本文探讨了如何在限定的城市地图中合法放置城堡以最大化城堡数量，通过深度优先搜索（DFS）算法解决该问题。示例输入包括城市规模、地图描述和最终合法配置的最大城堡数。
Fire Net
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 5076 Accepted Submission(s): 2847
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.
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
思路：DFS，我是看了别人的代码才过的
代码：
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
char map[6][6];
int max_sum;
int sum;
int n;
bool canput(int k)
{
int flag = 1;
int i = k / n;int j = k % n;
for(int p = 1;i - p >= 0;p ++)
{
if(map[i - p][j] == 'o')
{
flag = 0;
break;
}
if(map[i - p][j] == 'X')
break;
}
for(int p = 1;j - p >= 0;p ++)
{
if(map[i][j - p] == 'o')
{
flag = 0;
break;
}
if(map[i][j - p] == 'X')
break;
}
return flag;
}
void DFS(int k,int sum)
{
int i = k / n;int j = k % n;
if(k == n * n)
{
if(max_sum < sum)
max_sum = sum;
return ;
}
else
{
if(map[i][j] == '.'
&& canput(k))
{
map[i][j] = 'o';
DFS(k + 1,sum + 1);
map[i][j] = '.';
}
DFS(k + 1,sum);
}
}
int main()
{
while(scanf("%d",&n),n != 0)
{
for(int i = 0;i < n;i ++)
for(int j = 0;j < n;j ++)
scanf(" %c",&map[i][j]);
max_sum = 0;
DFS(0,0);
printf("%d\n",max_sum);
}
return 0;
}
#include <cstdio>
#include <cstring>
using namespace std;
char map[6][6];
int max_sum;
int sum;
int n;
bool canput(int k)
{
int flag = 1;
int i = k / n;int j = k % n;
for(int p = 1;i - p >= 0;p ++)
{
if(map[i - p][j] == 'o')
{
flag = 0;
break;
}
if(map[i - p][j] == 'X')
break;
}
for(int p = 1;j - p >= 0;p ++)
{
if(map[i][j - p] == 'o')
{
flag = 0;
break;
}
if(map[i][j - p] == 'X')
break;
}
return flag;
}
void DFS(int k,int sum)
{
int i = k / n;int j = k % n;
if(k == n * n)
{
if(max_sum < sum)
max_sum = sum;
return ;
}
else
{
if(map[i][j] == '.'
&& canput(k))
{
map[i][j] = 'o';
DFS(k + 1,sum + 1);
map[i][j] = '.';
}
DFS(k + 1,sum);
}
}
int main()
{
while(scanf("%d",&n),n != 0)
{
for(int i = 0;i < n;i ++)
for(int j = 0;j < n;j ++)
scanf(" %c",&map[i][j]);
max_sum = 0;
DFS(0,0);
printf("%d\n",max_sum);
}
return 0;
}
Sample Output
5 1 5 2 4
Source
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