Pascal's Triangle

pascal-triangle.hs

-- Takes an array of integers, and adds pairs of numbers to create a new 
-- array. For example, [1,2,3,4] changes to [(1+2), (2+3), (3+4)], resulting
-- in [3,5,7]
sumOfPairs :: [Integer] -> [Integer]
sumOfPairs [] = []
sumOfPairs (x:[]) = []
sumOfPairs (x:y:ys) = (x+y) : sumOfPairs (y:ys)


-- Given a row of Pascal's triangle, returns the next row
next :: [Integer] -> [Integer]
next xs = 1 :  (sumOfPairs xs) ++ [1]


-- Generates the Pascal's triangle. This function generates an
-- infinite triangle, so its usage needs to be coupled with the 
-- take command. For example: take 5 pascalTriangle
pascalTriangle :: [[Integer]]
pascalTriangle = iterate next [1]


-- A: Function that finds the co-efficient of Pascal's Triangle for a given row & column
pascal :: Int -> Int -> Int
pascal 0 _ = 1
pascal _ 0 = 1
pascal row col
	| row == col = 1
	| col > row  = error "Column can't be greater than row"
	| otherwise  = (pascal (row-1) (col-1)) + (pascal (row-1) col)