网络流模板

Dinic

#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#define maxn 10500
#define inf 1e9
using namespace std;
int n,m,tot=1,head[maxn],S,T,t1,t2,t3;
int d[maxn],flag[maxn],cur[maxn],ans,fl[maxn];
long long anse,ansv;
struct node{
    int v,nex,cap;
}e[200005];
void Q(){
    tot=1;
    memset(head,0,sizeof head);
}
void lj(int t1,int t2,int t3){
    tot++;e[tot].v=t2,e[tot].cap=t3;e[tot].nex=head[t1];head[t1]=tot;
}
bool BFS(){
    for(int i=1;i<=Max;i++)d[i]=inf,flag[i]=0;
    queue<int>q;q.push(S);d[S]=0;
    while(!q.empty()){
        int x=q.front();q.pop();cur[x]=head[x];
        for(int i=head[x];i;i=e[i].nex){
            if(d[e[i].v]>d[x]+1&&e[i].cap){
                d[e[i].v]=d[x]+1;
                if(!flag[e[i].v]){
                    flag[e[i].v]=1;q.push(e[i].v);
                }
            }
        }
        flag[x]=0;
    }
    return d[T]!=inf;
}
int lian(int k,int a){
    //cout<<k<<' '<<a<<endl;
    if(k==T||!a)return a;
    int f,flow=0;
    for(int& i=cur[k];i;i=e[i].nex){
        if(d[e[i].v]==d[k]+1&&(f=lian(e[i].v,min(a,e[i].cap)))>0){
            flow+=f;a-=f;
            e[i].cap-=f;e[i^1].cap+=f;
            if(!a)break;
        }
    }
    return flow;
}
int main()
{
    scanf("%d%d%d%d",&n,&m,&S,&T);
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&t1,&t2,&t3);
        lj(t1,t2,t3);lj(t2,t1,0);
    }
    ans=0;
    while(BFS())ans+=lian(S,inf);
    cout<<ans<<endl;
    return 0;
}

ISAP（现在不会了）

#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<cmath>
#include<map>
#include<queue>
#define maxn 10005
#define maxm 100005
#define inf 1e9
using namespace std;
int n,m,S,T,now[maxn],head[maxn],t1,t2,t3,tot=1;
int flag[maxn],d[maxn],pre[maxn],num[maxn],ans;
struct node
{
    int nex,v,cap;
}e[maxm*2];
void lj(int t1,int t2,int t3)
{
    tot++;e[tot].v=t2,e[tot].cap=t3;e[tot].nex=head[t1];head[t1]=tot;
}
void BFS(){
    queue<int>q;
    flag[T]=1;q.push(T);
    while(!q.empty()){
        int x=q.front();q.pop();
        ///printf("orz %d
",x);
        for(int i=head[x];i;i=e[i].nex){
            if(!flag[e[i].v]&&e[i^1].cap>0){
                flag[e[i].v]=1;
                d[e[i].v]=d[x]+1;
                q.push(e[i].v);
            }
        }
    }
}
int get()
{
    int flow=inf;
    for(int i=T;;i=e[pre[i]].v)
    {
        if(i==S)break;
        flow=min(e[pre[i]^1].cap,flow);
    }
    for(int i=T;;i=e[pre[i]].v){
        if(i==S)break;
        e[pre[i]].cap+=flow;
        e[pre[i]^1].cap-=flow;
    }
    return flow;
}
void lian()
{
    BFS();
    memset(num,0,sizeof(num));
    //for(int i=1;i<=n;i++)cout<<d[i]<<' ';cout<<endl;
    for(int i=1;i<=n;i++){now[i]=head[i];num[d[i]]++;}
    int x=S;
    while(d[S]<n)
    {
        if(x==T)ans+=get(),x=S;
        bool ff=0;
        for(int i=now[x];i;i=e[i].nex){
        //	printf("%d %d %d %d
",x,e[i].v,d[x],d[e[i].v]);
            if(d[e[i].v]==d[x]-1&&e[i].cap){
                ff=1;pre[e[i].v]=i^1;
                now[x]=i;x=e[i].v;
                break;
            }
        }
        //printf("%d %d %d
",x,ans,ff);
        if(!ff){
            int mi=inf;
            for(int i=head[x];i;i=e[i].nex){
                if(e[i].cap>0){
                    //cout<<i<<' '<<d[i]<<'
';
                    mi=min(d[e[i].v],mi);
                }
            }
            //cout<<endl;
            num[d[x]]--;
            //printf("trsae %d %d
",d[x],mi);
            if(num[d[x]]==0)break;
            if(mi==inf)mi=n;
            d[x]=mi+1;num[d[x]]++;now[x]=head[x];
            if(x!=S)x=e[pre[x]].v;
        }
    }
}
int main(){
    cin>>n>>m>>S>>T;
    for(int i=1;i<=m;i++)
    {
        scanf("%d%d%d",&t1,&t2,&t3);
        lj(t1,t2,t3);lj(t2,t1,0);
    }
    lian();
    printf("%d
",ans);
    return 0;
}

费用流（单路增广）

#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<cmath>
#include<map>
#include<queue>
#define maxn 5002
#define inf 1e9
using namespace std;
int n,m,S,T,head[maxn],tot=1,t1,t2,t3,t4,fl;
int d[maxn],flag[maxn],ans,cur[maxn];
struct node{
    int v,nex,cap,w;
}e[100002];
void lj(int t1,int t2,int t3,int t4){
    tot++;e[tot].v=t2;e[tot].cap=t3;e[tot].w=t4;e[tot].nex=head[t1];head[t1]=tot;
}
bool spfa(){
    for(int i=1;i<=n;i++)d[i]=inf,flag[i]=0;
    queue<int>q;q.push(S);d[S]=0;
    while(!q.empty()){
        
        int x=q.front();q.pop();
        for(int i=head[x];i;i=e[i].nex){
            if(e[i].cap>0&&d[e[i].v]>d[x]+e[i].w){
                d[e[i].v]=d[x]+e[i].w;
                if(!flag[e[i].v])flag[e[i].v]=1,q.push(e[i].v);
            }
        }
        flag[x]=0;
    }
    return d[T]!=inf;
}
int dfs(int k,int a){
    flag[k]=1;
    if(k==T||a==0)return a;
    int f,flow=0;
    for(int &i=cur[k];i;i=e[i].nex){
        if(d[e[i].v]==d[k]+e[i].w&&e[i].cap&&!flag[e[i].v]){//attention!!!
            f=dfs(e[i].v,min(e[i].cap,a));
            flow+=f;a-=f;e[i].cap-=f;e[i^1].cap+=f;
            ans+=f*e[i].w;
            if(a==0)break;
        }
    }
    return flow;
}
int main(){
    cin>>n>>m>>S>>T;
    for(int i=1;i<=m;i++){
        scanf("%d%d%d%d",&t1,&t2,&t3,&t4);
        lj(t1,t2,t3,t4);lj(t2,t1,0,-t4);
    }
    while(spfa()){
        flag[T]=1;
        while(flag[T]){
            memset(flag,0,sizeof(flag));
            for(int i=1;i<=n;i++)cur[i]=head[i];
            fl+=dfs(S,inf);
        }
    }
    cout<<fl<<' '<<ans<<endl;
    return 0;
}

费用流（zkw）

#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<cmath>
#include<map>
#include<queue>
#define maxn 5002
#define inf 1e9
using namespace std;
int n,m,S,T,head[maxn],tot=1,t1,t2,t3,t4,fl;
int d[maxn],flag[maxn],ans,cur[maxn];
struct node{
    int v,nex,cap,w;
}e[100002];
void lj(int t1,int t2,int t3,int t4){
    tot++;e[tot].v=t2;e[tot].cap=t3;e[tot].w=t4;e[tot].nex=head[t1];head[t1]=tot;
}
bool spfa(){
    for(int i=1;i<=n;i++)d[i]=inf,flag[i]=0;
    queue<int>q;q.push(S);d[S]=0;
    while(!q.empty()){
        
        int x=q.front();q.pop();
        for(int i=head[x];i;i=e[i].nex){
            if(e[i].cap>0&&d[e[i].v]>d[x]+e[i].w){
                d[e[i].v]=d[x]+e[i].w;
                if(!flag[e[i].v])flag[e[i].v]=1,q.push(e[i].v);
            }
        }
        flag[x]=0;
    }
    return d[T]!=inf;
}
int dfs(int k,int a){
    flag[k]=1;
    if(k==T||a==0)return a;
    int f,flow=0;
    for(int &i=cur[k];i;i=e[i].nex){
        if(d[e[i].v]==d[k]+e[i].w&&e[i].cap&&!flag[e[i].v]){//attention!!!
            f=dfs(e[i].v,min(e[i].cap,a));
            flow+=f;a-=f;e[i].cap-=f;e[i^1].cap+=f;
            ans+=f*e[i].w;
            if(a==0)break;
        }
    }
    return flow;
}
int main(){
    cin>>n>>m>>S>>T;
    for(int i=1;i<=m;i++){
        scanf("%d%d%d%d",&t1,&t2,&t3,&t4);
        lj(t1,t2,t3,t4);lj(t2,t1,0,-t4);
    }
    while(spfa()){
        flag[T]=1;
        while(flag[T]){
            memset(flag,0,sizeof(flag));
            for(int i=1;i<=n;i++)cur[i]=head[i];
            fl+=dfs(S,inf);
        }
    }
    cout<<fl<<' '<<ans<<endl;
    return 0;
}