最小费用流

#include <cstdio>
#include <cstring>
#define maxn 61
#define maxv (maxn*maxn*2 + 1)
#define maxe (maxv*5)
#define oo 2147483647
#define min(a,b) ((a>(b)?(b):(a)))
#define maxq maxe

using namespace std;

struct edge_type
{
    int x,y,flow,cost,next,op;
};

int n,m;
int a[maxn + 1][maxn + 1];

int total,totalv,source,sink;
int first[maxv + 1];
edge_type g[maxe + 1];

int dist[maxv + 1],fa[maxv + 1];
bool mark[maxv + 1];
int q[maxq + 1];

bool spfa()
{
    memset(mark,0,sizeof(mark));
    memset(fa,0,sizeof(fa)); //
    for (int i=0;i<=totalv;i++)
        dist[i] = -1;
    dist[source] = 0;
    int head,tail;
    head = 1; tail = 2;
    q[1] = source;
    while (head!=tail){
        int b = q[head];
        mark[b] = 0;
        for (int temp=first[b];temp;temp=g[temp].next){
            if (!g[temp].flow) continue;
            int y = g[temp].y;
            int tt;
            if ((tt = dist[b] + g[temp].cost)>dist[y]){
                dist[y] = tt;
                fa[y] = temp;
                if (!mark[y]){
                    mark[y] = 1;
                    q[tail ++] = y;
                    if (tail>maxq) tail = 1;
                }
            }
        }
        head ++;
        if (head>maxq) head = 1;
    }
    return dist[sink]>=0;
}

int mincost_maxflow()
{
    int total_flow,total_cost,cur_flow,cur_cost;
    total_flow = total_cost = 0;
    while (spfa()){/*
        for (int i=1;i<=totalv;i++){
            printf("%d ",dist[i]);
        }
        printf("\n");*/
        cur_flow = oo; cur_cost = 0;
        for (int temp=fa[sink];temp;temp=fa[g[temp].x]){
            cur_flow = min(cur_flow,g[temp].flow);
            cur_cost += g[temp].cost;
        }
        for (int temp=fa[sink];temp;temp=fa[g[temp].x]){
            g[temp].flow -= cur_flow;
            g[g[temp].op].flow += cur_flow;
        }
//        printf("%d\n",cur_flow);
        total_flow += cur_flow;
        total_cost += cur_cost*cur_flow;
    }
//    printf("%d\n",total_flow);
    return total_cost;
}

void add(int x,int y,int flow,int cost)
{
    g[++total].x = x; g[total].y = y;
    g[total].flow = flow; g[total].cost = cost;
    g[total].op = total + 1;
    g[total].next = first[x];
    first[x] = total;

    g[++total].x = y; g[total].y = x;
    g[total].flow = 0; g[total].cost = -cost;
    g[total].op = total - 1;
    g[total].next = first[y];
    first[y] = total;
}

int main()
{
    while (scanf("%d%d",&n,&m)==2){
        for (int i=1;i<=n;i++){
            for (int j=1;j<=n;j++)
                scanf("%d",&a[i][j]);
        }
        total = 0;
        memset(first,0,sizeof(first));
        source = n*n*2 + 1;
        totalv = source;
        sink = n*n*2;
        add(source,1,m,0);
        for (int i=1;i<=n;i++){
            for (int j=1;j<=n;j++){
                add((i - 1)*n + j,(i - 1)*n + j + n*n,1,a[i][j]);
                add((i - 1)*n + j,(i - 1)*n + j + n*n,oo,0);
                if (i<n)
                    add((i - 1)*n + j + n*n,i*n + j,oo,0);
                if (j<n)
                    add((i - 1)*n + j + n*n,(i - 1)*n + j + 1,oo,0);
            }
        }

        int ans = mincost_maxflow();
        printf("%d\n",ans);
    }
    return 0;
}

最大费用最大流和最小费用最大流一样可以用SPFA + Edmonds-Karp解决。//显然SPFA可以求最长路的

貌似先用spfa找出一条增光路，再用ek增加流

有时间再研究研究

http://rekonq.appspot.com/%3Fp%3D119001