Bucket sort

Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, a generalization of pigeonhole sort that allows multiple keys per bucket, and is a cousin of radix sort in the most-to-least significant digit flavor. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity depends on the algorithm used to sort each bucket, the number of buckets to use, and whether the input is uniformly distributed.

Bucket sort

Class	Sorting algorithm
Data structure	Array
Worst-case performance	${\displaystyle O\left(n^{2}\right)}$
Average performance	${\displaystyle O\left(n+{\frac {n^{2}}{k}}+k\right)}$, where k is the number of buckets. ${\displaystyle O(n),{\text{when }}k\approx n}$.
Worst-case space complexity	${\displaystyle O(n+k)}$

Bucket sort works as follows:

1. Set up an array of initially empty "buckets".
2. Scatter: Go over the original array, putting each object in its bucket.
3. Sort each non-empty bucket.
4. Gather: Visit the buckets in order and put all elements back into the original array.