#+TITLE: 99 Haskell Problems
#+Author: Joseph Ferano

https://wiki.haskell.org/H-99:_Ninety-Nine_Haskell_Problems

*** #1 Find the last element of a list.

#+begin_src haskell
λ> myLast [1,2,3,4]
4
λ> myLast ['x','y','z']
'z'
#+end_src


**** Solution
#+begin_src haskell
myLast [] = error "Cannot accept an empty list"
myLast [x] = x
myLast (_:xs) = myLast xs

myLast [1..5]
#+end_src


*** #2 Find the last but one element of a list.

#+begin_src haskell
λ> myButLast [1,2,3,4]
3
λ> myButLast ['a'..'z']
'y'
#+end_src


**** Solution
#+begin_src haskell
myButLast x
  | length x < 2 = error "Cannot accept an empty list"
  | otherwise = case x of
                  [x,y] -> x
                  (x:xs) -> myButLast xs
#+end_src


*** #3 Find the K'th element of a list.

The first element in the list is number 1.

#+begin_src haskell
λ> elementAt [1,2,3] 2
2
λ> elementAt "haskell" 5
'e'
#+end_src


**** Solution
#+begin_src haskell
elementAt (x:xs) i = if i == 1 then x else elementAt xs (i - 1)
#+end_src


*** #4 Find the number of elements of a list.

#+begin_src haskell
λ> myLength [123, 456, 789]
3
λ> myLength "Hello, world!"
13
#+end_src


**** Solution

#+begin_src haskell
myLength [] = 0
myLength xs = foldl (\acc _ -> acc + 1) 0 xs
-- or
myLength' [] = 0
myLength' [x] = 1
myLength' (_:xs) = 1 + myLength xs
#+end_src

*** #5 Reverse a list.

#+begin_src haskell
λ> myReverse "A man, a plan, a canal, panama!"
"!amanap ,lanac a ,nalp a ,nam A"
λ> myReverse [1,2,3,4]
[4,3,2,1]
#+end_src


**** Solution

#+begin_src haskell
myReverse = go []
  where go acc [] = acc
        go acc (x:xs) = go (x:acc) xs
#+end_src

*** #6 Find out whether a list is a palindrome

#+begin_src haskell
λ> isPalindrome [1,2,3]
False
λ> isPalindrome "madamimadam"
True
λ> isPalindrome [1,2,4,8,16,8,4,2,1]
True
#+end_src

**** Solution
#+begin_src haskell
isPalindrome xs = xs == reverse xs
#+end_src
*** #7 Flatten a nested list structure.
Transform a list, possibly holding lists as elements into a `flat' list by replacing each list with its elements (recursively).

Example:
#+begin_src haskell
,* (my-flatten '(a (b (c d) e)))
(A B C D E)
#+end_src

Example in Haskell:

We have to define a new data type, because lists in Haskell are homogeneous.

#+begin_src haskell
data NestedList a = Elem a | List [NestedList a]
#+end_src

#+begin_src haskell
λ> flatten (Elem 5)
[5]
λ> flatten (List [Elem 1, List [Elem 2, List [Elem 3, Elem 4], Elem 5]])
[1,2,3,4,5]
λ> flatten (List [])
[]
#+end_src

**** Solution
#+begin_src haskell
flatten = reverse . go []
  where go acc (List []) = acc
        go acc (Elem x) = x:acc
        go acc (List (x:xs)) = go (go acc x) (List xs)
#+end_src