【TJOI2015】线性代数

题面

https://www.luogu.org/problem/P3973

题解

花个图理解一下，就是要选$b[x][y])$，必须选$c[x]$和$c[y]$。

最大权闭即可。

#include<cstdio>
#include<cstring>
#include<iostream>
#include<queue>
#include<vector>
#include<map>
#include<utility>
#define ri register int
#define N 400050
#define INF 1000000007
#define S 0
#define T (n*n+1)
using namespace std;

int n,x;

struct graph {
  vector<int> ed[N];
  vector<int> w,to;
  int d[N],cur[N];
  void add_edge(int u,int v,int tw) {
    to.push_back(v); w.push_back(tw); ed[u].push_back(to.size()-1);
    to.push_back(u); w.push_back(0) ; ed[v].push_back(to.size()-1);
  }
  bool bfs() {
    queue<int> q;
    memset(d,0x3f,sizeof(d));
    d[S]=0; q.push(S);
    while (!q.empty()) {
      int x=q.front(); q.pop();
      for (ri i=0;i<ed[x].size();i++) {
        int e=ed[x][i];
        if (d[x]+1<d[to[e]] && w[e]) {
          d[to[e]]=d[x]+1;
          q.push(to[e]);
        }
      }
    }
    return d[T]<INF;
  }
  int dfs(int x,int limit) {
    if (x==T || limit==0) return limit;
    int sum=0; 
    for (ri &i=cur[x];i<ed[x].size();i++) {
      int e=ed[x][i];
      if (w[e] && d[x]+1==d[to[e]]) {
        int f=dfs(to[e],min(limit,w[e]));
        if (!f) continue;
        sum+=f; limit-=f; 
        w[e]-=f; w[1^e]+=f;
        if (!limit) return sum;
      }
    }
    return sum;
  }
  int dinic() {
    int ret=0;
    while (bfs()) {
      memset(cur,0,sizeof(cur));
      ret+=dfs(S,INF);
    }
    return ret;
  }
} G;

int main(){
  cin>>n;
  int sum=0;
  for (ri i=1;i<=n;i++) 
    for (ri j=1;j<=n;j++) {
      cin>>x; sum+=x;
      G.add_edge(i,i*n+j,INF);
      G.add_edge(j,i*n+j,INF);
      G.add_edge(i*n+j,T,x);
    }
  for (ri i=1;i<=n;i++) {
    cin>>x;
    G.add_edge(S,i,x);
  }
  cout<<sum-G.dinic()<<endl;
}