Question

How do I evaluate an expression in Postfix Notation?

Answer 1

To evaluate an expression in postfix notation, you can use a stack-based algorithm. Here's a step-by-step guide on how to do it:

1. Initialize an empty stack.
2. Start scanning the expression from left to right.
3. For each element in the expression:
   • If the element is an operand (a number), push it onto the stack.
   • If the element is an operator:
     • Pop the required number of operands from the stack (based on the arity of the operator).
     • Apply the operator to the popped operands.
     • Push the result back onto the stack.
4. Continue this process until the entire expression is scanned.
5. Once the expression is fully evaluated, the result will be the value left on the stack.

Let's walk through an example of evaluating a postfix expression:

Expression: 5 3 + 2 *

1. Start with an empty stack.
2. Scan the expression from left to right:
   • Push 5 onto the stack. Stack: [5]
   • Push 3 onto the stack. Stack: [5, 3]
   • Encounter '+': Pop 3 and 5, add them, and push the result (8) onto the stack. Stack: [8]
   • Push 2 onto the stack. Stack: [8, 2]
   • Encounter '*': Pop 2 and 8, multiply them, and push the result (16) onto the stack. Stack: [16]
3. The expression is fully evaluated, and the result is 16.

So, the expression "5 3 + 2 *" evaluates to 16 in postfix notation.