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Return to Complexities of Basic Sorting Algorithms.

Algorithm Worst Case Average Case Best Case Min. no. of swaps Max. no. of swaps
Bubble $\theta(n^{2})$ $\theta(n^{2})$ $\theta(n^{2})$ $\theta(n^{2})$ $\theta(n^{2})$
Selection $\theta(n^{2})$ $\theta(n^{2})$ $\theta(n^{2})$ 0 (when array is already sorted) $\theta(n^{2})$
Insertion $\theta(n^{2})$ $\theta(n^{2})$ $\theta(n)$ (when array is sorted) 0 (when array is already sorted) $\theta(n^{2})$
Quick $\theta(n^{2})$ (when array is sorted, and pivot taken from one end) $\theta(nlgn)$ $\theta(nlgn)$ 0 (when array is already sorted) $\theta(n^{2})$
Merge $\theta(nlgn)$ $\theta(nlgn)$ $\theta(nlgn)$ Is not in-place sorting Is not in-place sorting
Heap $\theta(nlgn)$ $\theta(nlgn)$ $\theta(nlgn)$ $O(nlgn)$ $\theta(nlgn)$




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