stack

A warm-up that screens for the stack instinct. The signal is recognizing last-opened-first-closed maps to a stack, and handling the edge cases (leftover opens, early close). Here is the pattern.

The brute force is O(n squared) nested scans. A monotonic stack does it in one O(n) pass by keeping only the candidates that can still be a future answer. Here is the pattern and why each element is pushed and popped exactly once.

Evaluating arithmetic with precedence and nested parentheses is a parsing problem, and a stack handles both cleanly. The traps are operator precedence, multi-digit numbers, and the sign of truncated division. Here is a single-pass solution.