1. Review 1 Merge Sort Merge Sort Algorithm Time Complexity Best case Average case Worst case Examples

2. Example 2

3. Selection Sort 3 Selection Sort Algorithm Time Complexity Best case Average case Worst case Examples

4. Selection Sort The list is divided into two sublists, sorted and unsorted, which are divided by an imaginary wall. We find the smallest element from the unsorted sublist and swap it with the element at the beginning of the unsorted data. After each selection and swapping, the imaginary wall between the two sublists move one element ahead, increasing the number of sorted elements and decreasing the number of unsorted ones. Each time we move one element from the unsorted sublist to the sorted sublist, we say that we have completed a sort pass. A list of n elements requires n-1 passes to completely rearrange the data.

5. Selection Sort Algorithm 1. Scan the array to find its smallest element and swap it with the first element. 2. Then, starting with the second element, scan the elements to its right to find the smallest among them and swap it with the second elements. 3. Generally, on pass i (0  i  n-2), find the smallest element in A[i..n-1] and swap it with A[i]: A[0] ...  A[i-1] | A[i],..., A[min],..., A[n-1] in their final positions

6. Selection Sort 1. Start with the 1st element, scan the entire list to find its smallest element and exchange it with the 1st element 2. Start with the 2 nd element, scan the remaining list to find the the smallest among the last (N-1) elements and exchange it with the 2 nd element Example: 89 45 68 90 29 34 17 17 | 45 68 90 29 34 89 29 | 68 90 45 34 89 34 | 90 45 68 89 45 | 90 68 89 68 | 90 89 89 | 90 90

7. 23784583256 87845233256 82345783256 82332784556 82332457856 82332455678 Original List After pass 1 After pass 2 After pass 3 After pass 4 After pass 5 SortedUnsorted

8. Selection Sort Algorithm for i  0 to N-2 do { min  i; for j  i+1 to N-1 do { if (A[j] < A[min]) min  j; } swap A[i] and A[min] ; }

9. Selection Sort -- Analysis In general, we compare keys and move items (or exchange items) in a sorting algorithm (which uses key comparisons).  So, to analyze a sorting algorithm we should count the number of key comparisons and the number of moves. Ignoring other operations does not affect our final result. In selection Sort function, the outer for loop executes n-1 times. We invoke swap function once at each iteration.  Total Swaps: n-1  Total Moves: 3*(n-1) (Each swap has three moves)

10. Selection Sort – Analysis (cont.) The inner for loop executes the size of the unsorted part minus 1 (from 1 to n-1), and in each iteration we make one key comparison.  # of key comparisons = 1+2+...+n-1 = n*(n-1)/2  So, Selection sort is O(n 2 ) The best case, the worst case, and the average case of the selection sort algorithm are same.  all of them are O(n 2 ) This means that the behavior of the selection sort algorithm does not depend on the initial organization of data. Since O(n 2 ) grows so rapidly, the selection sort algorithm is appropriate only for small n. Although the selection sort algorithm requires O(n 2 ) key comparisons, it only requires O(n) moves. A selection sort could be a good choice if data moves are costly but key comparisons are not costly (short keys, long records).

11. Selection Sort 513462 Comparison Data Movement Sorted

12. Selection Sort 513462 Comparison Data Movement Sorted

13. Selection Sort 513462 Comparison Data Movement Sorted

14. Selection Sort 513462 Comparison Data Movement Sorted

15. Selection Sort 513462 Comparison Data Movement Sorted

16. Selection Sort 513462 Comparison Data Movement Sorted

17. Selection Sort 513462 Comparison Data Movement Sorted

18. Selection Sort 513462 Comparison Data Movement Sorted  Largest

19. Selection Sort 513426 Comparison Data Movement Sorted

20. Selection Sort 513426 Comparison Data Movement Sorted

21. Selection Sort 513426 Comparison Data Movement Sorted

22. Selection Sort 513426 Comparison Data Movement Sorted

23. Selection Sort 513426 Comparison Data Movement Sorted

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25. Selection Sort 513426 Comparison Data Movement Sorted

26. Selection Sort 513426 Comparison Data Movement Sorted  Largest

27. Selection Sort 213456 Comparison Data Movement Sorted

28. Selection Sort 213456 Comparison Data Movement Sorted

29. Selection Sort 213456 Comparison Data Movement Sorted

30. Selection Sort 213456 Comparison Data Movement Sorted

31. Selection Sort 213456 Comparison Data Movement Sorted

32. Selection Sort 213456 Comparison Data Movement Sorted

33. Selection Sort 213456 Comparison Data Movement Sorted  Largest

34. Selection Sort 213456 Comparison Data Movement Sorted

35. Selection Sort 213456 Comparison Data Movement Sorted

36. Selection Sort 213456 Comparison Data Movement Sorted

37. Selection Sort 213456 Comparison Data Movement Sorted

38. Selection Sort 213456 Comparison Data Movement Sorted

39. Selection Sort 213456 Comparison Data Movement Sorted  Largest

40. Selection Sort 213456 Comparison Data Movement Sorted

41. Selection Sort 213456 Comparison Data Movement Sorted

42. Selection Sort 213456 Comparison Data Movement Sorted

43. Selection Sort 213456 Comparison Data Movement Sorted

44. Selection Sort 213456 Comparison Data Movement Sorted  Largest

45. Selection Sort 123456 Comparison Data Movement Sorted

46. Selection Sort 123456 Comparison Data Movement Sorted DONE!

47. Example 47

48. Summary 48 Selection Sort Selection Sort Algorithm Time Complexity Best case Average case Worst case Examples