Squares
习题4-2正方形（Squares，ACM/ICPC World Finals 1990，UVa201）
有n行n列（2≤n≤9）的小圆点，还有m条线段连接其中的一些黑点。统计这些线段连成了多少个正方形（每种边长分别统计）。
行从上到下编号为1~n，列从左到右编号为1~n。边用Hij和Vij表示，分别代表边(i,j)-{i,j+1}和(i,j)-(i+1,j)。
原题描述
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 n2 dots (where 2 ≤ n ≤ 9) and some interconnecting horizontal and vertical lines. A record for a single board with n2 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:
Hij 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
Vij 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.
样例输入和样例输出：
习题4-2正方形（Squares，ACM/ICPC World Finals 1990，UVa201）
有n行n列（2≤n≤9）的小圆点，还有m条线段连接其中的一些黑点。统计这些线段连成了多少个正方形（每种边长分别统计）。
行从上到下编号为1~n，列从左到右编号为1~n。边用Hij和Vij表示，分别代表边(i,j)-{i,j+1}和(i,j)-(i+1,j)。
原题描述
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 n2 dots (where 2 ≤ n ≤ 9) and some interconnecting horizontal and vertical lines. A record for a single board with n2 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:
Hij 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
Vij 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.