ZOJ-1002 Fire Net 火力网 题解

ZOJ Problem Set - 1002 Fire Net

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Time Limit: 1 Second      Memory Limit: 32768 KB

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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.

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

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Source: Zhejiang University Local Contest 2001 DFS，类似八皇后问题，不多讲，看代码。 /* * poblem name: fire net * coder: mike * time: afternoon * note: DFS,类似八皇后,0s AC ^_^ */ #include<stdio.h> #define MAX_SIZE 4 int map[MAX_SIZE][MAX_SIZE], /**< 地图 */ n, /**< 尺寸 */ nwall, /**< 有多少墙 */ ntower, /**< there are n walls and n towers */ finish; /**< 是否结束，剪枝用的。因为如果当前可放置堡垒数量已达到最大，就无需继续搜索 */ int safe(int x,int y) { int i; if(map[x][y]=='X') /**< 这里是墙。。。 */ return 0; if(x>0) /**< 以下是四个方向搜索 */ for(i=x-1;i>=0;i--) { if(map[i][y]=='X') /**< 撞了南墙就回头 */ break; if(map[i][y]=='x') return 0; } if(x<n-1) for(i=x+1;i<n;i++) { if(map[i][y]=='X') break; if(map[i][y]=='x') return 0; } if(y>0) for(i=y-1;i>=0;i--) { if(map[x][i]=='X') break; if(map[x][i]=='x') return 0; } if(y<n-1) for(i=y+1;i<n;i++) { if(map[x][i]=='X') break; if(map[x][i]=='x') return 0; } return 1; /**< SAFE! */ } int dfs(int depth,int x,int y) { if(depth>n*n-nwall) /**< 堡垒数目达到最大，搜索结束，标记finish变量 */ { finish=1; return 0; } int i,j; for(i=x;i<n;i++) { for(j=y+1;j<n;j++) { if(!safe(i,j)) /**< 会被爆头。。。 */ continue; if(depth>ntower) /**< 更新 */ ntower=depth; map[i][j]='x'; /**< 标记 */ if(finish==1) /**< 提前结束 */ return 0; dfs(depth+1,i,j); map[i][j]='.'; /**< 擦除标记 */ } y=-1; /**< 这里需要注意，不大好理解 */ } return 0; } int main(void) { while(scanf("%d",&n)!=EOF) { finish=ntower=nwall=0; /**< initialize */ if(n==0) /**< 结束 */ break; getchar(); /**< skip '/n' */ int i,j; for(i=0;i<n;i++) { for(j=0;j<n;j++) { scanf("%c",&map[i][j]); if(map[i][j]=='X') nwall++; /**< update nwall */ } getchar(); /**< skip '/n' */ } dfs(1,0,-1); /**< 有趣的参数。。。 */ printf("%d/n",ntower); } return 0; } /*-----------THIS FILE IS GENERATED BY MIKE WANG----------------------*/