如何确定Bucket Sort的平均和最差情况空间复杂度

Question

有人能说出如何找到Bucket排序的平均和最差情况SPACE复杂度吗？

Answer 1

Well first off we need to understand how bucket sort works:

1. Create an empty array
2. Loop through the original array and put each object in a bucket
3. Sort each of the non-empty buckets
4. Check the buckets in order and then put all objects back into the original array.

This makes bucket sort a great algorithm for big lists that need to be sorted. The average time complexity is O(n+k) where n is the number of your buckets. The worst time complexity is Θ(n^2). The reason for that is because bucket sort is useful when input is uniformly distributed over a range since whenever there are keys that are close to each other they are probably going to end up in the same bucket otherwise we would need a bucket for each key in the original array.

The worst case space complexity is O(nk). Space complexity is a measure of the amount of working storage an algorithm needs. That means how much memory, in the worst case, is needed at any point in the algorithm. As with time complexity, we're mostly concerned with how the space needs grow, in big-Oh terms, as the size N of the input problem grows.

I hope that helped!