[UVa 201]Squares 正方形，ACM/ICPC World Finals 1990

A children’s board game consists of a square array of dots that contains lines connecting some of the pairs of adjacent dots. One part of the game requires that the players count the number of squares of certain sizes that are formed by these lines. For example, in the figure shown below, there are 3 squares — 2 of size 1 and 1 of size 2. (The “size” of a square is the number of lines segments required to form a side.) Your problem is to write a program that automates the process of counting all the possible squares.

Input

The input file represents a series of game boards. Each board consists of a description of a square array of n 2 dots (where 2 ≤ n ≤ 9) and some interconnecting horizontal and vertical lines. A record for a single board with n 2 dots and m interconnecting lines is formatted as follows: Line 1: n the number of dots in a single row or column of the array Line 2: m the number of interconnecting lines Each of the next m lines are of one of two types: H i j indicates a horizontal line in row i which connects the dot in column j to the one to its right in column j + 1 or V i j indicates a vertical line in column i which connects the dot in row j to the one below in row j + 1 Information for each line begins in column 1. The end of input is indicated by end-of-file. The first record of the sample input below represents the board of the square above.

Output

For each record, label the corresponding output with ‘Problem #1’, ‘Problem #2’, and so forth. Output for a record consists of the number of squares of each size on the board, from the smallest to the largest. lf no squares of any size exist, your program should print an appropriate message indicating so. Separate output for successive input records by a line of asterisks between two blank lines, like in the sample below.

Sample Input

4 16 H 1 1 H 1 3 H 2 1 H 2 2 H 2 3 H 3 2 H 4 2 H 4 3 V 1 1 V 2 1 V 2 2 V 2 3 V 3 2 V 4 1 V 4 2 V 4 3 2 3 H 1 1 H 2 1 V 2 1

Sample Output Problem #1 2 square (s) of size 1 1 square (s) of size 2 ‘**********************************’（两个单引号是我加的，由于我用的是MarkDown编辑器。。。） Problem #2 No completed squares can be found.

题意：有n行n列（2<=n<=9）的点，还有m条线段链接其中的一些点。统计这些线段练成了多少个正方形。

解题思路：将读进来的要添加的边分别用两个bool数组存，添加后就将相应的位置赋值成true，而后枚举正方形的边长和左上角顶点的位置，统计答案。

代码：

#include<bits/stdc++.h>
using namespace std;
int n,m,cnt;
int ans[20];
bool a[20][20],b[20][20];
int read(){
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int main(){
	while(scanf("%d%d\n",&n,&m)!=EOF){
		cnt++;
		if(cnt!=1)puts("\n**********************************\n");
		memset(ans,0,sizeof(ans));
		memset(a,0,sizeof(a));
		memset(b,0,sizeof(b));
		for(int i=1;i<=m;i++){
			char ch=getchar();int x=read(),y=read();
			if(ch=='H')a[x][y]=true;
			else b[y][x]=true;//这个lrj的紫书上的描述应该是b[x][y]，可是原题上的描述是b[y][x] 
		}
		for(int s=1;s<n;s++){//枚举正方形的边长 
			int Ans=0;bool flag;
			for(int i=1;i<=n-s;i++)
				for(int j=1;j<=n-s;j++){//枚举正方形左上角顶点的位置 
					flag=true;
					for(int x=i,y=j;flag&&x<i+s;x++)
						if(!b[x][y]||!b[x][y+s])flag=false;//处理列 
					for(int x=i,y=j;flag&&y<j+s;y++)
						if(!a[x][y]||!a[x+s][y])flag=false;//处理行 
					if(flag)Ans++;
				}
			ans[s]=Ans;
		}
		printf("Problem #%d\n\n",cnt);
		bool flag=false;
		for(int i=1;i<n;i++)
			if(ans[i]){printf("%d square (s) of size %d\n",ans[i],i);flag=true;}
		if(!flag)printf("No completed squares can be found.\n");//输出 
	}
	return 0;
}