HDU 1045 Fire Net 二分圖匹配

機智建圖法。行爲一個集合裏的點，不能互相攻擊的行算兩個；列爲另一個集合裏的點。這樣做一個二分圖匹配，一個行就不能跟多個列匹配，避免出現互相攻擊的狀況，相當於做了一次縮點。

#include<iostream>
#include<cstdio>
#include<string.h>
#include<algorithm>
using namespace std;

int n,cntx,cnty,girl[100],h[100][100],l[100][100];
bool line[100][100],used[100];
char mapp[100][100];

bool finds(int x)
{
    //cout<<"yes"<<endl;
    //cout<<"cntx="<<cntx<<" cnty="<<cnty<<endl;
    for (int j=0; j<cnty; j++)
    {
        //cout<<"x="<<x<<" j="<<j<<endl;
        if (line[x][j] && !used[j])
        {
            used[j]=1;
            if (girl[j]==-1 || finds(girl[j]))
            {
                girl[j]=x;
                //cout<<"x="<<x<<" j="<<j<<endl;
                return true;
            }
        }
    }
    return false;
}

int main()
{
    while (~scanf("%d",&n) && n)
    {
        for (int i=1; i<=n; i++)
        {
            for (int j=1; j<=n; j++)
            {
                char ch; cin>>ch; mapp[i][j]=ch;
            }
        }
        cntx=0; cnty=0;
        for (int i=1; i<=n; i++)
        {
            for (int j=1; j<=n; j++)
            {
                if (mapp[i][j]=='.')
                {
                    if (j==0) h[i][j]=cntx++;
                    else if (mapp[i][j-1]=='.') h[i][j]=h[i][j-1];
                    else h[i][j]=cntx++;
                    if (i==0) l[i][j]=cnty++;
                    else if (mapp[i-1][j]=='.') l[i][j]=l[i-1][j];
                    else l[i][j]=cnty++;
                }
            }
        }

        memset(line,false,sizeof(line));
        for (int i=1; i<=n; i++)
        {
            for (int j=1; j<=n; j++)
            {
                if (mapp[i][j]=='.')
                line[h[i][j]][l[i][j]]=true;
            }
        }
        int all=0;
        memset(girl,-1,sizeof(girl));
        for (int i=0; i<cntx; i++)
        {
            memset(used,false,sizeof(used));
            //cout<<"i="<<i<<endl;
            //cout<<"!cntx="<<cntx<<" cnty="<<cnty<<endl;
            if (finds(i)) all+=1;
        }
        cout<<all<<endl;
    }
    return 0;
}