Powerful | Topcoder Archive

Problem Statement

A number is a Perfect Square if it can be expressed as k^2 for some positive integer k. A number is a Perfect Power if it can be expressed as k^n (k to the n^th power) for some positive integers k and n, where n and k must both be greater than 1.

Create a class Powerful that contains the method power that takes an int, number, as input and returns the String "<k>^<n>", where <k> to the <n>^th power is equal to number. If a number cannot be represented as a Perfect Power, your method should return "NOT A PERFECT POWER".

Definition

Class:: Powerful
Method:: power
Parameters:: int
Returns:: String
Method signature:: String power(int number)
(be sure your method is public)

Notes

If there is more than one way to express a number as a Perfect Power, your method should express it with the highest exponent possible. (see example 1)
Your method should return "<k>^<n>"; (quotes and angle brackets for clarity only) with no blanks or leading zeroes.

Constraints

number is between 1 and 2,000,000,000 inclusive.

Examples

```
8
```
```
Returns: "2^3"
```
```
81
```
```
Returns: "3^4"
```
Do NOT return "9^2"
```
675
```
```
Returns: "NOT A PERFECT POWER"
```
```
1
```
```
Returns: "NOT A PERFECT POWER"
```

2000000000

Returns: "NOT A PERFECT POWER"

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