module BC where

--indexInto returns the index of the first argument in a list
--(don't worry about error checking -- can assume in list)
indexInto :: Eq a => a -> [a] -> Int
indexInto x ys = fst $ head $ filter ((== x) . snd) $ zip [0..] ys

--converts a character into its corresponding integer value
-- e.g. '0' to 0, 'A' to 10, 'Z' to 35
-- like hex, except with more digits
-- (consider using elem -- look it up)
dig2Int :: Char -> Int
dig2Int dChar
  | elem dChar ['0'..'9'] = indexInto dChar ['0'..'9']
  | elem dChar ['A'..'Z'] = 10 + indexInto dChar ['A'..'Z']
  | otherwise             = -1

--converts an integer in range 0..35 into its
-- corresponding digit (0,1..Z)
-- again, don't care about ints out of bounds
num2char :: Int -> Char
num2char n
  | 0 <= n && n < 10 = ['0'..'9'] !! n
  | otherwise        = ['A'..'Z'] !! (n-10)

--converts an integer value to a string representing
-- the number in base b
-- suggest looking up repeated division strategy
-- for how to convert base 10 to binary and
-- then generalize
int2Base :: Int -> Int -> String
int2Base n b
  | n < b     = [num2char n]
  | otherwise = int2Base (n `div` b) b ++ [num2char (n `mod` b)]

--convert a number string in base b1 into an Int
-- can assume input is valid
valNumString :: String -> Int -> Int
valNumString xs b1 = sum $ zipWith (*) (map (b1^) [0..]) (reverse $ map dig2Int xs)

--convert String of numbers in base b1 into
-- equivalent value in base b2, as a String
-- again, all input will be valid
convert :: String -> Int -> Int -> String
convert numString b1 b2 = int2Base (valNumString numString b1) b2