Question

Apply binary search for the following sequence of numbers 10,20,30,40,50,60,70,80,90.search for item =30

Answer 1

1. Initialize: Set the lower bound (start) to index 0 and the upper bound (end) to the index of the last element in the sequence.

   • Start: 0
   • End: 8

2. Calculate mid: Find the index of the middle element by averaging the start and end indices (round down if necessary).

   • Mid: (0 + 8) / 2 = 4

3. Compare: Check if the middle element is equal to the item you're searching for (30). Since 50 ≠ 30:

   • Sequence: 10, 20, 30, 40, 50, 60, 70, 80, 90
   • Mid value: 50 ≠ 30

4. Update bounds: Update the start or end index based on whether the item is greater or smaller than the middle element. Since 30 < 50, update the end index to mid - 1.

   • Start: 0
   • End: 3

5. Repeat: Continue the process until the item is found or the bounds cross each other.

   • New Mid: (0 + 3) / 2 = 1
   • Sequence: 10, 20, 30, 40, 50, 60, 70, 80, 90
   • Mid value: 20 ≠ 30
   • New Start: 2
   • End: 3

6. Repeat:

   • New Mid: (2 + 3) / 2 = 2
   • Sequence: 10, 20, 30, 40, 50, 60, 70, 80, 90
   • Mid value: 30 = 30

7. Found: The item 30 is found at index 2.

So, the binary search algorithm successfully finds the item 30 at index 2 in the given sequence of numbers.