BZOJ3931 [CQOI2015]网络吞吐量（最大流）

没啥好说的，有写过类似的，就是预处理出最短路上的边建容量网络。

#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
using namespace std;
#define INF (1LL<<60)
#define MAXN 1111
#define MAXM 1111*1111*2

struct Edge{
    int v,next;
    long long cap,flow;
}edge[MAXM];
int vs,vt,NE,NV;
int head[MAXN];

void addEdge(int u,int v,long long cap){
    edge[NE].v=v; edge[NE].cap=cap; edge[NE].flow=0;
    edge[NE].next=head[u]; head[u]=NE++;
    edge[NE].v=u; edge[NE].cap=0; edge[NE].flow=0;
    edge[NE].next=head[v]; head[v]=NE++;
}

int level[MAXN];
int gap[MAXN];
void bfs(){
    memset(level,-1,sizeof(level));
    memset(gap,0,sizeof(gap));
    level[vt]=0;
    gap[level[vt]]++;
    queue<int> que;
    que.push(vt);
    while(!que.empty()){
        int u=que.front(); que.pop();
        for(int i=head[u]; i!=-1; i=edge[i].next){
            int v=edge[i].v;
            if(level[v]!=-1) continue;
            level[v]=level[u]+1;
            gap[level[v]]++;
            que.push(v);
        }
    }
}

int pre[MAXN];
int cur[MAXN];
long long ISAP(){
    bfs();
    memset(pre,-1,sizeof(pre));
    memcpy(cur,head,sizeof(head));
    int u=pre[vs]=vs;
    long long flow=0,aug=INF;
    gap[0]=NV;
    while(level[vs]<NV){
        bool flag=false;
        for(int &i=cur[u]; i!=-1; i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].cap!=edge[i].flow && level[u]==level[v]+1){
                flag=true;
                pre[v]=u;
                u=v;
                //aug=(aug==-1?edge[i].cap:min(aug,edge[i].cap));
                aug=min(aug,edge[i].cap-edge[i].flow);
                if(v==vt){
                    flow+=aug;
                    for(u=pre[v]; v!=vs; v=u,u=pre[u]){
                        edge[cur[u]].flow+=aug;
                        edge[cur[u]^1].flow-=aug;
                    }
                    //aug=-1;
                    aug=INF;
                }
                break;
            }
        }
        if(flag) continue;
        int minlevel=NV;
        for(int i=head[u]; i!=-1; i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].cap!=edge[i].flow && level[v]<minlevel){
                minlevel=level[v];
                cur[u]=i;
            }
        }
        if(--gap[level[u]]==0) break;
        level[u]=minlevel+1;
        gap[level[u]]++;
        u=pre[u];
    }
    return flow;
}
int n;
long long G[555][555],d[555];
bool vis[555];
void SPFA(){
    for(int i=1; i<=n; ++i) d[i]=INF,vis[i]=0;
    d[1]=0; vis[1]=1;
    queue<int> que;
    que.push(1);
    while(!que.empty()){
        int u=que.front(); que.pop();
        for(int v=1; v<=n; ++v){
            if(G[u][v]==-1) continue;
            if(d[v]>d[u]+G[u][v]){
                d[v]=d[u]+G[u][v];
                if(!vis[v]){
                    vis[v]=1;
                    que.push(v);
                }
            }
        }
        vis[u]=0;
    }
}
int main(){
    memset(G,-1,sizeof(G));
    int m,a,b,c;
    scanf("%d%d",&n,&m);
    while(m--){
        scanf("%d%d%d",&a,&b,&c);
        if(G[a][b]==-1 || G[a][b]>c) G[b][a]=G[a][b]=c;
    }
    for(int i=1; i<=n; ++i) G[i][i]=0;
    SPFA();
    vs=1; vt=n+n; NV=vt+1; NE=0;
    memset(head,-1,sizeof(head));
    for(int i=1; i<=n; ++i){
        scanf("%d",&a);
        if(i==1 || i==n) addEdge(i,i+n,INF);
        else addEdge(i,i+n,a);
    }
    for(int i=1; i<=n; ++i){
        for(int j=1; j<=n; ++j){
            if(G[i][j]==-1 || i==j || d[i]==INF || d[j]==INF) continue;
            if(d[i]+G[i][j]==d[j]) addEdge(i+n,j,INF);
        }
    }
    printf("%lld",ISAP());
    return 0;
}