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

If the range of numbers (L) is known, you can do a modified counting sort.

given L, x, input[]
counts <- array[0..L]
for each number in input
    increment counts[number]
next

#populate the output
index <- 0
xIndex <- 0
while xIndex < x and index <= L
   if counts[index] > 0 then
       decrement counts[index]
       output[xIndex] = index
       increment xIndex
   else
       increment index
   end if
loop

This has a runtime of O(n + L) (with memory overhead of O(L)) which makes it pretty attractive if the range is small (L < n log n).