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Exploring Sorting and Selection Algorithms: A Comparative Analysis

Discover the efficiency of counting sort, radix sort, and selection algorithms through running time analysis. Learn about stable sorting methods and the lower bounds for comparison sorts. Explore selection problems and expected linear time selections.

rmaynard
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Exploring Sorting and Selection Algorithms: A Comparative Analysis

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  1. Lecture 3 Sorting and Selection

  2. Comparison Sort

  3. Decision Tree

  4. Running Time Is there a faster sorting of other type?

  5. Counting sort

  6. Counting sort (Running Time)

  7. A Student’s Variation

  8. Counting sort is stable. That is, the same value appear in the output array in the same order as they do in the input array.

  9. Radix Sort

  10. Running Time

  11. An Application: Selection Problem

  12. If we use comparison, what is the lower bound?

  13. Randomized Selection

  14. Running time

  15. Selection with O(n) Comparisons

  16. Why? See next page!!!

  17. ( + low side) contains red part ( + high side) contains blue part

  18. Analysis

  19. Analysis basis induction

  20. What we learnt in this lecture? • What is “comparison sort”?. • Lower bound for comparison sort. • Counting sort and Radix sort. • What is selection problem? • expected linear time andlinear time selections.

  21. Puzzle

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