{-
Problem 42

The nth term of the sequence of triangle numbers is given by, 
tn = ½n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

By converting each letter in a word to a number corresponding to 
its alphabetical position and adding these values we form a word value. 

For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. 
If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?
-}

import Data.List.Split

fileName = "p042_words.txt"

euler42 = do
            file <- readFile fileName
            let words = map (filter ('\"' /=)) $ splitOn "," file
                ints = map (getValue) words
            print $ length $ filter (isTriangle) ints

getValue :: String -> Int
getValue x = sum $ map (\c -> 1 + fromEnum c - fromEnum 'A') x

isTriangle :: Int -> Bool
isTriangle n = odd m && n `elem` (takeWhile (<= n) triangles)
    where m = 8*n + 1
          triangles = 1 : zipWith (+) triangles [2..]

