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# Lazyselect

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• ### Lazyselect

1. 1. LAZYSELECT 09M6358
2. 2. n Q p
3. 3. 3 5 2 7 1 6 4 8
4. 4. n=8 3 5 2 7 1 6 4 8
5. 5. n=8 3 5 2 7 1 6 4 8
6. 6. n=8 3 5 2 7 1 6 4 8
7. 7. n=8 3 Q. 5 A(n = 8) 2 7 1 p=5 A. 5 6 4 8
8. 8. QUICKSELECT : O(n) SELECT : O(n)
9. 9. LAZYSELECT
10. 10. LAZYSELECT O(n)
11. 11. 1. A n ( n < 50), A , p . A n3/4 , B .
12. 12. A
13. 13. n
14. 14. n n = 500
15. 15. n 3/4 n = 500
16. 16. n 3/4 n = 500
17. 17. n 3/4 n = 500 n = 106
18. 18. B n = 106
19. 19. n n = 50
20. 20. p
21. 21. p p
22. 22. 2. A p B q=pn3/4/n=pn-1/4 . , l=max{ q- √n , 0}, h=min{ q+√n ,n3/4} ( , q √n ) ,B l L h H ( B LAZYSELECT .)
23. 23. B n = 106
24. 24. B p q
25. 25. q= pn3/4 / n
26. 26. q= pn-1/4
27. 27. q= pn-1/4
28. 28. q
29. 29. q
30. 30. -√n +√n q
31. 31. -√n +√n q L H
32. 32. l = max{ q - √n , 0} h = min{ q + √n , n3/4 }
33. 33. B l L B h H
34. 34. LAZYSELECT B l L B h H LAZYSELECT
35. 35. 3. A , A A[i]<H A1 A2 (QUICKSORT partition ). A1 |A1| p , A2 p-|A1| (A2 LAZYSELECT ). |A1|≧p , A1 A[i]<L A11 A12 . |A11|≧p A11 p (A11 LAZYSELECT ). , A12 p-|A11| (A12 LAZYSELECT ).
36. 36. A
37. 37. A H
38. 38. A1 A2 H
39. 39. A1 A2 ? P
40. 40. A1 A2 |A1| P
41. 41. A2 P’ = P - |A1|
42. 42. A2 P’ = P - |A1|
43. 43. A1 A2 P ≦ |A1|
44. 44. A1 A2 L
45. 45. A11 A12 A2 L
46. 46. A11 A12 A2 ? P
47. 47. A1 A11 A12 A2 LAZYSELECT LAZYSELECT LAZYSELECT or or p’ = p p’ = p - |A11| p’ = p - |A1|
48. 48. n3/4 √n
49. 49. A11 A2 A12
50. 50. p A11 A2 A12
51. 51. O(n)