Postfix Expression Evaluation

CSC-211 · Semester III · Data Structures and Algorithms

intermediate25 minAvailable

StackLIFO · push / pop / peek · O(1)

562+*

Operand stack (top ↑)

Lab brief

Objective

Evaluate a postfix expression with a value stack, applying each operator to the two most recent operands.

Theory & concepts

Postfix evaluation is a single left-to-right scan. Operands are pushed onto a value stack; when an operator appears, pop the top two values, apply the operator in the correct order, and push the result back. When the input is exhausted, the single value left on the stack is the answer — no parentheses and no precedence needed.

Rendering diagram…

Postfix evaluation with a value stack

4 2 3 * +  →
   push 4, push 2, push 3
   *: pop 2, pop 3 → push 6
   +: pop 4, pop 6 → push 10  → answer 10
For subtraction/division order matters: a b -  means a − b.

Prerequisites

Lab: Infix to Postfix Conversion
Stack operations

Instructions

1Step through each token of the postfix expression.
2Watch operands accumulate on the value stack.
3When an operator is read, watch the top two operands combine into one result.
4Note the operand order for − and ÷.
5Confirm the final single value equals the hand-computed result.

Tasks

Evaluate 2 3 4 + *
Step through and confirm the result is 14.
Order sensitivity
Evaluate 10 4 - and 4 10 - and explain why they differ.
Multi-operator chain
Evaluate 5 1 2 + 4 * + 3 - and verify 14.

Self-check

The final stack value is correct.
Operand order for − and ÷ is applied correctly.
The student explains why postfix needs no parentheses.

Environment

value stacktoken stepperoperator applicationresult readout