Implement lower_bound and upper_bound binary search

Q: Implement lower_bound and upper_bound binary search

This question evaluates proficiency with binary search, precise index and boundary management in sorted arrays, and the ability to reason about algorithmic correctness, loop invariants, and time/space complexity.

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Question

Implement two functions for a nondecreasing sorted integer array nums of length n: lower_bound(target) returns the smallest index i such that nums[i] >= target, or n if no such index exists; upper_bound(target) returns the smallest index i such that nums[i] > target, or n if no such index exists. Provide iterative implementations with O(log n) time and O(

space, handle edge cases (empty array, all elements < or > target, duplicates, negatives), include tests, and briefly argue correctness and boundary invariants.

Implement lower_bound and upper_bound binary search

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