loj2057 「TJOI / HEOI2016」游戏

记横联通是一块横着的没有硬石头的地，把他们编号。竖联通同理。

对于一个空地，将其横联通编号和竖联通编号连边，二分图匹配，最大匹配为答案。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;
int n, m, hr[55][55], sr[55][55], hcnt, scnt, hea[5005], cnt, yy, tt, lev[5005];
int maxFlow, cur[5005];
const int oo=0x3f3f3f3f;
char ss[55][55];
queue<int> d;
struct Edge{
	int too, nxt, val;
}edge[10005];
void add_edge(int fro, int too, int val){
	edge[cnt].nxt = hea[fro];
	edge[cnt].val = val;
	edge[cnt].too = too;
	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[yy] = 1;
	d.push(yy);
	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){
			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=yy; i<=tt; i++)	cur[i] = hea[i];
		maxFlow += dfs(yy, oo);
	}
}
int main(){
	cin>>n>>m;
	for(int i=1; i<=n; i++)
		scanf("%s", ss[i]+1);
	for(int i=1; i<=n; i++)
		for(int j=1; j<=m; j++)
			if(!hr[i][j] && ss[i][j]!='#'){
				hcnt++;
				for(int k=j; k<=m && ss[i][k]!='#'; k++)
					hr[i][k] = hcnt;
			}
	for(int i=1; i<=n; i++)
		for(int j=1; j<=m; j++)
			if(!sr[i][j] && ss[i][j]!='#'){
				scnt++;
				for(int k=i; k<=n && ss[k][j]!='#'; k++)
					sr[k][j] = scnt;
			}
	memset(hea, -1, sizeof(hea));
	for(int i=1; i<=n; i++)
		for(int j=1; j<=m; j++)
			if(ss[i][j]=='*')
				addEdge(hr[i][j], hcnt+sr[i][j], 1);
	yy = 0; tt = hcnt + scnt + 1;
	for(int i=1; i<=hcnt; i++)
		addEdge(yy, i, 1);
	for(int i=1; i<=scnt; i++)
		addEdge(i+hcnt, tt, 1);
	dinic();
	cout<<maxFlow<<endl;
	return 0;
}