Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
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<metadesc>Complexities of basic sorting algorithms. Minimum no. of swaps required for sorting algorithms </metadesc> | <metadesc>Complexities of basic sorting algorithms. Minimum no. of swaps required for sorting algorithms </metadesc> | ||
| − | {|class="wikitable" style="text-align: center; color: black;" | + | {|class="wikitable" style="text-align: center; color: black;" width="85%" |
! align="left"| Algorithm | ! align="left"| Algorithm | ||
! Worst Case | ! Worst Case | ||
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|$\theta(nlgn)$ | |$\theta(nlgn)$ | ||
|$\theta(nlgn)$ | |$\theta(nlgn)$ | ||
| − | | | + | |Is not in-place sorting |
| − | | | + | |Is not in-place sorting |
|- | |- | ||
|Heap | |Heap | ||
| 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 | $\theta(nlgn)$ | $\theta(nlgn)$ | $\theta(nlgn)$ | $O(nlgn)$ | $\theta(nlgn)$ |
| 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 | $\theta(nlgn)$ | $\theta(nlgn)$ | $\theta(nlgn)$ | $O(nlgn)$ | $\theta(nlgn)$ |
GATECSE