(string[] args)
 10     {
 11       Graph g = new Graph(6);
 12       g.AddEdge(0, 1, 16);
 13       g.AddEdge(0, 2, 13);
 14       g.AddEdge(1, 2, 10);
 15       g.AddEdge(1, 3, 12);
 16       g.AddEdge(2, 1, 4);
 17       g.AddEdge(2, 4, 14);
 18       g.AddEdge(3, 2, 9);
 19       g.AddEdge(3, 5, 20);
 20       g.AddEdge(4, 3, 7);
 21       g.AddEdge(4, 5, 4);
 22 
 23       Console.WriteLine();
 24       Console.WriteLine("Graph Vertex Count : {0}", g.VertexCount);
 25       Console.WriteLine("Graph Edge Count : {0}", g.EdgeCount);
 26       Console.WriteLine();
 27 
 28       int maxFlow = g.FordFulkerson(0, 5);
 29       Console.WriteLine("The Max Flow is : {0}", maxFlow);
 30 
 31       Console.ReadKey();
 32     }
 33 
 34     class Edge
 35     {
 36       public Edge(int begin, int end, int weight)
 37       {
 38         this.Begin = begin;
 39         this.End = end;
 40         this.Weight = weight;
 41       }
 42 
 43       public int Begin { get; private set; }
 44       public int End { get; private set; }
 45       public int Weight { get; private set; }
 46 
 47       public override string ToString()
 48       {
 49         return string.Format(
 50           "Begin[{0}], End[{1}], Weight[{2}]",
 51           Begin, End, Weight);
 52       }
 53     }
 54 
 55     class Graph
 56     {
 57       private Dictionary<int, List<Edge>> _adjacentEdges
 58         = new Dictionary<int, List<Edge>>();
 59 
 60       public Graph(int vertexCount)
 61       {
 62         this.VertexCount = vertexCount;
 63       }
 64 
 65       public int VertexCount { get; private set; }
 66 
 67       public IEnumerable<int> Vertices
 68       {
 69         get
 70         {
 71           return _adjacentEdges.Keys;
 72         }
 73       }
 74 
 75       public IEnumerable<Edge> Edges
 76       {
 77         get
 78         {
 79           return _adjacentEdges.Values.SelectMany(e => e);
 80         }
 81       }
 82 
 83       public int EdgeCount
 84       {
 85         get
 86         {
 87           return this.Edges.Count();
 88         }
 89       }
 90 
 91       public void AddEdge(int begin, int end, int weight)
 92       {
 93         if (!_adjacentEdges.ContainsKey(begin))
 94         {
 95           var edges = new List<Edge>();
 96           _adjacentEdges.Add(begin, edges);
 97         }
 98 
 99         _adjacentEdges[begin].Add(new Edge(begin, end, weight));
100       }
101 
102       public int FordFulkerson(int s, int t)
103       {
104         int u, v;
105 
106         // Create a residual graph and fill the residual graph with
107         // given capacities in the original graph as residual capacities
108         // in residual graph
109         int[,] residual = new int[VertexCount, VertexCount];
110 
111         // Residual graph where rGraph[i,j] indicates 
112         // residual capacity of edge from i to j (if there
113         // is an edge. If rGraph[i,j] is 0, then there is not) 
114         for (u = 0; u < VertexCount; u++)
115           for (v = 0; v < VertexCount; v++)
116             residual[u, v] = 0;
117         foreach (var edge in this.Edges)
118         {
119           residual[edge.Begin, edge.End] = edge.Weight;
120         }
121 
122         // This array is filled by BFS and to store path
123         int[] parent = new int[VertexCount];
124 
125         // There is no flow initially
126         int maxFlow = 0;
127 
128         // Augment the flow while there is path from source to sink
129         while (BFS(residual, s, t, parent))
130         {
131           // Find minimum residual capacity of the edhes along the
132           // path filled by BFS. Or we can say find the maximum flow
133           // through the path found.
134           int pathFlow = int.MaxValue;
135           for (v = t; v != s; v = parent[v])
136           {
137             u = parent[v];
138             pathFlow = pathFlow < residual[u, v]
139               ? pathFlow : residual[u, v];
140           }
141 
142           // update residual capacities of the edges and reverse edges
143           // along the path
144           for (v = t; v != s; v = parent[v])
145           {
146             u = parent[v];
147             residual[u, v] -= pathFlow;
148             residual[v, u] += pathFlow;
149           }
150 
151           // Add path flow to overall flow
152           maxFlow += pathFlow;
153         }
154 
155         // Return the overall flow
156         return maxFlow;
157       }
158 
159       // Returns true if there is a path from source ‘s‘ to sink ‘t‘ in
160       // residual graph. Also fills parent[] to store the path.
161       private bool BFS(int[,] residual, int s, int t, int[] parent)
162       {
163         bool[] visited = new bool[VertexCount];
164         for (int i = 0; i < visited.Length; i++)
165         {
166           visited[i] = false;
167         }
168 
169         Queue<int> q = new Queue<int>();
170 
171         visited[s] = true;
172         q.Enqueue(s);
173         parent[s] = -1;
174 
175         // standard BFS loop
176         while (q.Count > 0)
177         {
178           int u = q.Dequeue();
179 
180           for (int v = 0; v < VertexCount; v++)
181           {
182             if (!visited[v]
183               && residual[u, v] > 0)
184             {
185               q.Enqueue(v);
186               visited[v] = true;
187               parent[v] = u;
188             }
189           }
190         }
191 
192         // If we reached sink in BFS starting from source, 
193         // then return true, else false
194         return visited[t] == true;
195       }
196     }
197   }
198 }