【HEOI2016/TJOI2016】游戏

题面

https://www.luogu.org/problemnew/show/P2825

题解

水题

二分图匹配的经典模型。

对于硬石头，拆点。

// luogu-judger-enable-o2
#include<cstdio>
#include<iostream>
#include<cstring>
#include<vector>
#include<queue>
#define ri register int
#define N 505000
#define INF 1000000007
#define T (n+m+1)

using namespace std;

int n,m,han[100][100],lie[100][100];
vector<int> to,w,ed[N];
int cur[N],d[N],tn,tm;
char g[100][100];

void add_edge(int u,int v,int w1,int w2) {
  to.push_back(v); w.push_back(w1); ed[u].push_back(to.size()-1);
  to.push_back(u); w.push_back(w2); ed[v].push_back(to.size()-1);
}

bool bfs() {
  queue<int> q;
  memset(d,0x3f,sizeof(d));
  d[0]=0; q.push(0);
  while (!q.empty()) {
    int x=q.front(); q.pop();
    for (ri i=0,l=ed[x].size();i<l;i++) {
      int e=ed[x][i];
      if (w[e] && d[x]+1<d[to[e]]) {
        d[to[e]]=d[x]+1;
        q.push(to[e]);
      }
    }
  }
  return d[T]<=1000000;
}

int dfs(int x,int limit) {
  if (x==T || !limit) return limit;
  int tot=0;
  for (ri &i=cur[x];i<ed[x].size();i++) {
    int e=ed[x][i];
    if (d[to[e]]==d[x]+1 && w[e]) {
      int f=dfs(to[e],min(limit,w[e]));
      if (!f) continue;
      w[e]-=f; w[1^e]+=f; 
      tot+=f; limit-=f;
      if (!limit) return tot;
    }
  }
  return tot;
}

int dinic() {
  int ret=0;
  while (bfs()) {
    memset(cur,0,sizeof(cur));
    ret+=dfs(0,INF);
  }
  return ret;
}

void init() {
    int tn=0,tm=0;
  for (ri i=1;i<=n;i++) {
    ++tn;
    for (ri j=1;j<=m;j++) {
        han[i][j]=tn;
        if (g[i][j]=='#') tn++;
      }
    }
    for (ri i=1;i<=m;i++) {
      ++tm;
      for (ri j=1;j<=n;j++) {
        lie[j][i]=tm;
        if (g[j][i]=='#') tm++;
      }
    }
    n=tn; m=tm;
    return;
}

void makegraph() {
  for (ri i=1;i<=n;i++) add_edge(0,i,1,0);
  for (ri i=1;i<=m;i++) add_edge(n+i,T,1,0);
  for (ri i=1;i<=tn;i++)
    for (ri j=1;j<=tm;j++) if (g[i][j]=='*') add_edge(han[i][j],n+lie[i][j],1,0);
}

int main() {
  scanf("%d %d",&n,&m); tn=n; tm=m;
  for (ri i=1;i<=n;i++) scanf("%s",g[i]+1);
  init();
  makegraph();
  printf("%d
",dinic());
}