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Fixes and improvements to recursion. #4

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Fixes and improvements to recursion. #4

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27 changes: 12 additions & 15 deletions 5-recursion.hs
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Original file line number Diff line number Diff line change
@@ -1,19 +1,18 @@
-- Raise x to the power y, using recursion
-- For example, power 5 2 = 25
power :: Int -> Int -> Int
power x y = undefined
power x 1 = x
power x y = x * power x (y-1)

-- create a list of length n of the fibbonaci sequence in reverse order
-- examples: fib 0 = [0]
-- fib 1 = [1, 0]
-- fib 10 = [55,34,21,13,8,5,3,2,1,1,0]
-- fib 10 = [55,34,21,13,8,5,3,2,1,1,0]
-- try to use a where clause
fib :: (Num a, Eq a) => a -> [a]
fib 0 = [0]
fib 1 = [1, 0]
fib n = head prev + head prev2 : prev
where prev = fib (n-1)
prev2 = fib (n-2)
fib n = let all@(x:y:_) = fib (n-1) in (x+y):all

-- This is not recursive, but have a go anyway.
-- Create a function which takes two parameters, a number and a step
Expand All @@ -22,9 +21,9 @@ fib n = head prev + head prev2 : prev
-- stepReverseSign -3 1 = 4
-- stepReverseSign 1 2 = -3
stepReverseSign :: (Fractional a, Ord a) => a -> a -> a
stepReverseSign num step = ((if num > 0
then -1
else 1) * (abs(num) + step))
stepReverseSign num step
| num < 0 = (abs num) + step
| otherwise = (-1) * (num + step)

{- Lets calculate pi.
- The Leibniz formula for pi (http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80)
Expand All @@ -42,7 +41,7 @@ stepReverseSign num step = ((if num > 0
- snd is the number of recursive steps taken to calculate it, after all this chapter is about recursion!
- Example: piCalc 0.001 = (3.1420924036835256,2000)

- The piCalc' function is defined as
- The piCalc' function is defined as
- piCalc' :: (Ord a, Fractional a, Integral b) => a -> a -> a -> b -> (a, b)
- Lots of parameters!
- The first parameter is the current denominator from the Leibniz formula
Expand All @@ -53,7 +52,7 @@ stepReverseSign num step = ((if num > 0
-
- Feel free to change the parameter order, what parameters you need etc in order to get this to work for you,
- But, of course the output of piCalc should remain as (pi, count)
-
-
- You may find the stepReverseSign function handy
-}

Expand All @@ -62,8 +61,6 @@ piCalc tolerance = piCalc' 1 0.0 tolerance 0

piCalc' :: (Ord a, Fractional a, Integral b) => a -> a -> a -> b -> (a, b)
piCalc' denom prevPi tolerance count = if abs(newPi - prevPi) < tolerance
then (newPi, count)
else piCalc' (stepReverseSign denom) newPi tolerance (count + 1)
where newPi = prevPi + (4 / denom)


then (newPi, count)
else piCalc' (stepReverseSign denom 2) newPi tolerance (count + 1)
where newPi = prevPi + (4 / denom)