Binary Search — Reasoning Check

1. For the sorted array [-3,-1,2,2,8], what zero-based index does lower_bound(target=2) return, where lower_bound means the first value greater than or equal to the target? Enter one integer.

2. To find the minimum of the distinct rotated array [5,6,1,2,3,4], start with inclusive lo=0, hi=5 and mid=2. Since nums[mid] < nums[hi], which update preserves the answer?

Select one answer.

Return nums[hi], because the suffix is sorted. Set hi=mid, retaining index 2 as a possible minimum. Set lo=mid+1, because the right endpoint is larger. Set hi=mid-1, because the midpoint was already inspected.

3. SearchRange must find all occurrences of the largest representable int. Which upper-bound computation avoids overflowing the target?

Select one answer.

Use the last array position whenever target equals the maximum int. Search for the first value at least target, then subtract one from that index. Search directly for the first value strictly greater than target, then subtract one from that index. Search for the first value at least target+1, computing target+1 as an int.

4. A matrix-search implementation treats [[1,6,9],[2,7,10]] as one virtual row-major array and applies ordinary binary search. Which diagnosis is correct?

Select one answer.

Virtual flattening is invalid because binary search always requires a newly allocated flat array. The algorithm is valid because every row and every column is individually sorted. Sorted rows and columns do not guarantee sorted row-major order; the transition from 9 to 2 breaks this search premise. The only problem is that a rectangular matrix must be square for index mapping.

5. FindPeakElement receives [3,8,4,7,2], with outside neighbors treated as negative infinity. Which statement correctly describes acceptable zero-based outputs?

Select one answer.

Either index 1 or index 3 is valid because each is larger than its two neighbors. Every interior index is valid because the outside neighbors are negative infinity. Only index 1 is valid because a peak must be the global maximum. Only index 3 is valid because a peak must be the rightmost local maximum.

6. For sorted arrays A=[2,8] and B=[1,3,5,7], cuts i=1 in A and j=2 in B put three values on the left. What median follows from this valid partition? Enter the numeric value.