Fire Net

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

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

Source

Zhejiang University Local Contest 2001

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题意：问可以放多少个碉堡，碉堡不能在同一行或列，除非有墙隔开，就是两个碉堡在同一行或列的条件是必须有墙隔开

回溯搜索~

#include <stdio.h>
#include <string.h>
#include <algorithm>

using namespace std;

char Map[5][5];
int res;
int n;

bool judge(int x,int y)
{
	if(Map[x][y]!='.')return false; //X.S都不可以放
	for(int i=x-1;i>=0;i--){//判断点的上方
		if(Map[i][y]=='X')break;
		if(Map[i][y]=='O')return false;
	}
	for(int i=y-1;i>=0;i--){//判断点的左方
		if(Map[x][i]=='X')break;
		if(Map[x][i]=='O')return false;
	}
	return true;
}

void DFS(int x,int y,int tot)
{
	if(x==n&&y==0){ //已经搜索了n行，求最大值
		res=max(res,tot);
		return;
	}
	if(y==n){ //这一行已经求完，从下一行第一列重新开始
		DFS(x+1,0,tot);
		return;
	}
	for(int i=y;i<n;i++){
		if(judge(x,i)){
			Map[x][i]='O';
			DFS(x,i+1,tot+1);
			Map[x][i]='.';
		}
	}
	DFS(x+1,0,tot);//上一行搜索结束，从下一行重新开始
}

int main()
{
	while(scanf("%d",&n),n){
		res=0;
		for(int i=0;i<n;i++)
			scanf("%s",Map[i]);
		DFS(0,0,0);
		printf("%d\n",res);
	}
	return 0;
 } 

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