MassiveNumbers | Topcoder Archive

Problem Statement

Massive numbers can be represented using the exponent notation. For example, 3^100 is 3 raised to the power of 100. 3 is the base and 100 is the exponent.

Suppose we want to compare two massive numbers. Instead of computing the exact value of each number we can rely on a useful mathematical trick. Suppose m = a^b and n = c^d are two massive numbers. Let R be a relationship operator: less, equal or greater. Then we have the following:

If b*Log(a) R d*Log(c) then it is also the case that m R n,
where a, b, c, d, m and n are defined above.

So which is greater: 3^100 or 2^150? Let's do the math. 100*Log(3) = 47.7..., 150*Log(2) = 45.2.... Since 47.7 > 45.2, our rule tells us that 3^100 > 2^150.

Given two numbers numberA and numberB return the larger number formatted exactly the same as the input. numberA and numberB will be formatted as <base>^<exponent>. Constraints will ensure that numberA and numberB are not equal.

Definition

Class:: MassiveNumbers
Method:: getLargest
Parameters:: String, String
Returns:: String
Method signature:: String getLargest(String numberA, String numberB)
(be sure your method is public)

Notes

In Java, the log of a number can be found with Math.log().
In C++, the log of a number can be found with log().
In C# and VB, the log of a number can be found with Math.Log().

Constraints

numberA and numberB will contain between 3 and 9 characters inclusive.
numberA and numberB will be formatted as <base>^<exponent>, where <base> and <exponent> are integers between 1 and 1000 inclusive. <base> and <exponent> cannot have leading zeroes.
The relative difference between b*Log(a) and d*Log(c) (where a, b, c and d are defined in the problem statement) will be at least 1e-6.

Examples

```
"3^100"
```
```
"2^150"
```
```
Returns: "3^100"
```
Above example.
```
"1^1000"
```
```
"2^1"
```
```
Returns: "2^1"
```
numberA is equal to 1, while numberB is equal to 2.
```
"893^605"
```
```
"396^906"
```
```
Returns: "396^906"
```
```
"999^1000"
```
```
"1000^999"
```
```
Returns: "999^1000"
```

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