30.17. Sorting Part 1¶
30.17.1. Sorting Part 1¶
30.17.1.1. Sorting¶
- Each record contains a field called the key.
- Linear order: comparison.
- Measures of cost:
- Comparisons
- Swaps
30.17.1.2. Insertion Sort¶
What would you do if you have a stack of phone bills from the past two years and you want to order by date? A fairly natural way to handle this is to look at the first two bills and put them in order. Then take the third bill and put it into the right position with respect to the first two, and so on.
30.17.1.3. Initial Step¶
30.17.1.7. Bubble Sort¶
30.17.1.9. Selection Sort¶
30.17.1.11. Summary¶
\[\begin{split}\begin{array}{rccc} &\textbf{Insertion}&\textbf{Bubble}&\textbf{Selection}\\ \textbf{Comparisons:}\\ \textrm{Best Case}&\Theta(n)&\Theta(n^2)&\Theta(n^2)\\ \textrm{Average Case}&\Theta(n^2)&\Theta(n^2)&\Theta(n^2)\\ \textrm{Worst Case}&\Theta(n^2)&\Theta(n^2)&\Theta(n^2)\\ \\ \textbf{Swaps:}\\ \textrm{Best Case}&0&0&\Theta(n)\\ \textrm{Average Case}&\Theta(n^2)&\Theta(n^2)&\Theta(n)\\ \textrm{Worst Case}&\Theta(n^2)&\Theta(n^2)&\Theta(n)\\ \end{array}\end{split}\]
30.17.1.12. Code Tuning (1)¶
- General strategy: Test to avoid work
- Balance test cost, success probability, work saved
- "Optimizations" for quadratic sorts:
- Insertion Sort shift vs swaps: Works
- Selection Sort viewed as an optimization of Bubble Sort: Works
- Selection Sort avoid self-swaps: Does not work
- Bubble Sort "i" vs "1": Works
- Bubble Sort avoid/count comparisions: Does not work
- Bubble Sort O(1) lower bound claim: Bogus
