Upper Bound: When to Use It

Start with the idea

A problem is a good match for Upper Bound when it asks for duplicate counts, right insertion positions. Here the concrete task is: Return the first index whose value is greater than 4. The visible input [1,2,4,4,7] is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. It needs ordering, a monotone predicate, or another proved structure that lets one half be discarded; merely containing numbers is not enough. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Maintain the first position whose value is strictly greater than target. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? Binary search maintains an interval that is still capable of containing the answer. State precisely why the discarded half cannot contain it. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(log n) time · O(1) space; identify the operation responsible for it and the extra memory it needs.