poj 2526 Minimum Cost【最小费用最大流】

题目链接：http://poj.org/problem?id=2516

题意：

n个店主 m个供应商 k种货物 给你店主对k种货物的需求及供货商k种货物的囤货量及K种运输费用。

解法：k次费用流，分别求每种货物的费用。源点到供应点建边，店主到汇点建边，费用均为0，容量为1。然后供应点到店主建边，费用为矩阵，容量无穷大即可。

代码：

/*
POJ 2195 Going Home
邻接矩阵形式最小费用最大流
*/

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string.h>
#include<queue>
using namespace std;

//************************************************************
//最小费用最大流算法
//SPFA求最短路
//邻接矩阵形式
//初始化:cap:容量，没有边为0
//cost:耗费，对称形式，没有边的也为0
//c是最小费用
//f是最大流
//*******************************************************
const int MAXN = 500;
const int INF = 0x3fffffff;
int cap[MAXN][MAXN];//容量，没有边为0
int flow[MAXN][MAXN];
//耗费矩阵是对称的，有i到j的费用，则j到i的费用为其相反数
int cost[MAXN][MAXN];//花费

int n;//顶点数目0~n-1
int f;//最大流
int c;//最小费用
int start, End;//源点和汇点

bool vis[MAXN];//在队列标志
int que[MAXN];
int pre[MAXN];
int dist[MAXN];//s-t路径最小耗费
bool SPFA()
{
    int front = 0, rear = 0;
    for (int u = 0; u <= n; u++)
    {
        if (u == start)
        {
            que[rear++] = u;
            dist[u] = 0;
            vis[u] = true;
        }
        else
        {
            dist[u] = INF;
            vis[u] = false;
        }
    }
    while (front != rear)
    {
        int u = que[front++];
        vis[u] = false;
        if (front >= MAXN)front = 0;
        for (int v = 0; v <= n; v++)
        {
            if (cap[u][v]>flow[u][v] && dist[v]>dist[u] + cost[u][v])
            {
                dist[v] = dist[u] + cost[u][v];
                pre[v] = u;
                if (!vis[v])
                {
                    vis[v] = true;
                    que[rear++] = v;
                    if (rear >= MAXN)rear = 0;
                }
            }
        }
    }
    if (dist[End] >= INF)return false;
    return true;
}

void minCostMaxflow()
{
    memset(flow, 0, sizeof(flow));
    c = f = 0;
    while (SPFA())
    {
        int Min = INF;
        for (int u = End; u != start; u = pre[u])
            Min = min(Min, cap[pre[u]][u] - flow[pre[u]][u]);
        for (int u = End; u != start; u = pre[u])
        {
            flow[pre[u]][u] += Min;
            flow[u][pre[u]] -= Min;
        }
        c += dist[End] * Min;
        f += Min;
    }
}
//************************************************************

int tmp;
int a[10000][55];
int b[10000][55];

int main()
{
    int N, M, K;
    while (~scanf("%d%d%d", &N, &M, &K))
    {
        if (N == 0 && M == 0 && K == 0) break;
        memset(a, 0, sizeof(a));
        memset(b, 0, sizeof(b));

        start = 0;
        n = N + M+ 2;
        End = M + N + 1;

        int need = 0;

        for (int i = 1; i <= N; i++)
        {
            for (int k = 1; k <= K;k++)
            {
                scanf("%d",&a[i][k]);
                need += a[i][k];
            }
        }

        for (int i = 1; i <= M; i++)
        {
            for (int k = 1; k <= K; k++)
            {
                scanf("%d", &b[i][k]);
            }
        }

        int ans = 0;
        int res = 0;

        for (int kk = 1; kk <= K; kk++)
        {
            memset(cap, 0, sizeof(cap));
            memset(cost, 0, sizeof(cost));

            for (int i = 1; i <= M; i++) //源点向供应点建边
                cap[start][i] = b[i][kk];
            for(int i = 1; i <= N; i++) //店主向汇点建边
                cap[M + i][End] = a[i][kk];

            for (int i = 1; i <= N; i++)
                for (int j = 1; j <= M; j++)
                {
                    scanf("%d", &tmp);
                    cost[j][i + M] = tmp;
                    cost[i + M][j] = -tmp;
                    cap[j][i + M] = 1000000;
                }
            minCostMaxflow();
            ans += c;
            res += f;
        }

        if (res == need)
            printf("%d\n", ans);
        else
            printf("-1\n");
    }
    return 0;
}

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