Given a list of integers whose length is unknown, and each of its elements lies between 1 to 1000, how does one sort this list in linear time?

  • sorry about that. I thought I would clarify all the constraints when describing the problem.
    – user270386
    Dec 3, 2015 at 15:04
  • integer is inferred but suggest you add that to the question to be clear
    – paparazzo
    Dec 3, 2015 at 16:25

1 Answer 1


You know that every element of your int arr[]; is in [1;1000].

So have an array of counters, int cnt[1001]; in C parlance. Clear it (all zeros).

Then, read the arr[] array sequentially. Suppose that you have read the value x at index i (so x==arr[i]). Then increment its counter, so cnt[x]++;

When you have reached the end of the input array arr, iterate on cnt so for (int i=0; i<=1000; i++) and output the number i exactly cnt[i] times.

This is O(n) (because the bound 1000 is a constant).

This sort is often known as the counting sort.

  • Woah! that was such a simple and nice solution. Thanks :)
    – user270386
    Dec 3, 2015 at 14:57
  • Although this achieves linearity, is there a practical reason you would want to normalize the time to the highest possible value like this?
    – Flosculus
    Dec 3, 2015 at 14:57
  • Don't know. Just got asked in interview, suggested radix sort but got stuck.. I rarely use counting , radix, shell etc linear time sorting...i kinda forgot them and paid for it :(
    – user270386
    Dec 3, 2015 at 15:06
  • BTW, I did not know about counting sort terminology; I figured out that algorithm myself. Dec 3, 2015 at 18:19
  • That must be why you explained it so much clearly and suscintly than wikipedia
    – radarbob
    Dec 5, 2015 at 23:08

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