UVa 201 - Squares

201 - Squares

 * http://acm.uva.es/p/v2/201.html

Summary
Bruteforce. Since $$N \leq 9$$, we can simply iterate all the possible squares.

Explanation
We can think that vertical or horizontal lines are edges between two adjecent point. After that we can take a three dimensional array (say a [N][N][2]) to store the count of horizontal(a[i][j][0]) edges and vertical(a[i][j][1]) edges. a[i][j][0] contains number of horizontal edges at row i upto coloumn j. and a[i][j][1] contains number of vertical edges at coloumn j upto row i. Next you use a O(n^2) loop to find a square. a square of size 1 is found if there is an edge from (i,j) to (i,j+1) and (i,j+1) to (i+1,j+1) and (i,j) to (i+1,j) and (i+1,j) to (i+1,j+1) we can get this just by subtarcting values calculated above.

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 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 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

Output
Problem #1

2 square (s) of size 1 1 square (s) of size 2



Problem #2

No completed squares can be found.



Problem #3

2 square (s) of size 1 1 square (s) of size 2



Problem #4

No completed squares can be found.



Problem #5

2 square (s) of size 1 1 square (s) of size 2



Problem #6

No completed squares can be found.