A bucket sort is a sorting algorithm that divides an array’s components into several buckets. Each of those buckets is sorted separately using a different sorting method or applying Bucket sort on it cyclically.

It’s a distribution sort, which is a broadening of the pigeonhole sort. The computing difficulty is determined by the algorithm used to sort each bucket, the number of buckets utilised, and whether the input is distributed equally. When numerous keys are adjacent to each other in the input (clustering), those items are more likely to be placed in the same bucket, resulting in some buckets containing more elements than the average.

The following is the primary technique for executing a bucket sort:

• To begin, divide the range into a predetermined number of buckets.
• Toss each item into the appropriate container.
• After that, use a sorting algorithm to sort each bucket separately.
• Finally, combine all of the sorted buckets.

Bucket Sort Characteristics

• The input for bucket sort is assumed to be derived from a uniform distribution.
• The quantity of buckets is used to evaluate computational complexity.
• Because components are often assigned to buckets using an index array, bucket sort can be extremely quick.
• The buckets demand more supplementary memory at the expense of execution times than more comparison sorts.
• Bucket Sort has an O(n k) average time complexity. O(n²) is the most time-consuming. Bucket Sort has an O(n k) spatial complexity.

 Advantages Disadvantages The number of comparisons is reduced with bucket sort If we have a large array, it is not useful because it raises the cost Because of the uniform distribution of elements, it is asymptotically fast Because sorting the buckets requires some extra space, it is not an in-place sorting method

Bucket Sort Algorithm Steps

• Make an array that is empty.
• Each object in the original array is placed in a “bucket” by looping through it.
• Sort the containers that aren’t empty.
• After checking the buckets in order, return all objects to the original array.

The Bucket sort algorithm can be deciphered using a scatter-gather technique. The provided materials are first strewn about in buckets. Following scattering, each bucket’s elements are sorted using a stable sorting method. Finally, the sorted elements will be gathered in chronological order.

Let’s look at an unsorted array to see how bucket sort works, Let’s understand bucket sort with example.

Assume that the array’s elements are:

Create buckets with a number range of 0 to 25. 0-5, 5-10, 10-15, 15-20, 20-25 are the bucket sizes. According to the bucket range, elements are inserted into the buckets. If an object has a value of 16, it will be placed in a bucket with a range of 15-20. Every element of the array will be inserted in the same way.

The scattering of array items is the name for this phase.

Sort each bucket separately now. Any of the stable sorting algorithms can be used to sort the elements of each bucket.

Finally, organise the sorted elements from each bucket.

Finally, organise the elements from each bucket that have been sorted.

Conclusion

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