IsoscelesTriangles | Topcoder Archive

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

```
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.
```
2
```
```
2
```
```
Returns: 4
```
We can select 4 triples of centers of grid cells, and all these triples will form isosceles triangles.
```
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
```
5
```
```
4
```
```
Returns: 248
```

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.