CSharp ford fulkerson源代码
时间: 2023-11-25 22:08:03 浏览: 34
由于Ford-Fulkerson算法是一种基于增广路径的算法,因此需要一个图数据结构来表示图,同时需要一个函数来找到增广路径。以下是一个C#实现:
```
using System;
using System.Collections.Generic;
class FordFulkerson
{
private int[,] graph;
private int[,] residualGraph;
private bool[] visited;
private int[] parent;
public FordFulkerson(int[,] graph)
{
this.graph = graph;
}
private bool BFS(int source, int sink)
{
visited = new bool[graph.GetLength(0)];
parent = new int[graph.GetLength(0)];
Queue<int> queue = new Queue<int>();
queue.Enqueue(source);
visited[source] = true;
parent[source] = -1;
while (queue.Count > 0)
{
int current = queue.Dequeue();
for (int i = 0; i < graph.GetLength(0); i++)
{
if (!visited[i] && residualGraph[current, i] > 0)
{
queue.Enqueue(i);
visited[i] = true;
parent[i] = current;
}
}
}
return visited[sink];
}
private int FindMinCapacity(int source, int sink)
{
int current = sink;
int minCapacity = int.MaxValue;
while (current != source)
{
int previous = parent[current];
int capacity = residualGraph[previous, current];
minCapacity = Math.Min(minCapacity, capacity);
current = previous;
}
return minCapacity;
}
public int MaxFlow(int source, int sink)
{
residualGraph = (int[,])graph.Clone();
int maxFlow = 0;
while (BFS(source, sink))
{
int minCapacity = FindMinCapacity(source, sink);
for (int current = sink; current != source; current = parent[current])
{
int previous = parent[current];
residualGraph[previous, current] -= minCapacity;
residualGraph[current, previous] += minCapacity;
}
maxFlow += minCapacity;
}
return maxFlow;
}
}
```
在这个实现中,我们使用一个二维数组来表示图,其中第一个维度表示源节点,第二个维度表示汇节点,数组中的值表示从一个节点到另一个节点的边的容量。在算法的过程中,我们使用一个二维数组来表示剩余图,这个剩余图表示从源节点到汇节点的最大流量。我们首先创建一个剩余图,它与原始图相同。然后,我们在while循环中不断寻找增广路径,如果找到了增广路径,则将其上的最小容量加入到最大流中,并更新剩余图。最后,我们返回最大流。