# What is Bucket Sorting in C#? | Time Complexity

Bucket sorting, also known as bin sorting, is an efficient algorithm for sorting a collection of elements.

It works by distributing the elements into several “buckets” and then using a different sorting method to sort each bucket individually. This can provide significant performance gains over traditional algorithms like bubble sort or insertion sort. The C programming language implements bucket sorting, making it easy to use in applications where speed is important.

The basic idea behind bucket sorting is to divide the data set into smaller buckets or bins and then apply some other sorting algorithm on each individual bin. This means that instead of comparing every element to every other element in the data set, only those elements within a given bucket need to be compared. In most cases this will result in fewer comparisons and thus faster overall processing times.

Buckets are given ranges according to the data to be sorted. Bucket sort is a good sorting algorithm because it runs in linear time; for those familiar with Big-Oh notation, it runs O(n). Why is this good? Because any comparison-based sorting algorithm (which is most common) can run no faster than O(n log n).

## Benefits of Bucket Sorting

Bucket sorting is a fast and efficient sorting algorithm that is well suited for large data sets. It is a comparison-based sorting algorithm, which uses a comparison function to compare two elements and determine their order. The comparison function is provided by the user and can be any function that returns a value that can be compared.

Since bucket sort is not comparison-based, it is limited in the types of data it can sort. It works on data that has some numeric value attached to it. For argument’s sake, let’s sort integers, which are numeric values.

The overall algorithm is to create a “bucket” that will hold each value. Each value will simply be inserted into its appropriate index in the bucket. When the bucket is emptied, the values will come out in order.

So the first thing you need is to find the maximum value from the elements to sort and make the size of the bucket. Since this is simply scanning through the elements, it runs in O(n) time.

Then you want to create a bucket. The bucket cannot simply be an array of integers because you can’t add duplicate elements into the same cell. Therefore the bucket has to be an array of lists. The lists can be anything you want (ArrayList, LinkedList, etc.). If necessary, initialize each list. This step runs in constant time.

Next, insert all the unsorted elements into the bucket, again running in O(n).

Finally, empty the bucket in order, ignoring empty cells, which will once again run in O(n). Since none of the steps exceeded O(n) running time, the total running time of the algorithm is also O(n).