{- Pascal's triangle example, by Janet Hollier
   CSE 341, Autumn 2008 -}

module Pascal (pascal)
  where


{- pascal:  creates a list of lists, where each sublist represents a row as defined
            within Pascal's Triangle.  That is, each row begins and ends with 1 and 
            the values in between are the sums of each sequential pair of numbers in 
            the preceding row.  Useful for many things, such as taking powers of a 
            binomial. 
            -}
pascal ::[[Integer]]
pascal = [1] : [1,1] : formrows (tail pascal)

{- formrows: helper function for pascal that takes the tail of 'pascal', which
             is a list of lists beginning with [1,1], and recursively makes a 
             new list, each time from the values of the current list, "x".  -}
formrows :: [[Integer]] -> [[Integer]] 
formrows (x:xs) = (nextrow x) : (formrows xs)

{- nextrow: helper function that builds each row list by placing a '1' on each end and
            the sums of the previous row's number pairs in between.  -}
nextrow :: [Integer] -> [Integer] 
nextrow x = [1] ++ (addmiddle x) ++ [1]

{- addmiddle: adds each sequential pair of numbers in a list together to get the values
              that will go into the subsequent row.  -}
addmiddle :: [Integer] -> [Integer]
addmiddle (1:[]) = []
addmiddle (x:xs) = (x + (head xs)) : addmiddle xs


{- showTriangle: displays Pascal's Triangle (left-justified) one row per line  -}
showTriangle = do
  putStrLn "Pascal's Triangle"
  putStrLn ""
  let pt = pascal
  showRows pt
    
{- showRows: shows each row of the triangle  -}
showRows pt = do
  let row = head pt
  let rowStr = strRow row
  putStrLn rowStr
  showRows (tail pt)

{- strRow: converts an incoming list to a string representation -}
strRow :: [Integer] -> String
strRow [] = []
strRow (x:xs) = (show x) ++ "  " ++ strRow xs