In a binary search algorithm, if the middle element is greater than the target, what happens next?

Question

BlackTom AI · Accepted Answer

In binary search, the middle element is compared to the target; if the middle element is greater than the target, the algorithm continues by searching the left half of the list.

1. Relevant knowledge points and concepts
- Binary search requires a sorted array (commonly ascending).
- At each step compute mid = floor((low + high) / 2).
- Compare A[mid] to target: if equal → found; if A[mid] > target → target, if present, must be left of mid; if A[mid] < target → target, if present, must be right of mid.
- Time complexity is O(log n) because the search range halves each step.

2. Complete reasoning process step by step
- Start with indices low = 0 and high = n − 1.
- Compute mid = (low + high) // 2.
- If A[mid] > target, all elements at indices ≥ mid are ≥ A[mid] (because array is sorted ascending), so the target cannot be at mid or any index to the right. Therefore set high = mid − 1 and continue the loop on the left subarray.

3. Intermediate steps / example calculations
- Example array: [2, 4, 6, 8, 10], target = 5.
- low = 0, high = 4 ⇒ mid = (0+4)//2 = 2, A[2] = 6.
- Since 6 > 5, update high = mid − 1 = 1 and continue searching indices 0..1 (the left half).

4. Why the correct answer is correct
- A[mid] > target implies any element at index ≥ mid is ≥ A[mid] > target in a sorted ascending array, so the target can only lie to the left. Restricting the search to the left half preserves correctness while halving the search space.

5. Why other options are incorrect
- "Search the entire list again": defeats the purpose and is unnecessary; does not reduce the problem.
- "Return -1 immediately": wrong because the target might still exist in the left half.
- "Search the right half of the list": incorrect direction; right-side elements are greater or equal to A[mid] and thus > target.

6. Conclusion
This reasoning confirms the correct choice: Search the left half of the list.

In a binary search algorithm, if the middle element is greater than the target, what happens next?单项选择题

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