HDU4185 Oil Skimming(二分图匹配,匈牙利算法)

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Problem Description

Thanks to a certain “green” resources company, there is a new
profitable industry of oil skimming. There are large slicks of crude
oil floating in the Gulf of Mexico just waiting to be scooped up by
enterprising oil barons. One such oil baron has a special plane that
can skim the surface of the water collecting oil on the water’s
surface. However, each scoop covers a 10m by 20m rectangle (going
either east/west or north/south). It also requires that the rectangle
be completely covered in oil, otherwise the product is contaminated by
pure ocean water and thus unprofitable! Given a map of an oil slick,
the oil baron would like you to compute the maximum number of scoops
that may be extracted. The map is an NxN grid where each cell
represents a 10m square of water, and each cell is marked as either
being covered in oil or pure water.

Input

The input starts with an integer K (1 <= K <= 100) indicating the
number of cases. Each case starts with an integer N (1 <= N <= 600)
indicating the size of the square grid. Each of the following N lines
contains N characters that represent the cells of a row in the grid. A
character of ‘#’ represents an oily cell, and a character of ‘.’
represents a pure water cell.

Output

For each case, one line should be produced, formatted exactly as
follows: “Case X: M” where X is the case number (starting from 1) and
M is the maximum number of scoops of oil that may be extracted.

Sample Input

1
6
......
.##...
.##...
....#.
....##
......

Sample Output

Case 1: 3

思路

有一个石油大亨要在一片 N∗N $N*N$区域里面打捞石油，它的网能网住的区域面积是$1×2$，#代表这个地方是石油，.代表这个地方是海水，问在这一片水域，最多能打捞多少石油（不能石油和海水一起捞）。

先给石油编上号码，编号为：1 2 3 4 5…这种，然后我们遍历这个区域，如果在$1×2$的区域有石油，那么就给他们的编号加一条边，建立二分图，最后求这个二分图的最大匹配就是答案。

因为建立的是双向边，所以要最后结果除以2

代码

#include <bits/stdc++.h>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a))
const int N=1000+20;
int e[N][N],vis[N],match[N],n,temp[N][N],num;
char s[N][N];
int dfs(int u)
{for(int i=1; i<=num; i++){if(e[u][i]&&!vis[i]){vis[i]=1;if(!match[i]||dfs(match[i])){match[i]=u;return 1;}}}return 0;
}
int query()
{mem(match,0);int sum=0;for(int i=1; i<=num; i++){mem(vis,0);if(dfs(i))sum++;}return sum;
}
int main()
{int t,q=1;scanf("%d",&t);while(t--){mem(temp,0);mem(e,0);num=0;scanf("%d",&n);for(int i=1; i<=n; i++){scanf("%s",s[i]+1);for(int j=1; j<=n; j++)if(s[i][j]=='#')temp[i][j]=++num;}for(int i=1; i<=n; i++)for(int j=1; j<=n; j++)if(s[i][j]=='#'){if(i!=1&&s[i-1][j]=='#') e[temp[i][j]][temp[i-1][j]]=1;if(j!=1&&s[i][j-1]=='#') e[temp[i][j]][temp[i][j-1]]=1;if(i!=n&&s[i+1][j]=='#') e[temp[i][j]][temp[i+1][j]]=1;if(j!=n&&s[i][j+1]=='#') e[temp[i][j]][temp[i][j+1]]=1;}printf("Case %d: %d\n",q++,query()/2);}return 0;
}

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