Bucket Sort

Introduction

In this article, we are going to discuss Bucket Sort. Bucket Sorting is a technique where we sort the elements in the unsorted array and place them using buckets. Following that, these items are sorted in order of priority where each bucket is sorted separately like all the elements will be arranged in an order and after that, they will be sorted accordingly to the required range.

This is a non-comparison-based sorting algorithm. We can also call Bucket sort “Bin Sort”. Bucket Sort is an extension of pigeonhole sort that enables multiple keys per bucket. The computational complexity is determined by the number of buckets utilized or the bucket list’s size as well as the range across which the lists or arrays have been spread.

Why Bucket Sort is important?

In product management, the backlog serves as a list of all projects and activities linked to a product. The backlog differs substantially from team to team in terms of content. Although all product teams want to prioritize the projects and initiatives in the backlog is how they select what to work on next. A project or endeavor that isn’t on the backlog is unlikely to be completed. This method sets the path for a more simplified prioritization of development efforts by focusing on high-impact activities, allowing firms to achieve perfection in products by creating innovatory ones & releasing them into the market rapidly.

Working

Bucket Sort will work as follows:

1. First we have to create an array of initially empty buckets.

2. Then we have to put all the elements in the buckets according to their range.

3. Now we have to sort all the elements in the buckets.

4. At last we have to combine all the elements present in the bucket to get the required output.

Let’s understand better through an example.

Example

Fig.1

In the above example, if you see you can observe an unsorted array given to us. Now according to the working process, we have to create the buckets and arrange the elements into them according to their range. In this example the size is 0.10, so if you observe all were arranged accordingly.

Fig.2

Now we have to sort within the bucket as the elements were not in order, to be more specific we have sorted 0.21, 0.23, 0.29 in order.

Fig.3

Finally, we combined all the elements from the buckets in order to get the required output. In the above fig we got 0.16, 0.18, 0.21, 0.23, 0.29, 0.32, 0.65, 0.73, 0.79, 0.96. If you see Fig.3 it is a completely sorted array where all the elements are sorted and placed in order. In this way bucket sort will be done.

Algorithm

Fig.4

First, we have to create N buckets and for all the buckets we have to initialize the value of the bucket with 0. Then we have to push the elements into the buckets which match their given range. Now we have to sort the elements in the buckets and at last, we have to gather the elements from each bucket by concatenating the lists together in order. In this way Bucket Sort algorithm works.

Time Complexity:

Best-case — O(n+k)

Worst-case — O(n²)

Average-case — O(n)

Space Complexity — O(n+k)

The time complexities for each case were calculated based on the algorithm which was given above.

Pros and Cons

Pros:

1. It is easier to set up and utilize.

2. We can sort small arrays easily if they are in the given range.

Cons:

1. If the buckets are distributed incorrectly then the cost will increase and we can’t get the desired output.

2. When compared to other algorithms, bucket sort may require some additional performance adjustment as the performance of bucket sort is dependent on the number of buckets used.

-Thank You,

Nandan😊