I had a working stack-based solution in my head pretty fast, then they said no stack.
First, clarify the problem constraints and edge cases (e.g., division by zero, integer division truncation). Then, explain the standard two-pass approach using a stack, and finally present the single-pass O(1) space solution by maintaining a running total and a current term, applying multiplication/division immediately and deferring addition/subtraction.
Pro tip: Emphasize that the O(1) space solution is not just about avoiding a stack but about recognizing that only the last term's value and operator need to be remembered; this demonstrates deep understanding of expression evaluation and memory optimization.
Ask about integer division behavior (truncation toward zero), division by zero, and whether the expression is guaranteed valid. Confirm that operators have standard precedence and left-to-right associativity.
Describe the typical two-pass method: parse numbers and operators, use a stack to handle precedence by evaluating * and / immediately, then sum the stack for + and -. Mention time O(n) and space O(n).
Explain that we can avoid a stack by keeping a running total (result) and a current term. When encountering + or -, add the current term to result and start a new term with the sign. When encountering * or /, update the current term by applying the operator to the last number and the next number.
Trace the algorithm on a sample expression like '3+2*2' to show how result and current term are updated step by step, ensuring clarity and correctness.
State that the solution runs in O(n) time and O(1) extra space, and discuss trade-offs: the single-pass approach is more memory-efficient but slightly more complex to implement than the stack-based method.
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