归并

Transcript

1. Merge Sort
2. Merge Sort • In merge sort, the idea of the algorithm is to sort smaller arrays and then combine those arrays together (merge them) in sorted order. • Merge sort leverages something called recursion, which we’ll touch on in more detail in a future video. In pseudocode: • Sort the left half of the array (assuming n > 1) • Sort the right half of the array (assuming n > 1) • Merge the two halves together
3. Merge Sort 5 2 1 3 6 4 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
4. Merge Sort 5 2 1 3 6 4 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
5. Merge Sort 5 2 1 3 6 4 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
6. Merge Sort 5 2 1 3 6 4 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
7. Merge Sort 2 1 3 6 4 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
8. Merge Sort 2 1 3 6 4 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
9. Merge Sort 2 1 3 6 4 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
10. Merge Sort 1 3 6 4 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
11. Merge Sort 1 3 6 4 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
12. Merge Sort 3 6 4 2 1 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
13. Merge Sort 3 6 4 2 5 1 2 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
14. Merge Sort 3 6 4 5 1 2 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
15. Merge Sort 3 6 4 5 1 2 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
16. Merge Sort 3 6 4 5 2 1 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
17. Merge Sort 3 6 4 5 1 2 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
18. Merge Sort 3 6 4 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
19. Merge Sort 3 6 4 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
20. Merge Sort 3 6 4 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
21. Merge Sort 6 4 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
22. Merge Sort 6 4 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
23. Merge Sort 6 4 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
24. Merge Sort 4 6 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
25. Merge Sort 4 6 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
26. Merge Sort 6 4 3 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
27. Merge Sort 6 3 4 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
28. Merge Sort 3 4 6 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
29. Merge Sort 3 4 6 1 2 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
30. Merge Sort 4 6 1 2 5 3 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
31. Merge Sort 1 2 5 3 4 6 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
32. Merge Sort 1 2 5 3 4 6 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
33. Merge Sort 2 5 3 4 6 1 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
34. Merge Sort 5 3 4 6 1 2 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
35. Merge Sort 5 4 6 1 2 3 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
36. Merge Sort 5 6 1 2 3 4 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
37. Merge Sort 6 1 2 3 4 5 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
38. Merge Sort 1 2 3 4 5 6 In pseudocode: Sort the left half of the array (assuming n > 1) Sort the right half of the array (assuming n > 1) Merge the two halves together
39. Merge Sort • Worst-case scenario: We have to split n elements up and then recombine them, effectively doubling the sorted subarrays as we build them up. (combining sorted 1-element arrays into 2-element arrays, combining sorted 2-element arrays into 4-element arrays…) • Best-case scenario: The array is already perfectly sorted. But we still have to split and recombine it back together with this algorithm.
40. Merge Sort O(n log n) W(n log n)