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:

  1. Set up an array of initially empty "buckets" the size of the range.
  2. Go over the original array, putting each object in its bucket.
  3. Sort each non-empty bucket.
  4. 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.