Bucket sort

Bucket sort is a sort algorithm that works by partitioning an array into a finite number of buckets and then sorting each bucket. It is a generalization of pigeonhole sort. Bucket sort runs in linear time (&Theta(n)) when input is drawn from a uniform distribution.

It works as follows:

Set up an array of initially empty "buckets" the size of the range.
Go over the original array, putting each object in its bucket.
Sort each non-empty bucket.
Put elements from non-empty buckets back into the original array.

Pseudocode

' A is the array
' n is the number of buckets
' MSBITS(n) returns the most significant bits of n.
'    This could be k*n for sorting numbers, or
'    the first character of n for sorting strings.
' NEXT-SORT is a sort algorithm
BUCKET-SORT(A, n, MSBITS, NEXT-SORT):
  make array B of n lists
  for i = 1 to n:
    insert A[i] into list B[MSBITS(A[i])]
    for i = 0 to n - 1:
      NEXT-SORT(B[i])
  concatenate the lists B[0]...B[n-1] in order

Relationships to other sorting algorithms

Using BUCKET-SORT itself as the NEXT-SORT produces a relative of the radix sort. Using BUCKET-SORT with n == 2 and itself as the NEXT-SORT produces quicksort.