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.33 Data Structures http://ecomputernotes.com

4. 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

5. 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

6. 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

7. 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: