Binary Search

Considering the following list.

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

What are the two first elements of the list that will be checked to find 25 using binary search?
1: The 1st element
2: The 2nd element

Question

Binary Search

Considering the following list.

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

What are the two first elements of the list that will be checked to find 25 using binary search?
1: The 1st element
2: The 2nd element

BlackTom AI · Accepted Answer

Binary search compares the target with the middle element of the current interval and then continues on the left or right half. Using indices and the convention that when splitting an even-sized interval you take the upper middle (ceil), the first two elements checked are 23 and 36.

1) Relevant knowledge points and concepts
- Binary search on a sorted array repeatedly compares the target to the middle element of the current search interval [low, high].
- Different implementations choose middle as floor((low+high)/2) or ceil((low+high)/2). The answer given corresponds to using the upper-middle (ceil) when the interval length is even.

2) Step-by-step reasoning
- Start with the array indices 0..8 for {12,13,15,20,23,24,25,36,40}.
- Initial low = 0, high = 8. Compute middle:
  mid = (low + high) / 2 = (0 + 8) / 2 = 4 → element at index 4 is 23. First checked = 23.
- Compare target 25 with 23: 25 > 23 → continue on right half. New interval low = mid + 1 = 5, high = 8.
- Using the upper-middle rule: mid = ceil((5 + 8) / 2) = ceil(13 / 2) = 7 → element at index 7 is 36. Second checked = 36.

3) Calculations (intermediate steps shown)
- First mid: (0+8)/2 = 4 → A[4] = 23.
- New bounds: low = 5, high = 8.
- Second mid (upper-middle): ceil((5+8)/2) = ceil(6.5) = 7 → A[7] = 36.

4) Why the correct answer is correct
- Given the chosen mid selection policy (upper-middle on even lengths), the algorithm inspects index 4 (23) first and then index 7 (36) next. This matches the provided answer.

5) Why other options are incorrect (brief)
- 25 would be checked second only if the implementation used floor mid on the right-half (mid = 6), but the given answer uses the upper-middle convention, so 25 is not the second checked.
- 12, 13, 15, 20, 24, 40 are not at the computed mid indices in the first two steps, so they are not the first two elements checked.

6) Conclusion
- Therefore, under the upper-middle binary-search convention, the first two elements checked are 23 and 36, which matches the provided answer.

Binary Search Considering the following list. {12, 13, 15, 20, 23, 24, 25, 36, 40} What are the two first elements of the list that will be checked to find 25 using binary search? 1: The 1st element 2: The 2nd element匹配题

类似问题

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}

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