用SPFA的最小费用流算法

最新推荐文章于 2021-02-13 18:30:09 发布

zhou09039051698

最新推荐文章于 2021-02-13 18:30:09 发布

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分类专栏：最小费用流

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本文介绍了一种基于最小费用最大流算法的具体实现过程。该算法通过不断寻找从起点到终点费用最小且仍有剩余容量的路径，并沿此路径调整流量与成本，直至无法寻找到新的路径为止。文中提供了一个具体的C++实现示例。

作法就是每次找到一条合计费用最小的从起点到终点剩余容量不为0的路径。

把这条路径灌满水统计一下花费，之后再找新的路径，直到找不到为止。

数据结构方面定义一个构造体表示中两个相邻点的容量，流量和所需费用。

之后定义一个二位数组来标识点和点之间的相邻关系。

代码：

  
#include <iostream>  
using namespace std;

struct Node
{
	int cap, flow, cost;
};

Node edge[100][100];
int sum;
int size = 7;
int s = 0, t = 6, a=0;
int pre[10];
int q[200];
int vis[10], dis[10];

void init()
{
	int i, j;
	for(i = 0; i < size; i++)
		for(j = 0; j < size; j++)
		{
			edge[i][j].cost = 100000;
			edge[i][j].flow = 0;
			edge[i][j].cap = 0;
		}
	edge[0][1].cost = 0; edge[0][1].cap = 10000;
	
	edge[1][3].cost = 2; edge[1][3].cap = 8;
	edge[1][2].cost = 8; edge[1][2].cap = 7;
	edge[3][2].cost = 5; edge[3][2].cap = 5;
	edge[3][5].cost = 2; edge[3][5].cap = 9;
	edge[2][4].cost = 3; edge[2][4].cap = 9;
	edge[5][2].cost = 1; edge[5][2].cap = 2;
	edge[5][6].cost = 6; edge[5][6].cap = 5;
	edge[4][6].cost = 7; edge[4][6].cap = 10;
	edge[4][5].cost = 4; edge[4][5].cap = 6;
}

int spfa()
{
	int i, temp;
	for(i = 0; i < size; i++)
	{
		vis[i] = -1;
		dis[i] = 100000;
	}
	
	int front = 0, tail= 1;
	vis[s] = 1; dis[s] = 0;
	q[front] = s;
	while(front < tail)
	{
		
		temp = q[front];
		vis[temp] = -1;
		front++;
		for(i = 0; i < size; i++)
		{
			int res = edge[temp][i].cap - edge[temp][i].flow;
			if(res > 0 && dis[i] > dis[temp] + edge[temp][i].cost)
			{
				dis[i] = dis[temp] + edge[temp][i].cost;
				pre[i] =temp;
			    if(vis[i] == -1)
			    {
				    vis[i] = 1;
				    q[tail++] = i;
			    }
			}
		}
	}
	return dis[t];
}

int MCMF()
{
	int temp, min, flow, sum = 0, cost, val;


	while(spfa() < 8000)
	{   
		temp = t; 
		flow = 100000; cost = 0;
		while(temp != s)
		{
			val = edge[pre[temp]][temp].cap - edge[pre[temp]][temp].flow;
			cost += edge[pre[temp]][temp].cost;
			if(val < flow)
				flow = val;
			temp = pre[temp];
		}
		temp = t;
		cout << flow << " " << cost << endl;
		sum += flow * cost;
		while(temp != s)
		{
			edge[pre[temp]][temp].flow += flow;
			edge[temp][pre[temp]].flow -= flow;
//			cout << pre[temp] << " " << temp << " ";
//			cout << edge[pre[temp]][temp].flow << endl;
			temp = pre[temp];
		}
	}
	
	return sum;
}

int main()  
{  
	init();
	cout << MCMF() << endl;
    return 0;  
}