题目链接:https://www.luogu.org/problem/P2774
最小割建图。
先对格子分为黑白格,类似国际象棋。
然后S连黑,边权为黑点点权。
每个黑连周围4个白,边权为inf。
每个白连T,边权为白点点权。
#include <bits/stdc++.h>
#define rep(i, a, b) for(int i = (a); i <= (b); i++)
using namespace std;
const int N = 1e4+100;
int n,m,S,T,tot;
int head[N];
struct node{
int v,cap,nxt;
}edge[int(2e5+100)];
int cur[N],deep[N];
void ae(int u,int v,int cap){ //前向星加边
edge[++tot] = node{v,cap,head[u]};
head[u] = tot;
edge[++tot] = node{u,0,head[v]};
head[v] = tot;
}
bool bfs(){ //构建分层图
memset(deep,-1,sizeof(deep)); //-1表示未访问
queue<int>q;
q.push(S);
deep[S] = 0;
while(!q.empty()){
int u = q.front();
for(int i = head[u]; ~i;i = edge[i].nxt){
int v = edge[i].v;
if(deep[v]==-1&&edge[i].cap>0){
q.push(v);
deep[v] = deep[u]+1;
if(v==T) return 1; //提前退出
}
}
q.pop();
}
return 0;
}
int dfs(int u,int f){ //寻找增广网
int flow = 0,d;
if(u==T||f==0) return f;
for(int &i = cur[u]; ~i;i = edge[i].nxt){ //当前弧优化
int v = edge[i].v;
if(deep[v]>deep[u]&&edge[i].cap>0&&(d=dfs(v,min(f,edge[i].cap)))){
edge[i].cap -= d;
edge[i^1].cap += d;
f -= d;
flow += d;
if(!f) break;
}
}
if(flow==0) deep[u] = -1; //删除无法增广的点
return flow;
}
int dinic(){
int ans = 0;
while(bfs()){
memcpy(cur, head, sizeof(head)); //重置cur数组
ans += dfs(S,1e9);
}
return ans;
}
int v[N],sum;
int main() {
//freopen("a.txt","r",stdin);
ios::sync_with_stdio(0);
cin>>n>>m;
memset(head,-1,sizeof(head)); //head初始化-1
tot = -1; //边从0开始编号
rep(i, 0, n-1)
rep(j, 0, m-1) {
cin>>v[i*m+j];
sum += v[i*m+j];
}
S = n*m;
T = n*m+1;
rep(i, 0, n-1)
rep(j, 0, m-1) {
int u = i*m+j;
if((i+j)%2==0) {
ae(S,u,v[u]);
if(i>0) ae(u,u-m,1e9);
if(i<n-1) ae(u,u+m,1e9);
if(j>0) ae(u,u-1,1e9);
if(j<m-1) ae(u,u+1,1e9);
}
else ae(u,T,v[u]);
}
cout<<sum-dinic()<<endl;
return 0;
}