Given a list of 64 elements, how many elements will be checked to look for a value that is larger than the largest value in the list using binary search?

Question

BlackTom AI · Accepted Answer

Binary search halves the candidate interval on every comparison, so the worst-case number of checks equals floor(log2 n) + 1. For n = 64 this gives floor(log2 64) + 1 = 6 + 1 = 7.

1) Relevant concepts
- Binary search on a sorted list compares the target to the middle element and then discards half the interval each time.
- Each comparison reduces the remaining candidate size to at most half, so the number of comparisons grows logarithmically: k comparisons can distinguish at most 2^k different positions (including the “not found” result).

2) Step-by-step reasoning
- Start with low = 1, high = 64 (64 elements). Compute mid = floor((low+high)/2) and compare.
- Because the searched value is larger than the largest element, every comparison will go to the right half (low = mid + 1).
- Track the intervals and mids:

3) Intermediate steps / comparisons
- 1st: low=1, high=64 → mid=32 → compare A[32]; key > A[32] → new interval 33..64 (32 elements)
- 2nd: low=33, high=64 → mid=48 → compare A[48]; key > A[48] → new interval 49..64 (16 elements)
- 3rd: low=49, high=64 → mid=56 → compare A[56]; key > A[56] → new interval 57..64 (8 elements)
- 4th: low=57, high=64 → mid=60 → compare A[60]; key > A[60] → new interval 61..64 (4 elements)
- 5th: low=61, high=64 → mid=62 → compare A[62]; key > A[62] → new interval 63..64 (2 elements)
- 6th: low=63, high=64 → mid=63 → compare A[63]; key > A[63] → new interval 64..64 (1 element)
- 7th: low=64, high=64 → mid=64 → compare A[64]; key > A[64] → new interval low=65, high=64 → stop

4) Why this answer is correct
After 7 comparisons the search interval becomes empty; no further checks are needed. The general bound floor(log2 n) + 1 yields 7 for n = 64.

5) Why other answers would be incorrect
- Answer 6 would come from using log2 64 = 6 but forgetting the final comparison that proves “not found.” 
- Answer 64 would be linear search, not binary search.
- Answer 8 would overcount; binary search never needs more than floor(log2 n)+1 checks for n items.

6) Conclusion
Therefore the number of elements checked is 7, which matches the provided correct answer.

Given a list of 64 elements, how many elements will be checked to look for a value that is larger than the largest value in the list using binary search?Single choice

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