Binary search is like looking up a phone number or a word in the dictionary Start in middle of book If name you're looking for comes before names on page, look in first half Otherwise, look in second half

1. Class No.32 Data Structures http://ecomputernotes.com

2. Tables and Dictionaries http://ecomputernotes.com

13. Case 1: val == a[mid] val = 10 low = 0, high = 8 5 7 9 10 13 17 19 1 27 a: low high Binary Search http://ecomputernotes.com 1 2 3 4 5 6 7 0 8 mid mid = (0 + 8) / 2 = 4 10

14. Case 2: val > a[mid] val = 19 low = 0, high = 8 mid = (0 + 8) / 2 = 4 Binary Search -- Example 2 5 7 9 10 1 a: mid low high http://ecomputernotes.com 13 17 19 27 1 2 3 4 5 6 7 0 8 new low new low = mid+1 = 5 13 17 19 27

15. Case 3: val < a[mid] val = 7 low = 0, high = 8 mid = (0 + 8) / 2 = 4 Binary Search -- Example 3 10 13 17 19 27 a: mid low high http://ecomputernotes.com 5 7 9 1 1 2 3 4 5 6 7 0 8 new high new high = mid-1 = 3 5 7 9 1

16. val = 7 Binary Search -- Example 3 (cont) 5 7 9 10 13 17 19 1 27 1 2 3 4 5 6 7 0 8 a: 5 7 9 10 13 17 19 1 27 1 2 3 4 5 6 7 0 8 a: 5 7 9 10 13 17 19 1 27 1 2 3 4 5 6 7 0 8 a:

27. Lecture No.38 Data Structure Dr. Sohail Aslam

28. Skip List: formally 56 64 78  31 34 44  12 23 26 S 0 64  31 34  23 S 1  31  S 2   S 3

37. Skip List: Implementation   S 0 S 1 S 2 S 3   45 12 23 34   34   23 34

40. Skip Lists with Quad Nodes 56 64 78  31 34 44  12 23 26    31  64  31 34  23 S 0 S 1 S 2 S 3