-- These are some simple examples of Haskell functions introduced 
-- in the first lecture of CS 8.  Some are taken from SOE.
-- Several implement SOE functions in an alternate way, using
--   higher-order functions
-- by Scot Drysdale, 9/18/07

x :: Double
x =  1.234

lst :: [Double]
lst =  [1.0, 2.0, 3.0, 4.0]

-- Computes the area of a circle of a given radius
circleArea :: Double -> Double
circleArea radius =  pi * radius^2

-- Computes the areas of circles whose radii are in a list
circleAreas :: [Double] -> [Double]
circleAreas radii = map circleArea radii

-- Adds 1 to each item in a list
incrementList :: [Double] -> [Double]
incrementList list = map (+ 1) list

-- Triples each item in a list
tripleList :: [Double] -> [Double]
tripleList list = map (* 3) list

-- Scales each item in a list by multiplying it by a scale factor
scaleList :: Double -> [Double] -> [Double]
scaleList sf list =  map (* sf) list

-- Alternate way to triple each item in a list
tripleList2 :: [Double] -> [Double]
tripleList2 list = scaleList 3 list

-- Sums the items in a list
listSum :: [Double] -> Double
listSum list = foldl (+) 0.0 list

-- Computes the total area of circles whose radii are in a list
totalCircleArea :: [Double] -> Double
totalCircleArea radii = listSum (circleAreas radii)

-- Computes the total area of circles whose radii are given -
-- this time without helper functions
totalCircleArea2 :: [Double] -> Double
totalCircleArea2 radii = foldl (+) 0.0 (map circleArea radii)

-- Counts the number of times that a base appears in a genome
countBases :: Char -> [Char] -> Int
countBases base genome = length (filter (== base) genome)

-- Sum only the positive numbers in a list
sumPositives :: [Double] -> Double
sumPositives list = listSum (filter (> 0) list)

-- Create a merged list where each position contains the larger
-- of the numbers in the corresponding postitions in list1 and list2
mergeLargest :: [Double] -> [Double] -> [Double]
mergeLargest list1 list2 = zipWith max list1 list2

-- Computes the dot product of two vectors represented as lists
dotProd :: [Double] -> [Double] -> Double
dotProd a b = foldl (+) 0.0  (zipWith (*) a b)