Bucket sort is a basic idea in computer science that helps arrange data in a certain order for easy searching, processing, and retrieval. Of the numerous sorting algorithms, bucket sort is a popular method to sort floating-point numbers or uniformly distributed data at a low cost.
In this article, let’s study bucket sorting in C#, how it’s implemented, and how it differs from other sorts.
Understanding Bucket Sort
Bucket Sort is a sorting algorithm which puts elements into a number of buckets, sorts each bucket, and finally merges them to give the final sorted list. Bucket Sort performs optimally when input values are distributed uniformly over a range.
Also Read: What are functions in C and C++?
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 determine 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 to 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, initialise 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).
Limitations of Bucket Sort
Inefficient for Non-Uniform Data: Bucket sort is most effective when the data is uniformly distributed. For non-uniform or skewed distributions, elements may cluster in only a few buckets, degenerating the performance to O(n2)O(n2) in the worst case, as many values may end up in a single bucket that requires significant sorting.
Bucket Size and Count Selection: The performance relies heavily on the choice of the number of buckets and how data is mapped into them. Too few buckets lead to large, unsorted groups, while too many buckets can waste memory and increase overhead. Determining the optimal bucket count often requires knowledge of the input data’s distribution.
Space Complexity: Bucket sorting typically requires additional memory for the buckets, leading to a worst-case space complexity of O(n+k)O(n+k), where kk is the number of buckets. If you’re overly aggressive with the bucket count (e.g., aiming for one item per bucket), space usage can become substantial.
Requires Predefined Range: The range of input values must be known beforehand to determine the bucket size.
Conclusion
Bucket sort is a highly efficient algorithm for sorting numbers when dealing with uniformly distributed data. In C#, using lists and the built-in sorting functions, it is simple and efficient to implement bucket sort. Although it is not necessarily the best solution for every set of data, its efficiency with floating-point numbers and distributed datasets makes it a valuable sorting algorithm in a programmer’s arsenal.
