Given the following list of sorted elements, how many elements of the list will be checked to find 25 using binary search?

{12, 13, 15, 20, 23, 24, 25, 36, 40}

Question

Given the following list of sorted elements, how many elements of the list will be checked to find 25 using binary search?

{12, 13, 15, 20, 23, 24, 25, 36, 40}

BlackTom AI · Accepted Answer

Binary search compares the target to the list's middle element and then discards half the list each comparison. For a sorted list of 9 elements the middle position is 5 (using 1-based indexing), so we inspect the 5th element first.

1) Relevant concepts:
- Binary search operates on a sorted list by repeatedly comparing the target to the middle element and narrowing the search interval.
- Each comparison examines one element; the count asked is how many elements are inspected until the target is found.
- For an array of length n, the middle index is floor((low+high)/2) (1-based: low=1, high=n).

2) Step-by-step reasoning (1-based indexing):
- List: {12, 13, 15, 20, 23, 24, 25, 36, 40}, positions 1..9.
- Initial low = 1, high = 9. Compute mid = floor((1+9)/2) = floor(10/2) = 5. Inspect element at position 5 = 23. Comparison 1: 25 ?= 23. Since 25 > 23, discard left half (positions 1–5).
- Update low = 6, high = 9. Compute mid = floor((6+9)/2) = floor(15/2) = 7. Inspect element at position 7 = 25. Comparison 2: 25 = 25. Found.

3) Intermediate calculations shown:
- First mid = floor((1+9)/2) = 5 → element 23 (not target).
- Second mid = floor((6+9)/2) = 7 → element 25 (target found).

4) Why the correct answer is correct:
Two elements are inspected: first 23, then 25. Binary search locates 25 on the second comparison because the initial middle (position 5) directs the search to the subarray containing position 7, where the target sits.

5) Why other options are incorrect:
- "7" and "8": far too many checks; binary search eliminates half the list each step, so only a few checks are needed.
- "3": would imply the algorithm inspected one more element unnecessarily; here the second inspection finds the target, so only 2 checks occur.

Conclusion: The number of elements checked is 2, matching the provided correct answer.

Given the following list of sorted elements, how many elements of the list will be checked to find 25 using binary search? {12, 13, 15, 20, 23, 24, 25, 36, 40}单项选择题

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