Evaluate the following postfix expression

Evaluate the following postfix expression: 3 4 * 2 5 * + 6 –

The Correct Answer and Explanation is :

Evaluating the Postfix Expression:

Given postfix expression:
3 4 * 2 5 * + 6 –

Step 1: Understand Postfix Notation
Postfix notation (Reverse Polish Notation) is a mathematical notation where operators follow their operands. It eliminates the need for parentheses.

We evaluate postfix expressions using a stack:

Push operands onto the stack.
When an operator appears, pop the required number of operands, apply the operator, and push the result back.

Step 2: Solve Step-by-Step

Expression: `3 4 * 2 5 * + 6 -`

Processing:

Push 3 → Stack: [3]
Push 4 → Stack: [3, 4]
Encounter *, pop 4 and 3, compute 3 * 4 = 12 → Push 12
Stack: [12]
Push 2 → Stack: [12, 2]
Push 5 → Stack: [12, 2, 5]
Encounter *, pop 5 and 2, compute 2 * 5 = 10 → Push 10
Stack: [12, 10]
Encounter +, pop 10 and 12, compute 12 + 10 = 22 → Push 22
Stack: [22]
Push 6 → Stack: [22, 6]
Encounter -, pop 6 and 22, compute 22 - 6 = 16 → Push 16
Stack: [16]

Final Answer:

Explanation in 300 Words

Postfix notation is an efficient way to evaluate expressions without worrying about parentheses or operator precedence. It follows a stack-based approach, which makes it easier for computers to process mathematical operations.

In our expression (3 4 * 2 5 * + 6 -), multiplication and addition operations are performed in sequence using a stack. The key advantage of postfix notation is that it avoids ambiguity in evaluation. Unlike infix notation (3 * 4 + 2 * 5 - 6), where operator precedence must be considered, postfix expressions are evaluated in a direct, left-to-right manner.

We systematically push numbers onto the stack and perform operations when encountering operators, ensuring accuracy. The final value left in the stack is the result. In this case, after evaluating all operations, the result is 16.

This method is widely used in calculators, compilers, and programming languages like Forth and PostScript because it simplifies expression evaluation without requiring additional parsing rules for precedence.