SolveForTrisha | Topcoder Archive

Problem Statement

Trisha just finished her lesson on complex numbers. To test her knowledge, her professor gave her an assignment. Trisha should find the value of the following expression:

In the formula, Î±₁, Î±₂, . . . Î±_n-1 are all distinct n-th roots of unity other than 1.

You are given the int n. Let X be the value of the above expression. If X is an integer, return X. Otherwise, return -1.

Definition

Class:: SolveForTrisha
Method:: findSolution
Parameters:: int
Returns:: int
Method signature:: int findSolution(int n)
(be sure your method is public)

Notes

You can read more about roots of unity here: https://en.wikipedia.org/wiki/Root_of_unity
You can read more about complex numbers here: https://en.wikipedia.org/wiki/Complex_number

Constraints

n will be between 2 and 109, inclusive.

Examples

```
2
```
```
Returns: 0
```
The only second root of unity other than 1 is -1. The formula is a product that consists of one term: 1 - (-1)2 = 0.
```
3
```
```
Returns: 3
```
The third roots of unity are Î±0 = 1, Î±1 = cos(120) + i*sin(120), and Î±2 = cos(240) + i*sin(240), where all angles are in degrees. The expression (1 - Î±12) * (1 - Î±22) evaluates to exactly 3.

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