Which statement about time complexities is true for binary search compared to linear search?

• A. Binary search has O(n) time even if data is sorted.
• B. Binary search has O(log n) time and requires the data to be sorted.
• C. Linear search has O(log n) time on sorted data.
• D. Binary search is O(n) and does not require sorted data.

Answer: (D)

Binary search relies on halving the search space with each comparison, which leads to about log2(n) steps in the worst case. Because you can only safely discard half of the data if it’s sorted, this algorithm achieves O(log n) time when the data is in order. If the data isn’t sorted, that halving logic doesn’t reliably lead to the target, so you don’t get the log n efficiency without first sorting. Linear search, by contrast, may have to check every element, giving O(n) time. So the correct idea is that binary search runs in O(log n) time and requires sorted data.