Min Stack: When to Use It

Start with the idea

A problem is a good match for Min Stack when it asks for constant-time minimum beside normal stack operations. Here the concrete task is: After push 5, push 2, push 4, pop, return the minimum. The visible input push5 push2 push4 pop min is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Look for nested structure, next-greater relationships, or ordered processing. A plain scan is enough when no unresolved state must be retained. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Store each value together with the minimum at the moment it is pushed. 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 stack remembers unfinished work in last-in-first-out order; a queue processes work in first-in-first-out order. Say what each stored item still needs. 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(1) per operation · O(n) space; identify the operation responsible for it and the extra memory it needs. Then compare a straightforward alternative: a direct scan, full sort, or repeated recomputation may be easier but can pay for the same work many times.