What property of binary search enables halving the search space at every step?

What property of binary search enables halving the search space at every step?

• A. The elements are stored in sorted order, allowing comparison of the middle element to the target.
• B. The algorithm uses a hash table to locate the target.
• C. The search starts at a randomly chosen index.
• D. The algorithm scans sequentially from left to right.

Answer: (A)

Halving the search space comes from keeping the data in sorted order and using the middle element to decide which half could contain the target. In a sorted list, everything to the left of the middle is smaller and everything to the right is larger. By comparing the target to the middle value, you can conclude whether it lies in the left half or the right half and discard the other half. Repeating this, you halve the search area each time, giving the efficient logarithmic behavior of binary search. The other ideas don’t leverage this split: a hash table isn’t used for binary search, starting at a random index breaks the left/right distinction, and a linear scan checks elements one by one rather than cutting the search space in half.

Halving the search space comes from keeping the data in sorted order and using the middle element to decide which half could contain the target. In a sorted list, everything to the left of the middle is smaller and everything to the right is larger. By comparing the target to the middle value, you can conclude whether it lies in the left half or the right half and discard the other half. Repeating this, you halve the search area each time, giving the efficient logarithmic behavior of binary search. The other ideas don’t leverage this split: a hash table isn’t used for binary search, starting at a random index breaks the left/right distinction, and a linear scan checks elements one by one rather than cutting the search space in half.