HDU1045 Fire Net

Fire Net

                                                              Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

 

                                                              Total Submission(s): 11482    Accepted Submission(s): 6882

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

 

Source

Zhejiang University Local Contest 2001

我先概括一下题意，就是说，给你一个n*n的方格，‘.’表示可以放置炸弹的位置，‘X’表示墙的位置。然后问你最多可以放多少枚炸弹？当然炸弹的放置位置是有要求的，两个炸弹不能同行同列，但如果中间有墙间隔的话是符合条件的。请你来编程解决这个问题

思路：问最多可以放多少。那就是深搜问题了。看代码理解

#include<stdio.h>#include<string.h>#include<iostream>#include<algorithm>using namespace std;char map[100][100];int i,j,n,coun;bool isok(int x,int y)//判断是否可走{    //向上走    for(i=x-1;i>=0;i--)    {        if(map[i][y]=='0')//遇到同类不能再放            return false;        if(map[i][y]=='X')//遇到炸弹            break;    }    //向左走    for(j=y-1;j>=0;j--)    {        if(map[x][j]=='0')//遇到同类不能再放            return false;        if(map[x][j]=='X')//遇到炸弹            break;    }    return true;}void dfs(int corner,int s){    int x,y;    if(corner==n*n)//搜索完毕    {        if(s>coun)            coun=s;        return ;    }    else    {        x=corner/n;//对应行        y=corner%n;//对应列        if(map[x][y]=='.'&&isok(x,y))//可以走的情况        {            map[x][y]='0';//标记不能走            dfs(corner+1,s+1);//找到可以放的位置            map[x][y]='.';//回溯            dfs(corner+1,s);        }        else        {            dfs(corner+1,s);        }    }    return ;}int main(){    while(cin>>n,n!=0)    {        coun=0;        for(i=0;i<n;i++)            for(j=0;j<n;j++)            cin>>map[i][j];        dfs(0,0);//从头开始        cout<<coun<<endl;    }    return 0;}