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.

' 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

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.