就时间复杂度而言，计数或基数排序哪个更受欢迎？

Question

I'm given with an array of integers from the set {0,1,…,n} wherein I need to sort the array in time O(n). But I'm not sure whether to do Radix /Counting sort for this problem. Can anyone give your suggestions on this?

Answer 1

If you need to sort in O(n) time, then counting sort is the only option. It has Θ(n) time and Θ(n) space complexity.

Radix sort requires O(n log(n)) time in the worst case (since length of the key in your case is log(n) ), and quicksort is O(n log(n)) in average case and can be O(n²) in the worst case, depending on the implementation.

Answer 2

If n is small enough that an array of n elements will fit in memory, then a counting sort would be fastest.

For larger n, a radix sort is needed. If the keys are stored in 32 bit or 64 bit integers, then a base 256 radix sort will take 4 passes for 32 bits, 8 passes for 64 bits. Since time complexity ignores constants, then such a radix sort technically has time complexity O(n). However, if the radix sort uses the maximum key value to reduce the number of passes, then time complexity would be O(n log(n)) (actual complexity would be n ceil(log256(n))).