Sorting Algorithms: Complexity, Optimality, and Trade-offs
Students will explore simple methods for sorting data (e.g., arranging numbers from smallest to largest), understanding why order is useful.
About This Topic
Students will explore simple methods for sorting data (e.g., arranging numbers from smallest to largest), understanding why order is useful.
Key Questions
- Prove the Ω(n log n) lower bound for comparison-based sorting using a decision-tree argument and identify which sorting algorithms achieve this bound in the worst case.
- Compare merge sort, quicksort, and heapsort across best, worst, and average-case time complexity, space complexity, and stability, and determine which is preferable for different data characteristics.
- Explain how counting sort and radix sort circumvent the Ω(n log n) lower bound and specify the precise conditions on the key domain under which each algorithm achieves O(n) performance.
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