【NOI2008】志愿者招募

题面

https://www.luogu.org/problem/P3980

题解

套路作差，每个点代表一组等式，然后连边。

#include<cstdio>
#include<cstring>
#include<iostream>
#include<queue>
#include<vector>
#include<algorithm>
#define ri register int
#define N 1050
#define S (n+1)
#define T (n+2)
#define INF 1000000007
#define LL long long

using namespace std;

int n,m;
int need[N];

struct graph {
  vector<int> to,w,c;
  vector<int> ed[N];
  LL dis[N]; int cur[N];
  bool vis[N];
  void add_edge(int a,int b,int aw,int ac) {
    to.push_back(b); w.push_back(aw); c.push_back(ac);  ed[a].push_back(to.size()-1);
    to.push_back(a); w.push_back(0);  c.push_back(-ac); ed[b].push_back(to.size()-1);
  }
  bool spfa() {
    memset(dis,0x2f,sizeof(dis));
    memset(vis,0,sizeof(vis));
    queue<int> q;
    dis[S]=0;q.push(S);vis[S]=1;
    while (!q.empty()) {
      int x=q.front(); q.pop();
      for (ri i=0;i<ed[x].size();i++) {
        int e=ed[x][i];
        if (dis[to[e]]>dis[x]+c[e] && w[e]) {
          dis[to[e]]=dis[x]+c[e];
          if (!vis[to[e]]) vis[to[e]]=1,q.push(to[e]);
        }
      }
      vis[x]=0;
    }
    return dis[T]<INF;
  }
  int dfs(int x,int lim) {
    if (x==T || !lim) return lim;
    LL sum=0; vis[x]=1;
    for (ri &i=cur[x];i<ed[x].size();i++) {
      int e=ed[x][i];
      if (dis[x]+c[e]==dis[to[e]] && w[e] && !vis[to[e]]) {
        int f=dfs(to[e],min(lim,w[e]));
        w[e]-=f; w[1^e]+=f;
        lim-=f; sum+=f;
        if (!lim) return sum;
      }
    }
    return sum;
  }
  LL zkw() {
    LL ret=0;
    while (spfa()) {
      memset(vis,0,sizeof(vis));
      memset(cur,0,sizeof(cur));
      ret+=dfs(S,INF)*dis[T];
    }
    return ret;
  }
} G;

int main() {
  int s,t,c;
  scanf("%d %d",&n,&m);
  for (ri i=1;i<=n;i++) {
    scanf("%d",&need[i]);
  }
  for (ri i=0;i<=n;i++) {
    if (need[i]-need[i+1]>0) G.add_edge(S,i,need[i]-need[i+1],0);
    else if (need[i]-need[i+1]<0) G.add_edge(i,T,need[i+1]-need[i],0);
    if (i<n) G.add_edge(i,i+1,INF,0);
  }
  for (ri i=1;i<=m;i++) {
    scanf("%d %d %d",&s,&t,&c);
    G.add_edge(t,s-1,INF,c);
  }
  cout<<G.zkw()<<endl;
}