SAP

Sap模板：邻接表

const int MM = 555555;
#define maxint 0x3f3f3f3f
int N,M,K;
int S,T;

struct Edge {
    int v,w,next;
}edge[MM];
int head[MM],NE;

void reset() {memset(head,-1,sizeof(head)),NE=0;}

void add_edge(int u,int v,int c) {
    edge[NE].v=v, edge[NE].w=c, edge[NE].next=head[u];
    head[u]=NE++;
    edge[NE].v=u, edge[NE].w=0, edge[NE].next=head[v];
    head[v]=NE++;
}

int a[MM];
int gap[MM], dis[MM], pre[MM],cur[MM];

//返回s->t的最大流
int Sap(int s,int t) {
    memset(gap,0,sizeof(gap));
    memset(dis,0,sizeof(dis));
    int u,now,tmp,flow = 0;
    int v = t+1, i;
    a[u=s] = maxint, gap[0] = v;
    for(i=0; i<v ;i++)  cur[i] = head[i];
    while (dis[s]<v) {
        for(i=cur[u]; i!=-1;i=edge[i].next)
            if (edge[i].w && dis[u]==dis[edge[i].v] + 1)
                break;
            if(i!=-1) {
                tmp=edge[i].v;
                a[tmp]=min(a[u], edge[i].w);
                cur[u]=pre[tmp] = i;
                if ((u=tmp)==t) {
                    flow += (tmp=a[t]);
                    do {
                        edge[pre[u]].w -= tmp;
                        edge[pre[u]^1].w += tmp;
                        u = edge[pre[u]^1].v;
                    } while (u != s);
                    a[s] = maxint;
                }
            }
            else {
                if ((-- gap[dis[u]])==0) break;
                dis[u] = v;
                cur[u] = head[u];
                for (i = head[u]; i!=-1; i = edge[i].next)
                    if (edge[i].w && dis[u] > dis[edge[i].v] + 1)
                        dis[u] = dis[edge[i].v] + 1, cur[u] = i;
                    gap[dis[u]] ++;
                    if (u != s)
                        u = edge[pre[u]^1].v;
            }
    }
    return flow;
}

 邻接矩阵:初始clear(edge,0)

int edge[333][333]; 

int gap[MM],dis[MM],pre[MM],cur[MM];
int flow[333][333];//存最大流的容量
int Sap(int s,int t,int nodenum) {
    memset(cur,0,sizeof(cur));
    memset(dis,0,sizeof(dis));
    memset(gap,0,sizeof(gap));
    memset(flow,0,sizeof(flow));
    int u=pre[s]=s,maxflow=0,aug=-1;
    gap[0]=nodenum;
    while(dis[s]<nodenum) {
        loop:
          for(int v=cur[u];v<nodenum;v++)
            if(edge[u][v]-flow[u][v] && dis[u]==dis[v]+1) {
                if(aug==-1 || aug>edge[u][v]-flow[u][v])aug=edge[u][v]-flow[u][v];
                pre[v]=u;
                u=cur[u]=v;
                if(v==t) {
                    maxflow+=aug;
                    for(u=pre[u];v!=s;v=u,u=pre[u]) {
                        flow[u][v]+=aug;
                        flow[v][u]-=aug;
                    }
                    aug=-1;
                }
                goto loop;
            }
            int mindis=nodenum-1;
            for(int v=0;v<nodenum;v++)
               if(edge[u][v]-flow[u][v]&&mindis>dis[v]) {
                   cur[u]=v;
                   mindis=dis[v];
               }
            if((--gap[dis[u]])==0)break;
            gap[dis[u]=mindis+1]++;
            u=pre[u];
    }
    return maxflow;
}