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

8. Counting sort (Running Time)

9. A Student’s Variation

10. 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.

11. Radix Sort

12. Running Time

13. An Application: Selection Problem

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

15. Randomized Selection

16. Running time

17. Selection with O(n) Comparisons

21. Why? See next page!!!

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

23. Analysis

24. Analysis
basis
induction

26. 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 and linear time selections.

27. Puzzle