Sorting Without Duplicates, Revisited
February 10, 2017
This is a fun exercise because it makes us think about programs in a different way and because it provides two functions that can profitably be re-used in other programs. We start at the end, so you can see where we are going:
(define (sort-no-dups xs) (apply append (transpose (group-by = (sort < xs)))))
Sort is provided by most Scheme systems; if yours doesn’t have it, there is one in the Standard Prelude. Group-by repeatedly strips the common prefix from a list, producing a list of like sub-lists; it calls split-while from the Standard Prelude:
(define (group-by pred? xs)
(let loop ((xs xs) (zss (list)))
(if (null? xs) (reverse zss)
(call-with-values
(lambda () (split-while (lambda (x) (pred? x (car xs))) xs))
(lambda (head tail) (loop tail (cons head zss)))))))
Transpose repeatedly strips the car from each sub-list, being careful to remove empty sub-lists at each step:
(define (transpose xss)
(if (null? xss) (list)
(cons (map car xss) (transpose (filter pair? (map cdr xss))))))
And that’s it. Here’s an example:
> (sort-no-dups '(2 9 1 5 1 4 9 7 2 1 4)) (1 2 4 5 7 9 1 2 4 9 1)
Group-by and transpose are useful tools to keep in your toolbox. You can run the program at http://ideone.com/BtPE5F.
Programming Praxis 
Don’t you want
“`
(define (transpose l) (apply map list l))
“`
?
@Gambiteer: Your suggestion works if the list of lists is rectangular. For instance, (apply map list ‘((1 2 3) (4 5 6))) gives ((1 4) (2 5) (3 6)). But the result of the group-by is not necessarily rectangular. For instance, in the sample problem, the result of (group-by = (sort < '(2 9 1 5 1 4 9 7 2 1 4))) is ((1 1 1) (2 2) (4 4) (5) (7) (9 9)), which is not rectangular. The function you suggest is in the Standard Prelude with the name zip, where it would be called as (zip '(1 2 3) '(4 5 6)).
A Haskell version. The sorting and grouping are the same as in the previous problem. The foldr builds up two lists: the first consists of the head of each sublist produced by group; the second is the remaining elements (if any) of the sublists. Finally, we append the two lists from foldr.
With warnings enabled the compiler will complain that step doesn’t include a pattern match on [] (the empty list), but it can never be called that way since the sublists produced by group are always non-empty.
Equivalent Python version.
Uses the ’roundrobin’ recipe from the itertools documentation (https://docs.python.org/3.5/library/itertools.html#itertools-recipes)
from itertools import groupby from itertools_recipes import roundrobin def sortwithoutdups2(lst): return list(roundrobin(*(list(v) for _,v in groupby(sorted(d)))))Fixed a typo
from itertools import groupby from itertools_recipes import roundrobin def sortwithoutdups2(lst): return list(roundrobin(*(list(v) for _,v in groupby(sorted(lst)))))