TopCoder problem "MassiveNumbers" used in SRM 236 (Division II Level One)

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.



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


-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().


-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.


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

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PabloGilberto , lbackstrom , brett1479

Problem categories:

Simple Math, String Parsing