099-largest-exponential.hs

#!/usr/bin/env runhaskell 
{- https://projecteuler.net/problem=99
Problem 99
Largest exponential

Comparing two numbers written in index form like 2^11 and 3^7 is not difficult, as any calculator would confirm that 2^11 = 2048 < 3^7 = 2187.

However, confirming that 632382^518061 > 519432^525806 would be much more difficult, as both numbers contain over three million digits.

Using base_exp.txt (right click and 'Save Link/Target As...'), a 22K text file containing one thousand lines with a base/exponent pair on each line, determine which line number has the greatest numerical value.

NOTE: The first two lines in the file represent the numbers in the example given above.
-}

import qualified Data.List as DL (maximumBy)
import qualified Data.Ord as DO (comparing)

-- Take the logarithm of both sides and then apply the power rule (log_b(q^p) = p log_b(q)):
--   a^b < c^d
-- = log(a^b) < log(c^d)
-- = b * log(a) < d log(c)

-- Beware: index starts at 1.
findMaxIndexBy :: (Ord b) => (a -> b) -> [a] -> Int
findMaxIndexBy fn xs = fst . DL.maximumBy cmp $ zipWith (,) [1..] xs
  where cmp = DO.comparing $ fn . snd

main :: IO ()
main = do fileContents <- readFile "resources/p099_base_exp.txt"
          print . findMaxIndexBy (\(base, exponent) -> log base * exponent) . map makePair . lines $ fileContents
          where makePair :: [Char] -> (Double, Double)
                makePair s = read $ "(" ++ s ++ ")"