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Lecture 3 Sorting and Selection

Lecture 3 Sorting and Selection. Comparison Sort. Decision Tree. Running Time. Is there a faster sorting of other type?. Counting sort. Counting sort (Running Time). A Student’s Variation. Counting sort is stable. That is, the same value appear in the output

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Lecture 3 Sorting and Selection

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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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