Expm 10_2 实现Ford-Fulkerson算法，求出给定图中从源点s到汇点t的最大流，并输出最小割。

 package org.xiu68.exp.exp10;

 import java.util.ArrayDeque;
 import java.util.ArrayList;
 import java.util.Arrays;

 public class Exp10_2 {
     //实现Ford-Fulkerson算法，求出给定图中从源点s到汇点t的最大流，并输出最小割。
     public static void main(String[] args) {
         // TODO Auto-generated method stub
         int[][] c=new int[][]{
             {0,1,1,0},
             {0,0,1,1},
             {0,0,0,1},
             {0,0,0,0}
         };
         MGraph1 m1=new MGraph1(c);
         m1.fordFulkerson(0, 3);

         int[][] c1=new int[][]{
             {0,3,3,4,0,0,0},
             {0,0,0,0,2,0,0},
             {0,1,0,0,1,0,0},
             {0,0,0,0,0,5,0},
             {0,0,0,1,0,1,2},
             {0,0,0,0,0,0,5},
             {0,0,0,0,0,0,0}
         };
         MGraph1 m2=new MGraph1(c1);
         m2.fordFulkerson(0, 6);
     }
 }

 class MGraph1{
     private int[][] c;        //容量矩阵
     private int[][] e;        //残量矩阵
     private int[][] f;        //当前流矩阵
     private int vexNum;        //顶点数量

     public MGraph1(int[][] c){
         this.c=c;
         this.vexNum=c.length;
         this.e=new int[vexNum][vexNum];
         this.f=new int[vexNum][vexNum];

         //刚开始时残量矩阵等于容量矩阵
         for(int i=0;i<vexNum;i++){
             System.arraycopy(c[i], 0, e[i], 0, c[i].length);
         }

     }
     //fordFulkerson算法
     public void fordFulkerson(int s,int t){
         int[] route=new int[vexNum];    //s到t的路径数组,route[i]表示i的前一个顶点

         while(bfs(s,t,route)){             //若还能找到一条路径

             //寻找路径中流最小的边的大小(在残量矩阵中)
             int min=Integer.MAX_VALUE;
             int tail=t;
             int head=route[t];

             while(head!=-1){
                 if(e[head][tail]<min){
                     min=e[head][tail];
                 }
                 tail=head;
                 head=route[head];
             }        

             //更新当前流矩阵和残量矩阵
             int tail1=t;
             int head1=route[tail1];
             while(head1!=-1){
                 //更新当前流矩阵
                 if(c[head1][tail1]!=0){
                     f[head1][tail1]+=min;        //容量矩阵中存在边,增加head1到tail1的流的大小为min
                 }else{
                     f[head1][tail1]-=min;        //容量矩阵中不存在边，撤销head1到tail1的流的大小为min
                 }
                 //更新残量矩阵
                 e[head1][tail1]-=min;            //head1到tail1的流量减少min
                 e[tail1][head1]+=min;            //tail1到head1的流量增加min

                 tail1=head1;
                 head1=route[head1];
             }//while
             //route=new int[vexNum];
             Arrays.fill(route, 0);                 //初始化路径数组
         }//while 还能找到一条s到t的路径

         int maxFlow=0;
         for(int i=0;i<vexNum;i++)                //最大流为  当前流矩阵中  从s流出的量
             maxFlow+=f[s][i];
         System.out.println("最大流为:"+maxFlow);

         System.out.print("最小割为(集合S)：");
         ArrayList<Integer> cut=cut(s);
         for(int i=0;i<cut.size();i++)
             System.out.print(cut.get(i)+" ");
         System.out.println();

     }

     //广度优先搜索在残量图e中寻找s到t的路径
     public boolean bfs(int s,int t,int[] route){
         boolean[] visited=new boolean[vexNum];        //访问数组
         visited[s]=true;

         ArrayDeque<Integer> queue=new ArrayDeque<>();
         route[s]=-1;                                //设s的前一个顶点为-1

         for(int i=0;i<vexNum;i++){
             if(e[s][i]!=0 && !visited[i]){            //在残量矩阵中s到i存在一条路径
                 queue.add(i);
                 route[i]=s;
                 visited[i]=true;
             }
         }

         while(!queue.isEmpty()){
             int middleVex=queue.poll();
             if(middleVex==t){
                 return true;
             }else{
                 for(int i=0;i<vexNum;i++){
                     if(e[middleVex][i]!=0 && !visited[i]){
                         queue.add(i);
                         route[i]=middleVex;
                         visited[i]=true;
                     }
                 }
             }
         }//while
         return false;
     }

     //求最小割
     //在残量矩阵中,从s开始做一次搜索,从s能达到的所有的顶点都属于集合S
     public ArrayList<Integer> cut(int s){
         boolean[] visited=new boolean[vexNum];
         ArrayList<Integer> cut=new ArrayList<>();    //保存最小割,集合S
         dfs(visited,cut,s);
         return cut;
     }
     //深度优先搜索
     private void dfs(boolean[] visited,ArrayList<Integer> cut,int v){
         cut.add(v);
         visited[v]=true;
         for(int i=0;i<vexNum;i++){
             if(e[v][i]!=0 && !visited[i]){
                 dfs(visited,cut,i);
             }
         }
     }
 }