The multiplication-before-addition precedence is the whole point of the problem and it's easy to just iterate left-to-right and get the wrong answer on something like '3+2*2'.
Clarify that the expression contains only non-negative integers, '+', '*', and spaces, with no parentheses, and that standard operator precedence applies. Then propose a single-pass stack-based solution that processes multiplication immediately and defers addition, or a two-pass approach that first evaluates all multiplications and then sums the results. Walk through a small example to demonstrate correctness and discuss time/space complexity.
Pro tip: Mention that you can avoid a stack by maintaining a running sum and a current term, updating the term on '*' and adding it to the sum on '+' or at the end. This shows you can optimize space to O(1) while keeping the code clean and interview-friendly.
Confirm that the expression is valid, contains only non-negative integers, '+', '*', and spaces, and that operator precedence applies with no parentheses. Ask about input size, potential overflow, and whether the result fits in a standard integer.
Decide between a stack-based single-pass evaluation or a two-pass approach (first multiply, then add). Explain the trade-offs: stack uses O(n) space but is straightforward; two-pass may require extra space for tokens but can be simpler to reason about.
For the stack approach: iterate through the string, build numbers, and when an operator is encountered, apply the previous operator. For '*', pop the last number, multiply, and push the result; for '+', push the number. Finally, sum the stack. For the O(1) space approach: maintain a running sum and a current term, updating the term on '*' and adding it to the sum on '+' or at the end.
Trace the algorithm on a sample expression like '3 + 2 * 2' to show how multiplication is handled before addition. Highlight how the stack or running sum evolves step by step.
State that the time complexity is O(n) for a single pass (or O(n) for two passes) and space complexity is O(n) for the stack or O(1) for the optimized approach. Discuss potential edge cases like leading/trailing spaces, multiple-digit numbers, and expressions with only one number.
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