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Sorting a list of lists according to length of sublists

a) We suppose that a list contains elements that are lists themselves. The objective is to sort the elements of this list according to their length. E.g. short lists first, longer lists later, or vice versa.

Solution:

import List
import Data.Ord (comparing)
 
lsort :: [[a]] -> [[a]]
lsort = sortBy (comparing length)
This function also works for empty list. Import
List
to use
sortBy
. If you wanted to solve it without the
comparing
function, you could do:
import List
 
lsort :: [[a]] -> [[a]]
lsort = sortBy (\xs ys -> compare (length xs) (length ys))
 
lsort' = sortBy (compare `on` length)

b) Again, we suppose that a list contains elements that are lists themselves. But this time the objective is to sort the elements of this list according to their length frequency; i.e., in the default, where sorting is done ascendingly, lists with rare lengths are placed first, others with a more frequent length come later.

In the example for this problem, sub-lists of length N appear in the same order they were in the original list; here, "ijkl" comes before "o" in the original list and in the resulting output:

> lfsort ["abc", "de", "fgh", "de", "ijkl", "mn", "o"]
["ijkl","o","abc","fgh","de","de","mn"]

If the input were to have another list of length 5 at the end, one might presume that the output would look like this:

> lfsort ["abc", "de", "fgh", "de", "ijkl", "mn", "o", "abcde"]
["ijkl","o","abcde","abc","fgh","de","de","mn"]

This solution satisfies the description of the problem (that is, lists appear in order of length frequency), although it does not give the same result as the example:

lfsort :: [[a]] -> [[a]]
lfsort lists = concat groups
    where groups = lsort $ groupBy equalLength $ lsort lists
          equalLength xs ys = length xs == length ys

Since this solution first applies lsort, the resulting output will have sub-lists appearing in ascending order of length, rather than in the same order they appeared in the original list. Sample output:

> lfsort ["abc", "de", "fgh", "de", "ijkl", "mn", "o"]
["o","ijkl","abc","fgh","de","de","mn"]
 
> lfsort ["abc", "de", "fgh", "de", "ijkl", "mn", "o", "abcde"]
["o","ijkl","abcde","abc","fgh","de","de","mn"]


Different solution. Quite inefficient, but does give the same output as the example:

import List;
 
frequency len l = length (filter (\x -> length x == len) l)
 
lfsort :: [[a]] -> [[a]]
lfsort l = sortBy (\xs ys -> compare (frequency (length xs) l) (frequency (length ys) l)) l