stack

A warm-up that tests for the stack instinct. Interviewers look for recognizing that last-opened-first-closed maps onto a stack, plus handling the edge cases (leftover opens, early close). The pattern follows.

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

Working out arithmetic with precedence and nested parentheses is a parsing task, and a single stack manages both neatly. The traps are operator precedence, multi-digit numbers, and the sign of truncated division. Here is a one-pass solution.