Fire Net

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 5175    Accepted Submission(s): 2908

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

  1 #include<stdio.h>
  2 #include<stdlib.h>
  3 #include<string.h>
  4 #define maxn 10
  5 char maze[maxn][maxn];
  6 int ans,n,count,max;
  7 /*用p作为人的标记*/
  8 /*判断竖横是否有城堡*/
  9 bool judge(int x,int y)
 10 {
 11  int i;
 12  bool flag=true;
 13  for(i=y+1;i<=n;i++)
 14  {
 15      if(maze[x][i]=='P')
 16      {
 17          flag=false;
 18          break;
 19      }
 20      else
 21          if(maze[x][i]=='X')
 22                  break;
 23  }
 24   if(!flag)
 25         return false;
 26    for(i=y-1;i>=1;i--)
 27    {
 28      if(maze[x][i]=='P')
 29      {
 30          flag=false;
 31          break;
 32      }
 33      else
 34          if(maze[x][i]=='X')
 35                  break;
 36    }
 37   if(!flag)
 38         return false;
 39  for(i=x+1;i<=n;i++)
 40  {
 41      if(maze[i][y]=='P')
 42      {
 43          flag=false;
 44          break;
 45      }
 46      else if(maze[i][y]=='X')
 47             break;
 48  }
 49  if(!flag)
 50         return false;
 51  for(i=x-1;i>=1;i--)
 52  {
 53      if(maze[i][y]=='P')
 54      {
 55          flag=false;
 56          break;
 57      }
 58      else if(maze[i][y]=='X')
 59          break;
 60  }
 61  if(!flag)
 62         return false;
 63  else
 64      return true;
 65 }
 66 void dfs()
 67 {
 68   for(int i=1;i<=n;i++)
 69   {
 70       for(int j=1;j<=n;j++)
 71       {
 72       if(maze[i][j]=='.'&&true==judge(i,j))
 73       {
 74        count++;
 75        maze[i][j]='P';
 76        dfs();
 77        if(count>ans)  
 78              ans=count;
 79        maze[i][j]='.';
 80        count--;
 81       }
 82       }
 83   }
 84 }
 85 int main()
 86 {
 87     int i,j;
 88  while(scanf("%d",&n),n)
 89  {
 90    getchar();
 91    max=0;
 92   for( i=1;i<=n;i++)
 93   {
 94       for( j=1;j<=n;j++)
 95       {
 96           scanf("%c",&maze[i][j]);
 97       }
 98       getchar();
 99   }
100   for(i=1;i<=n;i++)
101   {
102       for(j=1;j<=n;j++)
103       {   
104           if(maze[i][j]!='X')
105           {
106              count=1;
107              ans=0;
108              maze[i][j]='P';
109              dfs();
110              maze[i][j]='.';
111              if(ans==0)  max=1;
112               else
113              if(ans>max)    max=ans;
114           }
115       }
116   }
117    printf("%dn",max);
118  }
119  return 0;
120 }

思路：   每次涂一个点，然后生成一张图，将其作为一张新图，又重新开始涂点.....周而复始.....

并不断记录点的最大个数.用栈，或者回溯都可以实现.....