PowerOfInteger | Topcoder Archive

Problem Statement

A number y is said to be the k-th power of a number x if y = x^k, i.e., y is the product of k copies of x.

You are given two Strings left and right. Return the greatest k such that there is an integer y (left <= y <= right) such that y is the k-th power of some integer x.

Definition

Class:: PowerOfInteger
Method:: greatestPower
Parameters:: String, String
Returns:: int
Method signature:: int greatestPower(String left, String right)
(be sure your method is public)

Constraints

left will be an integer between 2 and 10^12, inclusive, without extra leading zeroes.
right will be an integer between left and 10^12, inclusive, without extra leading zeroes.

Examples

```
"5"
```
```
"20"
```
```
Returns: 4
```
The greatest power between 5 and 20 is 16=2^4.
```
"10"
```
```
"12"
```
```
Returns: 1
```
No nontrivial power of integer between 10 and 12, so return 1.
```
"2"
```
```
"100"
```
```
Returns: 6
```

"1000000000000"

"1000000000000"

Returns: 12

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