hdu Fire Net（DFS）

Fire Net

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......2XX.X3.X.X.X.X.3....XX.XX4................0

 

Sample Output

51524

题意：为了使炮台不能互相攻击，同一行同一列只能放置一个炮台，但是中间若有城墙挡着说明互相攻击不到，则可以放置多个

思路：DFS枚举各种情况，每个为"."的点都可以选择放置炮台或者不放炮台，只要保证放置的炮台互相攻击不到即可，那就直接从（0，0）开始，遍历所有点找到最大可放置的炮台数目

代码：

#include<stdio.h>#define max(a,b) (a>b?a:b)char s[5][5];int n,ans;int judge(int x,int y)//判断是否可以放置炮台{    for(int i=x-1;i>=0;i--)    {        if(s[i][y]=='X')//找到墙，退出循环            break;        if(s[i][y]=='A')//已经放置过炮台，说明此行已经被标记，直接判断为不可以            return 0;    }    for(int i=y-1;i>=0;i--)    {        if(s[x][i]=='X')//找到墙，退出循环            break;        if(s[x][i]=='A')//已经放置过炮台，说明此行已经被标记，直接判断为不可以            return 0;    }    return 1;//当行和列都没有被标记过时才可以放置炮台}void dfs(int step,int sum)//step记录走的步数，sum记录放置的炮台的数目{    if(step==n*n)//遍历完了所有的点    {        ans=max(ans,sum);//更新结果        return ;    }    int x=step/n,y=step%n;    if(s[x][y]=='.'&&judge(x,y))//判断是否可以放置炮台    {        s[x][y]='A';//可以放置就将其置为A        dfs(step+1,sum+1);        s[x][y]='.';//还原    }    dfs(step+1,sum);//不放置炮台}int main(){    while(~scanf("%d",&n),n)    {        ans=0;        for(int i=0;i<n;i++)            scanf("%s",s[i]);        dfs(0,0);        printf("%d\n",ans);    }    return 0;}