hdu1045 暴力搜索，用二分图也可以做

http://acm.hdu.edu.cn/showproblem.php?pid=1045

Problem Description

Suppose that we have a square city with straight streets. A map of a city is a square board with n rows and n columns, each representing a street or a piece of wall. 

A blockhouse is a small castle that has four openings through which to shoot. The four openings are facing North, East, South, and West, respectively. There will be one machine gun shooting through each opening. 

Here we assume that a bullet is so powerful that it can run across any distance and destroy a blockhouse on its way. On the other hand, a wall is so strongly built that can stop the bullets. 

The goal is to place as many blockhouses in a city as possible so that no two can destroy each other. A configuration of blockhouses is legal provided that no two blockhouses are on the same horizontal row or vertical column in a map unless there is at least one wall separating them. In this problem we will consider small square cities (at most 4x4) that contain walls through which bullets cannot run through. 

The following image shows five pictures of the same board. The first picture is the empty board, the second and third pictures show legal configurations, and the fourth and fifth pictures show illegal configurations. For this board, the maximum number of blockhouses in a legal configuration is 5; the second picture shows one way to do it, but there are several other ways. 



Your task is to write a program that, given a description of a map, calculates the maximum number of blockhouses that can be placed in the city in a legal configuration. 

 

Input

The input file contains one or more map descriptions, followed by a line containing the number 0 that signals the end of the file. Each map description begins with a line containing a positive integer n that is the size of the city; n will be at most 4. The next n lines each describe one row of the map, with a '.' indicating an open space and an uppercase 'X' indicating a wall. There are no spaces in the input file. 

 

Output

For each test case, output one line containing the maximum number of blockhouses that can be placed in the city in a legal configuration.

 

Sample Input

   
   
   
   

    
    
    
    4
.X..
....
XX..
....
2
XX
.X
3
.X.
X.X
.X.
3
...
.XX
.XX
4
....
....
....
....
0
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    5
1
5
2
4
   
   
   
   

 

/***
hdu 1045  暴力搜索，用二分图也可以做
题目大意：给定一个n*n的棋盘可以放一些棋子任意两个棋子不能在同一行或同一列，除非二者之间有障碍点阻隔，已知所有障碍点的位置，
          问最多可以放的棋子数
解题思路：爆搜就行，也可以用二分图做，每一列两个障碍（起始位置也看做障碍）之间的点算一个，每一行同理，然后列和行匹配即可。
          给出爆搜代码。
          二分图：http://www.cnblogs.com/kuangbin/archive/2011/08/09/2132830.html
*/
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
using namespace std;

char map[5][5];
int maxnum;
int n;

bool build(int row,int col)
{
    for(int i=row;i>=0;i--)
    {
        if(map[i][col]=='O')
            return false;
        if(map[i][col]=='X')
            break;
    }
    for(int j=col;j>=0;j--)
    {
        if(map[row][j]=='O')
             return false;
        if(map[row][j]=='X')
             break;
    }
    return true;
}

void dfs(int i,int num)
{
    if(i==n*n)
    {
        if(num>maxnum)maxnum=num;
        return;
    }
    int row=i/n;
    int col=i%n;
    if(map[row][col]=='.'&&build(row,col))
    {
        map[row][col]='O';
        dfs(i+1,num+1);
        map[row][col]='.';
    }
    dfs(i+1,num);
}

int main()
{
    while(~scanf("%d",&n))
    {
        if(n==0)break;
        maxnum=0;
        for(int i=0;i<n;i++)
        {
            scanf("%s",&map[i]);
        }
        dfs(0,0);
        printf("%d\n",maxnum);
    }
    return 0;
}