part 2b done :)

exercises/Set2b.hs

@@ -16,7 +16,10 @@ import Data.List
 -- Hint! pattern matching is your friend.
 
 binomial :: Integer -> Integer -> Integer
-binomial = todo
+binomial n k
+    | k == 0 = 1
+    | n == 0 && k > 0 = 0
+    | otherwise = binomial (n-1) k  + binomial (n-1)  (k-1)
 
 ------------------------------------------------------------------------------
 -- Ex 2: implement the odd factorial function. Odd factorial is like
@@ -27,7 +30,10 @@ binomial = todo
 --   oddFactorial 6 ==> 5*3*1 ==> 15
 
 oddFactorial :: Integer -> Integer
-oddFactorial = todo
+oddFactorial n
+    | n <= 0 = 1
+    | n `mod` 2 == 0 = oddFactorial (n-1)
+    | otherwise = n * oddFactorial (n-2)
 
 ------------------------------------------------------------------------------
 -- Ex 3: implement the Euclidean Algorithm for finding the greatest
@@ -59,7 +65,11 @@ oddFactorial = todo
 -- * https://en.wikipedia.org/wiki/Euclidean_algorithm
 
 myGcd :: Integer -> Integer -> Integer
-myGcd = todo
+myGcd a b
+    | a == b = a
+    | a > b = myGcd (a-b) b
+    | a < b = myGcd a (b-a)
+    | otherwise = 9999999
 
 ------------------------------------------------------------------------------
 -- Ex 4: Implement the function leftpad which adds space characters
@@ -75,7 +85,9 @@ myGcd = todo
 -- * you can compute the length of a string with the length function
 
 leftpad :: String -> Int -> String
-leftpad = todo
+leftpad str n
+    | n > length str = leftpad (" " ++ str) n
+    | otherwise = str
 
 ------------------------------------------------------------------------------
 -- Ex 5: let's make a countdown for a rocket! Given a number, you
@@ -91,7 +103,14 @@ leftpad = todo
 -- * you'll probably need a recursive helper function
 
 countdown :: Integer -> String
-countdown = todo
+countdown n
+    | n > 0 = countdown' n "Ready!!"
+    | otherwise = "Ready! Liftoff!"
+
+countdown' :: Integer -> String -> String
+countdown' n str
+    | n > 0 = countdown' (n-1) (str ++ (show n) ++ "... ")
+    | otherwise = str ++ "Liftoff!"
 
 ------------------------------------------------------------------------------
 -- Ex 6: implement the function smallestDivisor that returns the
@@ -109,7 +128,14 @@ countdown = todo
 -- Hint: remember the mod function!
 
 smallestDivisor :: Integer -> Integer
-smallestDivisor = todo
+smallestDivisor n
+    | n > 1 = smallestDivisor' n 2
+
+smallestDivisor' :: Integer -> Integer -> Integer
+smallestDivisor' n t
+    | n > 1 = if n `mod` t == 0 then t
+                else smallestDivisor' n (t+1)
+    | otherwise = 0
 
 ------------------------------------------------------------------------------
 -- Ex 7: implement a function isPrime that checks if the given number
@@ -118,7 +144,10 @@ smallestDivisor = todo
 -- Ps. 0 and 1 are not prime numbers
 
 isPrime :: Integer -> Bool
-isPrime = todo
+isPrime n
+    | n <= 1 = False
+    | otherwise = if smallestDivisor n == n then True
+                    else False
 
 ------------------------------------------------------------------------------
 -- Ex 8: implement a function biggestPrimeAtMost that returns the
@@ -133,4 +162,7 @@ isPrime = todo
 --   biggestPrimeAtMost 10 ==> 7
 
 biggestPrimeAtMost :: Integer -> Integer
-biggestPrimeAtMost = todo
+biggestPrimeAtMost n
+    | n <= 2 = 2
+    | otherwise = if isPrime n then n
+                    else biggestPrimeAtMost (n-1)