ZOJ 1002 - Fire Net
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=1002
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 legalprovided 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.
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.
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
这题有点像八皇后，但是有变形，比如墙可以把炮弹隔开，炮弹只能沿上下左右四个方向等等，但整体思路还是一致的，dfs加回溯，一个一个位置试，判断是否与前面的炮冲突。如果冲突了，遍历下一个；如果没冲突，那么炮台数目加一，修改地图，遍历下一个，然后回溯，将地图和数目改回来，遍历下一个。
代码如下:
1 #include<stdio.h>
2 int map[6][6];
3 int max, n, count;
4 int isright(int x, int y) //判断当前位置放大炮的话是否与其他位置放的冲突
5 { //不必判断是否与右方和下方的冲突，因为还没有放
6 int i;
7 for(i = x - 1; i >= 0; i--)
8 {
9 if(map[i][y] == 2)
10 return 0;
11 if(!map[i][y])
12 break;
13 }
14 for(i = y - 1; i >= 0; i--)
15 {
16 if(map[x][i] == 2)
17 return 0;
18 if(!map[x][i])
19 break;
20 }
21 return 1;
22 }
23 void dfs(int u)
24 {
25 int x, y;
26 if(u == n * n)
27 {
28 if(count > max)
29 max = count;
30 return;
31 }
32 x = u / n;
33 y = u % n;
34 if(map[x][y] == 1 && isright(x, y))//可以放在这个位置
35 {
36 map[x][y] = 2; count ++; //修改地图和数目
37 dfs(u + 1);
38 map[x][y] = 1; count --; //回溯
39 }
40 dfs(u + 1);
41 }
42 int main()
43 {
44 int i, j;
45 char c;
46 while(scanf("%d", &n) && n)
47 {
48 getchar();
49 for(i = 0; i < n; i++)
50 {
51 for(j = 0; j < n; j++)
52 {
53 scanf("%c", &c);
54 if(c == '.')
55 map[i][j] = 1;
56 else map[i][j] = 0;
57 }
58 getchar();
59 }
60 max = 0; count = 0;
61 dfs(0);
62 printf("%d\n", max);
63 }
64 return 0;
65 }
