TopCoder problem "IsoscelesTriangles" used in TCO08 Semifinal 2 (Division I Level Two)



Problem Statement

    A triangle is called isosceles if it has two sides of equal length. Two triangles are considered to be different if they have different sets of vertices. You have a grid of N x M square cells. Return the number of different isosceles triangles you can form using only the centers of grid cells as vertices.
 

Definition

    
Class:IsoscelesTriangles
Method:count
Parameters:int, int
Returns:long
Method signature:long count(int N, int M)
(be sure your method is public)
    
 

Constraints

-N will be between 1 and 200, inclusive.
-M will be between 1 and 200, inclusive.
 

Examples

0)
    
1
10
Returns: 0
Any three centers of grid cells will lie on the same straight line, so it's impossible to form a triangle at all.
1)
    
2
2
Returns: 4
We can select 4 triples of centers of grid cells, and all these triples will form isosceles triangles.
2)
    
2
3
Returns: 10
All 10 isosceles triangles for a 2x3 grid are listed below ('X' stands for a triangle vertex): 
XX.  XX.  .X.  X..  X.X
X..  .X.  XX.  XX.  .X.

.XX  .XX  ..X  .X.  .X. 
.X.  ..X  .XX  .XX  X.X
3)
    
5
4
Returns: 248

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8043

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12016&pm=8043

Writer:

ivan_metelsky

Testers:

PabloGilberto , SnapDragon , Olexiy , Mike Mirzayanov

Problem categories:

Brute Force, Simple Math