import java.util.LinkedList;
import java.util.Queue;
import java.util.Random;
public class MinCost_MaxFlow_MinCostPath {
private int INF;
private int maxFlow;
private int capacity[][];
private double [][]cost;
private int rescap[][]; //残量网络流量
private double rescost[][]; //残量网络费用
private int flow[][]; //求最大流时的流量
private boolean visited[];
private int pre[]; //最大流时的增广前驱
private int[] p; //增广路前驱
private double[] d; //s-t路径最小耗费
private boolean[] inq; //队列标记
private int curr_flow; //当前流量
private int nodes;
private int src;
private int des;
private double minimumcost;
public MinCost_MaxFlow_MinCostPath(int asrc,int ades, int[][] acapacity, double [][]acost,int anodes,int ainf )
{
this.nodes = anodes;
src=asrc;
des=ades;
INF=ainf;
minimumcost=0;
maxFlow=0;
curr_flow=0;
this.capacity = new int[nodes][nodes];
this.rescap=new int[nodes][nodes];
cost=new double[nodes][nodes];
this.rescost=new double[nodes][nodes];
this.flow = new int[nodes][nodes];
this.pre = new int[nodes];
this.p=new int[nodes];
this.d=new double[nodes];
this.inq=new boolean[nodes];
this.visited = new boolean[nodes];
for(int i=0;i<nodes;i++)
{
pre[i]=-1;
p[i]=-1;
}
for(int i=0;i<nodes;i++)
{
for(int j=0;j<nodes;j++)
{
rescap[i][j]=capacity[i][j]=acapacity[i][j];
if(capacity[i][j]>0)
{
cost[i][j]=acost[i][j];
cost[j][i]=-acost[i][j];
}
}
}
for(int i=0;i<nodes;i++)
for(int j=0;j<nodes;j++)
{
if(rescap[i][j]>0||i==j)
rescost[i][j]=acost[i][j];
else
rescost[i][j]=INF;
}
}
/*
* step 0：先求出最大流
*/
public void maxFlow()
{
for( int i = 0; i < nodes; i++ )
for( int j = 0; j < nodes; j++ )
flow[i][j] = 0;
while( true )//find a augment path
{
for( int i = 0; i < nodes; i++ )
{
visited[i] = false;
}
pre[src] = -1;
if(!BFS()){// the BFS
break;
}
/*DFS(src,des);//DFS
44. if(!visited[des])
45. break;*/
int increment = Integer.MAX_VALUE;
for( int i = des; pre[i] >= src; i = pre[i] )
{
//find the min flow of the path
increment = Math.min( increment, capacity[pre[i]][i]
- flow[pre[i]][i] );
}
//update the flow
for( int i = des; pre[i] >= src; i = pre[i] )
{
flow[pre[i]][i] += increment;
flow[i][pre[i]] -= increment;
}
//increase the maxFow with the increment
maxFlow += increment;
}
}
// public void DFS(int src, int des){
// visited[src] = true;
// for(int i = 0; i < nodes; i++){
// if(!visited[i] && ( capacity[src][i] - flow[src][i] > 0) ){
// pre[i] = src;//record the augment path
// visited[i] = true;
// DFS(i,des);
// }
// }
// }
//
public boolean BFS()
{
Queue<Integer> queue = new LinkedList<Integer>();
queue.add( src );
visited[src] = true;
while( !queue.isEmpty() )
{
int node = queue.poll();
for( int i = 0; i < nodes; i++ )
{
if( !visited[i] && (capacity[node][i] - flow[node][i] > 0) )
{
queue.add( i );
visited[i] = true;
pre[i] = node;//record the augment path
}
}
}
return visited[des];
}
public void minCmaxF()
{
Queue<Integer > q=new LinkedList<Integer >();
while(curr_flow<maxFlow)
{
for(int k=0;k<nodes;k++)
inq[k]=false;
for(int i=0;i<nodes;i++)
{
d[i]= i==src ? 0:INF;
}
q.offer(src);
inq[src]=true;
while(!q.isEmpty())
{
int u=q.poll();//int u=q.front(); q.pop();
for(int v=0;v<nodes;v++)
{
if(rescap[u][v]>0&&d[v]>d[u]+rescost[u][v])
{
d[v]=d[u]+rescost[u][v];
p[v]=u;
if(!inq[v])
{
inq[v]=true;
q.offer(v);
}
}
}
inq[u]=false;
System.out.println("size "+q.size());
if(q.size()>0)
System.out.println(" "+q.peek());
System.out.println("loop in finding the shortest path to src");
}
for(int u=des;u!=src;u=p[u])
{
System.out.print(" "+u);
System.out.println("loop in the print shortest path");
}
System.out.println();
boolean flag = true;
// 判断是否有负环路
// for(int i=1; i<nodes; i++)
// {
//
// if(rescap[p[i]][i]>0&&d[i] > d[p[i]] + rescost[p[i]][i])
// {
// flag = false;
// break;
// }
// }
int augflow=INF;
for(int u=des;u!=src;u=p[u])
{
if(rescap[p[u]][u]<augflow)
{
augflow=rescap[p[u]][u];
}
System.out.println("loop in finding the augflow "+flag);
}
for(int u=des;u!=src;u=p[u])
{
rescap[p[u]][u]-=augflow;
rescap[u][p[u]]+=augflow;
System.out.println("loop in augflow");
}
System.out.println("current_augflow"+augflow);
this.minimumcost+=d[des]*augflow;
curr_flow+=augflow;
System.out.println("current_flow"+curr_flow);
for(int i=0;i<nodes;i++)
{
for(int j=0;j<nodes;j++)
{
if(rescap[i][j]>0||i==j)
rescost[i][j]=cost[i][j];
else
rescost[i][j]=INF;
}
} //System.out.println("loop for computing the flow");
}
}
public double getMiniCost()
{
return this.minimumcost;
}
public int getMaxFlow()
{
return this.maxFlow;
}
public static void main( String[] args )
{
int nodes=50;
int src=0;
int des=nodes-1;
int INF=1000;
Random r=new Random();
int[][] capacity=new int[nodes][nodes] ; //{{0,3,4,0},{0,0,1,4},{0,0,0,5},{0,0,0,0}};
double [][] cost=new double[nodes][nodes];//{{0,-1.2,-2.1,0},{0,0,-2.8,-5.1},{0,0,0,-1.7},{0,0,0,0}};
for (int i = 0; i < nodes; i++) {
for (int j = i+1; j < nodes; j++) {
if (r.nextDouble() < 0.3) {
capacity[i][j] = r.nextInt(5) + 1;
cost[i][j] = r.nextDouble() * 5;
}
}
}
System.out.println("the programe is running...");
MinCost_MaxFlow_MinCostPath mincost_maxflow = new MinCost_MaxFlow_MinCostPath(src,des, capacity,cost, nodes,INF);
mincost_maxflow.maxFlow(); //先计算该网络中的最大可行流
System.out.println("最大流: "+mincost_maxflow.getMaxFlow());
mincost_maxflow.minCmaxF();
System.out.println("最小费用"+mincost_maxflow.getMiniCost());
System.out.println("The programe has finished");
}
}
其中，自己在调试的过程中发现在寻找费用最短路（也就是红色部分的代码）过程中存在这么一种情况,节点49的前驱是18，然后节点18的前驱是49，导致程序陷入死循环。又由于这种情况也是偶然出现，所以本人没有找到导致这种情况的原因。还请教高手解答一下这种问题出现的原因！不胜感激！！
