【Luogu】P2469星际竞速（费用流）

　　题目链接

　　费用流，类似最小路径覆盖。

　　从起点向i连一条容量1费用0的边，从i'向终点连一条容量1费用0的边；

　　从起点向i'连一条容量1费用为瞬移的边，从i向j'连一条容量1费用为边权的边。

　　然后跑就可以了。

#include<cstdio>

#include<cstdlib>

#include<cctype>

#include<cstring>

#include<algorithm>

#include<queue>

#define maxn 200020

using namespace std;

inline long long read(){

    long long num=,f=;

    char ch=getchar();

    while(!isdigit(ch)){

        if(ch=='-')    f=-;

        ch=getchar();

    }

    while(isdigit(ch)){

        num=num*+ch-'';

        ch=getchar();

    }

    return num*f;

}

struct Edge{

    int next,from,to,val,dis;

}edge[maxn];

int head[maxn],num;

inline void addedge(int from,int to,int val,int dis){

    edge[++num]=(Edge){head[from],from,to,val,dis};

    head[from]=num;

}

inline void add(int from,int to,int val,int dis){

    addedge(from,to,val,dis);

    addedge(to,from,,-dis);

}

inline int count(int i){    return i&?i+:i-;    }

int dis[maxn];

int pre[maxn];

bool vis[maxn];

int Start,End;

int spfa(){

    memset(dis,/,sizeof(dis));    dis[Start]=;

    memset(pre,,sizeof(pre));

    queue<int>q;    q.push(Start);

    while(!q.empty()){

        int from=q.front();    q.pop();    vis[from]=;

        //printf("%d\n",from);

        for(int i=head[from];i;i=edge[i].next){

            int to=edge[i].to;

            if(edge[i].val<=||dis[to]<=dis[from]+edge[i].dis)    continue;

            dis[to]=dis[from]+edge[i].dis;

            pre[to]=i;

            if(vis[to])    continue;

            vis[to]=;    q.push(to);

        }

    }

    if(pre[End]==)    return ;

    int now=End;

    while(now!=Start){

        int ret=pre[now];

        edge[ret].val--;    edge[count(ret)].val++;

        now=edge[ret].from;

    }

    return dis[End];

}

int main(){

    int n=read(),m=read();

    End=n*+;

    for(int i=;i<=n;++i){

        add(Start,i+n,,read());

        add(Start,i,,);

        add(i+n,End,,);

    }

    for(int i=;i<=m;++i){

        int from=read(),to=read(),val=read();

        if(from>to)    swap(from,to);

        add(from,to+n,,val);

    }

    int ans=;

    while(){

        int now=spfa();

        if(now==)    break;

        ans+=now;

    }

    printf("%d",ans);

    return ;

}