# Problem 10

## Problem 10

(*) Run-length encoding of a list. Use the result of problem P09 to implement the so-called run-length encoding data compression method. Consecutive duplicates of elements are encoded as lists (N E) where N is the number of duplicates of the element E.

Example:

```* (encode '(a a a a b c c a a d e e e e))
((4 A) (1 B) (2 C) (2 A) (1 D)(4 E))
```

```encode "aaaabccaadeeee"
[(4,'a'),(1,'b'),(2,'c'),(2,'a'),(1,'d'),(4,'e')]```

Solution:

```encode :: Eq a => [a] -> [(Int, a)]
encode [] = []
encode x = encodePack (pack x)
encodePack [] = []
encodePack (x:xs) = (length x, head x):encodePack xs```

Note: The type signature of encode return a list of tuple (Int, a) as defined.

Use of list comprehension or lambda with map function can shorten the solution. The list comprehension describe the mathematics of creating the list of tuple by taking an element x from the list (pack xs) and use x to create the element of the tuple (length x, head x). The lambda function (\x -> (length x, head x)) take an argument of a list and turn it into a tuple. The map function map this lambda function to each element of (pack xs).

```encode xs = [(length x, head x) | x <- pack xs]
encode xs = map (\x -> (length x, head x)) (pack xs)```