Questions: Given list: (1,5,25,36,47,53,60,68,70,89) Which list elements will be compared to key 53 using binary search? Enter elements in the order checked. Ex: 42,32,12 (comma between values)

Solution Steps

Binary search works by repeatedly dividing the sorted list into two halves and comparing the middle element with the key. If the middle element is equal to the key, the search is successful. If the key is less than the middle element, the search continues in the left half; otherwise, it continues in the right half.

The given sorted list is:
\[ (1, 5, 25, 36, 47, 53, 60, 68, 70, 89) \] The key to search for is 53.

1. First Comparison:

   • The middle element of the list is 47 (index 4).
   • Since \(53 > 47\), we discard the left half and continue with the right half:
     \[ (53, 60, 68, 70, 89) \]

2. Second Comparison:

   • The middle element of the remaining list is 68 (index 7).
   • Since \(53 < 68\), we discard the right half and continue with the left half:
     \[ (53, 60) \]

3. Third Comparison:

   • The middle element of the remaining list is 53 (index 5).
   • Since \(53 = 53\), the search is successful.

Final Answer