P2774 方格取数问题 (最小割)

题目链接

 解法参见：https://www.luogu.com.cn/blog/cicos/solution-p2774#

Code:

#include <bits/stdc++.h>
#define LL long long
#define INF 0x3f3f3f3f;
using namespace std;

int M, N;
int S, T;
int dir[4][2]={{1,0},{-1,0},{0,1},{0,-1}};
struct Edge{
    int next, from, to, remain;
}e[30000];
int en;
int head[11000];
queue<int> q;
int visited[11000];
int preEdge[11000];
int minflow[11000];
int resflow;
int totalSum;

void addEdge(int from, int to, int flow){
    e[en].next=head[from];
    e[en].from=from;
    e[en].to=to;
    e[en].remain=flow;
    head[from]=en;
    ++en;
}

void add(int from, int to, int flow){
    addEdge(from, to, flow);
    addEdge(to, from, 0);
}

void bfs(){
    memset(visited,0,sizeof(visited));
    memset(preEdge,-1,sizeof(preEdge));
    memset(minflow,0,sizeof(minflow));
    q.push(S);
    visited[S]=1;
    minflow[S]=INF;
    while(!q.empty()){
        int u=q.front();
        q.pop();
        for(int i=head[u];i!=-1;i=e[i].next){
            if(e[i].remain>0 && !visited[e[i].to]){
                visited[e[i].to]=1;
                minflow[e[i].to]=min(minflow[u],e[i].remain);
                preEdge[e[i].to]=i;
                q.push(e[i].to);
            }
        }
    }
}

void EK(){
    while(true){
        bfs();
        if(preEdge[T]==-1) break;
        resflow+=minflow[T];
        int v=T;
        while(true){
            int edge=preEdge[v];
            if(edge==-1) break;
            e[edge].remain-=minflow[T];
            e[edge^1].remain+=minflow[T];
            v=e[edge].from;
        }
    }
}

int getIndex(int i, int j){
    return i*N+j;
}

int main(){
    memset(head,-1,sizeof(head));
    scanf("%d %d", &M, &N);
    S=2*M*N, T=3*M*N;
    for(int i=0;i<M;++i){
        for(int j=0;j<N;++j){
            int num;
            scanf("%d", &num);
            totalSum+=num;
            if((i+j)%2==0){
                add(S,getIndex(i,j),num);
            }else {
                add(getIndex(i,j),T,num);
            }
        }
    }
    for(int i=0;i<M;++i){
        for(int j=0;j<N;++j){
            if((i+j)%2==0){
                for(int d=0;d<4;++d){
                    int ni=i+dir[d][0];
                    int nj=j+dir[d][1];
                    if(ni>=0 && ni<M && nj>=0 && nj<N){
                        add(getIndex(i,j),getIndex(ni,nj),0x3f3f3f3f);
                    }
                }
            }
        }
    }

    EK();

    printf("%d", totalSum-resflow);
    return 0;
}