Find First and Last Position of Element in Sorted Array

Do not stop at an arbitrary binary-search hit because duplicates require boundaries. Compute lowerBound(target): the smallest index i such that nums[i] is at least target. If i equals n or nums[i] is not target, return [-1,-1]. Then compute upperBound(target): the smallest index whose value is greater than target; the final index is upperBound minus one. Use a half-open search interval [lo, hi), with lo advanced when the predicate is false and hi reduced when it is true, which makes termination and edge handling consistent. Explain the invariant that all indices before lo fail the predicate and all indices at or after hi satisfy it. Test empty input, target before or after the range, one occurrence, all values target, and a target at either endpoint. Each bound is O(log n) time and O(1) extra space.