Top-K with a Min-Heap: When to Use It

Start with the idea

A problem is a good match for Top-K with a Min-Heap when it asks for largest k values and bounded leaderboards. Here the concrete task is: Return the three largest values in descending order. The visible input [4,1,9,7,3,8] is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Use it when only top-ranked candidates or repeated next-best extraction matters; sorting the entire stream may waste work. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Keep a heap of only k winners and evict its smallest whenever it grows. 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? A heap keeps the current extremum accessible while new items arrive. Explain what belongs in the heap and what may be discarded. 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(n log k) time · O(k) space; identify the operation responsible for it and the extra memory it needs.