Remove duplicates from Array without using Hash Table

Question

i have an array which might contain duplicate elements(more than two duplicates of an element). I wonder if it\'s possible to find and remove the duplicates in the array:

Answer 1

In functional languages you can combine sorting and unicification (is that a real word?) in one pass. Let's take the standard quick sort algorithm:

- Take the first element of the input (x) and the remaining elements (xs)
- Make two new lists
- left: all elements in xs smaller than or equal to x
- right: all elements in xs larger than x
- apply quick sort on the left and right lists
- return the concatenation of the left list, x, and the right list
- P.S. quick sort on an empty list is an empty list (don't forget base case!)

If you want only unique entries, replace

left: all elements in xs smaller than or equal to x

with

left: all elements in xs smaller than x

This is a one-pass O(n log n) algorithm.

Example implementation in F#:

let rec qsort = function
    | [] -> []
    | x::xs -> let left,right = List.partition (fun el -> el <= x) xs
               qsort left @ [x] @ qsort right

let rec qsortu = function
    | [] -> []
    | x::xs -> let left = List.filter (fun el -> el < x) xs
               let right = List.filter (fun el -> el > x) xs
               qsortu left @ [x] @ qsortu right

And a test in interactive mode:

> qsortu [42;42;42;42;42];;
val it : int list = [42]
> qsortu [5;4;4;3;3;3;2;2;2;2;1];;
val it : int list = [1; 2; 3; 4; 5]
> qsortu [3;1;4;1;5;9;2;6;5;3;5;8;9];;
val it : int list = [1; 2; 3; 4; 5; 6; 8; 9]