How does the bucket sort algorithm work?

Bucket sort works by distributing the elements of an array into a number of buckets, then sorting these individually.

Bucket sort, also known as bin sort, is a distribution sort algorithm that operates 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 sort algorithm. The process is then reversed, and the sorted values are concatenated into a single, sorted array.

The first step in the bucket sort algorithm is to determine the number of buckets to be used. This is typically done by finding the maximum value in the array and dividing it by the size of the array, rounding up if necessary. Each bucket then represents a range of values, and the elements of the array are distributed into the buckets based on these ranges.

Once the elements have been distributed, each bucket is sorted individually. This can be done using any sorting algorithm, but often another recursive bucket sort is used. This is because the elements within each bucket are likely to be close in value, and so a simple comparison sort such as insertion sort can be very efficient.

After all the buckets have been sorted, the elements are concatenated back together to form a single, sorted array. This is done by simply iterating through the buckets in order and appending each element to the end of the array.

One of the key advantages of bucket sort is its efficiency. Because the elements are distributed into buckets, the sorting of each bucket can be performed in parallel, greatly improving performance on multi-core systems. However, bucket sort is not a comparison sort, and so it does not have the same performance guarantees as algorithms like quicksort or mergesort. It also requires a significant amount of additional memory to store the buckets, which can be a disadvantage on systems with limited memory.