loj2100 「TJOI2015」线性代数

先推公式,推出个,然后因为是 \(0/1\) 矩阵,选一个有损耗,两个一组有加成,就想到了最大权闭合子图,(飞行计划问题)

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;
int n, uu, ss, tt, hea[250505], cnt, cur[250505], maxFlow, lev[250505], ans;
const int oo=0x3f3f3f3f;
queue<int> d;
struct Edge{
    int too, nxt, val;
}edge[1600005];
void add_edge(int fro, int too, int val){
    edge[cnt].nxt = hea[fro];
    edge[cnt].too = too;
    edge[cnt].val = val;
    hea[fro] = cnt++;
}
void addEdge(int fro, int too, int val){
    add_edge(fro, too, val);
    add_edge(too, fro, 0);
}
bool bfs(){
    memset(lev, 0, sizeof(lev));
    lev[ss] = 1;
    d.push(ss);
    while(!d.empty()){
        int x=d.front();
        d.pop();
        for(int i=hea[x]; i!=-1; i=edge[i].nxt){
            int t=edge[i].too;
            if(!lev[t] && edge[i].val>0){
                lev[t] = lev[x] + 1;
                d.push(t);
            }
        }
    }
    return lev[tt]!=0;
}
int dfs(int x, int lim){
    if(x==tt)   return lim;
    int addFlow=0;
    for(int &i=cur[x]; i!=-1; i=edge[i].nxt){
        int t=edge[i].too;
        if(lev[t]==lev[x]+1 && edge[i].val>0){
            int tmp=dfs(t, min(lim-addFlow, edge[i].val));
            edge[i].val -= tmp;
            edge[i^1].val += tmp;
            addFlow += tmp;
            if(addFlow==lim)    break;
        }
    }
    return addFlow;
}
void dinic(){
    while(bfs()){
        for(int i=ss; i<=tt; i++)   cur[i] = hea[i];
        maxFlow += dfs(ss, oo);
    }
}
int main(){
    memset(hea, -1, sizeof(hea));
    cin>>n;
    ss = 0; tt = n + n * n + 1;
    for(int i=1; i<=n; i++)
        for(int j=1; j<=n; j++){
            scanf("%d", &uu);
            ans += uu;
            int p=(i-1)*n+j;
            addEdge(ss, p, uu);
            addEdge(p, n*n+i, oo);
            addEdge(p, n*n+j, oo);
        }
    for(int i=1; i<=n; i++){
        scanf("%d", &uu);
        addEdge(n*n+i, tt, uu);
    }
    dinic();
    cout<<ans-maxFlow<<endl;
    return 0;
}

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转载自www.cnblogs.com/poorpool/p/9087744.html