# 99 questions/Solutions/13

### From HaskellWiki

(**) Run-length encoding of a list (direct solution).

Implement the so-called run-length encoding data compression method directly. I.e. don't explicitly create the sublists containing the duplicates, as in problem 9, but only count them. As in problem P11, simplify the result list by replacing the singleton lists (1 X) by X.

encode' :: Eq a => [a] -> [(Int,a)] encode' = foldr helper [] where helper x [] = [(1,x)] helper x (y@(a,b):ys) | x == b = (1+a,x):ys | otherwise = (1,x):y:ys encodeDirect :: Eq a => [a] -> [ListItem a] encodeDirect = map encodeHelper . encode' where encodeHelper (1,x) = Single x encodeHelper (n,x) = Multiple n x

encode

foldr

encodeModified

encode'

Alternative direct writing without significant external functions:

encodeDirect :: (Eq a) => [a] -> [ListItem a] encodeDirect [] = [] encodeDirect (x:xs) = encodeDirect' 1 x xs encodeDirect' n y [] = [encodeElement n y] encodeDirect' n y (x:xs) | y == x = encodeDirect' (n+1) y xs | otherwise = encodeElement n y : (encodeDirect' 1 x xs) encodeElement 1 y = Single y encodeElement n y = Multiple n y

Yet another solution:

encodeDirect :: (Eq a)=> [a] -> [ListItem a] encodeDirect [] = [] encodeDirect (x:xs) | count==1 = (Single x) : (encodeDirect xs) | otherwise = (Multiple count x) : (encodeDirect rest) where (matched, rest) = span (==x) xs count = 1 + (length matched)

As a wrapper, with a helper:

encodeDirect :: Eq a => [a] -> [ListItem a] encodeDirect []=[] encodeDirect (x:xs) = encodeDirectHelper 1 x xs encodeDirectHelper :: Eq a => Int->a->[a]->[ListItem a] encodeDirectHelper n x [] = [encodeHelper(n,x)] encodeDirectHelper n x xs = if x==(head xs) then encodeDirectHelper (n+1) x (tail xs) else [encodeHelper(n,x)] ++ (encodeDirect xs) encodeHelper :: (Int, a)-> ListItem a encodeHelper (1,x)= Single x encodeHelper (n,x)= Multiple n x