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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.
Time Complexity : O(n)
- Worst Case : O(n^2)
- Average Case: O(n)
- Best Case : O(n)
Space complexity : The space complexity of the bucket sort is O(n+k). Auxiliary space: O(n)
Steps
The bucket sort algorithm works as follows.
- Assume the input array is:
- Else, we have to find the correct position of A by counting the number of elements smaller than it. Another element B is replaced to be moved to its correct position. This process continues until we get an element at the original position of A.
The above-illustrated process constitutes a cycle. Repeat this cycle for every element of the list until the list is sorted.
Example
arr[] = {10, 5, 2, 3}
index = 0 1 2 3
cycle_start = 0
item = 10 = arr[0]
Find position where we put the item
pos = cycle_start
i=pos+1
while(i < n)
if (arr[i] < item)
pos++;
We put 10 at arr[3] and change item to old value of arr[3].
arr[] = {10, 5, 2, 10}
item = 3
Again rotate rest cycle that start with index '0'
Find position where we put the item = 3
we swap item with element at arr[1] now
arr[] = {10, 3, 2, 10}
item = 5
Again rotate rest cycle that start with index '0' and item = 5
we swap item with element at arr[2].
arr[] = {10, 3, 5, 10 }
item = 2
Again rotate rest cycle that start with index '0' and item = 2
arr[] = {2, 3, 5, 10}
Above is one iteration for cycle_stat = 0.
Repeat above steps for cycle_start = 1, 2, ..n-2
Implementation
Video URL
Youtube Video about Bucket Sort