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;

}
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luogu2774 方格取数问题

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