luogu2774 方格取数问题

最大点权独立集，参见胡伯涛论文

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;
int m, n, a[105][105], hea[10005], ss, tt, tot, maxFlow, lev[10005], cnt;
const int oo=0x3f3f3f3f;
const int dx[]={0, 1, 0, -1, 0};
const int dy[]={0, 0, 1, 0, -1};
queue<int> d;
struct Edge{
	int too, nxt, val;
}edge[100005];
inline int f(int x, int y){
	return n*(x-1)+y;
}
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=hea[x]; i!=-1 && addFlow<lim; 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;
		}
	}
	return addFlow;
}
void dinic(){
	while(bfs())	maxFlow += dfs(ss, oo);
}
int main(){
	memset(hea, -1, sizeof(hea));
	cin>>m>>n;
	ss = 0; tt = m * n + 1;
	for(int i=1; i<=m; i++)
		for(int j=1; j<=n; j++)
			scanf("%d", &a[i][j]);
	for(int i=1; i<=m; i++)
		for(int j=1; j<=n; j++){
			tot += a[i][j];
			if((i+j)&1)	addEdge(ss, f(i,j), a[i][j]);
			else	addEdge(f(i,j), tt, a[i][j]);
			for(int k=1; k<=4; k++){
				int tx=i+dx[k];
				int ty=j+dy[k];
				if(tx<1 || tx>m || ty<1 || ty>n)	 continue;
				if((i+j)&1)	addEdge(f(i,j), f(tx,ty), oo);
				else	addEdge(f(tx,ty), f(i,j), oo);
			}
		}
	dinic();
	cout<<tot-maxFlow<<endl;
	return 0;
}