Find the x smallest integers in a list of length n

Question

You have a list of n integers and you want the x smallest. For example,

x_smallest([1, 2, 5, 4, 3], 3) should return [1, 2, 3].

I\'ll v

Answer 1

You can find the k-th smallest element in O(n) time. This has been discussed on StackOverflow before. There are relatively simple randomized algorithms, such as QuickSelect, that run in O(n) expected time and more complicated algorithms that run in O(n) worst-case time.

Given the k-th smallest element you can make one pass over the list to find all elements less than the k-th smallest and you are done. (I assume that the result array does not need to be sorted.)

Overall run-time is O(n).