How do you evaluate a postfix expression using a Stack?

Difficulty: 4/10

Stack Data Structure, Expression Parsing, Abstract Syntax Trees

Postfix Expression Evaluation

In postfix notation, operators appear after their operands, so parentheses are unnecessary for evaluation. A stack is used to store operands. When an operand is encountered, it is pushed; when an operator is encountered, the required operands are popped, the operation is performed, and the result is pushed back.

javascript

1
Example: 2 3 + 4 * evaluates to (2 + 3) * 4 = 20.
2
Time complexity: O(n).
3
Auxiliary space: O(n) in the worst case.
4
Operand order matters for subtraction and division.
5
Malformed expressions should be detected rather than blindly popping from an empty stack.

Scenario Questions

0-2 years experience

1We are building a simple command-line calculator that takes space-separated postfix strings like '3 4 + 2 *'. Could you walk me through how you'd use a stack to parse and evaluate this, and show me how you'd handle the order of operands during subtraction or division?
2Imagine we run your postfix evaluator on the input '5 0 /'. How would you write the evaluation logic to catch this division-by-zero error and return a clean error state instead of crashing the application?

Follow-up Questions

How would you modify your stack-based evaluator to support unary operators like negative (-) or logical NOT (!)?
If we receive a malformed expression like '4 5 + *', how does your code gracefully handle the empty stack exception and report the exact failure point?