Application of Stacks (Infix to Postfix) - Part 5

Summary

In this lecture, the concept of evaluating postfix expressions using stacks is explored in detail. The instructor walks through an algorithm that utilizes a stack to hold operands and apply operators step by step. The process involves scanning a postfix expression from left to right, pushing operands onto the stack, and performing operations when operators are encountered. A detailed example demonstrates how to evaluate an expression like '753 * 5 1 ^ / + 3 2 - +' to get the result of 11. This process illustrates how stacks are essential in managing postfix expression evaluation in C programming.

Takeaways

• 😀 The presentation is part 5 of a series on the application of stacks in fixed-to-postfix conversion.
• 😀 The main focus of this part is to evaluate a postfix expression using a stack.
• 😀 In the previous presentation, the conversion from infix to postfix was covered, while this one deals with evaluating the postfix expression.
• 😀 Instead of using a stack to hold operators as in the conversion process, here the stack holds the operands.
• 😀 The algorithm for evaluating a postfix expression involves scanning symbols left to right, pushing operands onto the stack, and applying operators to operands when encountered.
• 😀 When an operator is encountered, the top two operands are popped from the stack, the operation is applied, and the result is pushed back onto the stack.
• 😀 The order of operands is critical when applying operators—particularly in operations like subtraction and division where the order matters.
• 😀 The postfix expression used in the example is: 753* 5 1^ / + 3 2- +.
• 😀 After scanning and evaluating all symbols, the final result is obtained by popping the remaining symbol from the stack and printing it.
• 😀 The result of the given postfix expression (after applying the algorithm step by step) is 11.
• 😀 The presentation concludes by emphasizing the simplicity of postfix expression evaluation using the stack and preparing for program implementation in C.

Q & A

What is the main objective of evaluating a postfix expression using a stack?

The main objective is to evaluate a postfix expression by using a stack to store operands, perform operations, and ultimately derive the result after processing the entire expression.

How does the use of a stack differ between converting infix to postfix and evaluating postfix expressions?

When converting infix to postfix, a stack holds operators, but when evaluating a postfix expression, the stack holds operands (numbers) instead of operators.

What is the first step in evaluating a postfix expression using a stack?

The first step is to scan the postfix expression from left to right and process each symbol.

What should be done when an operand (number) is encountered in a postfix expression during evaluation?

When an operand is encountered, it should be pushed onto the stack.

What happens when an operator is encountered in a postfix expression during evaluation?

When an operator is encountered, two operands are popped from the stack, the operator is applied to them, and the result is pushed back onto the stack.

In the example expression '753 * 5 1 ^ / + 3 2 - +', what operation is performed first?

The first operation is the multiplication (3 * 5), which is evaluated and results in 15.

Why does the order of operands matter when dealing with subtraction or division in postfix evaluation?

The order matters because subtraction and division are non-commutative operations. For example, '5 - 3' is different from '3 - 5', and '15 / 5' is different from '5 / 15'.

What is the result of the postfix expression '753 * 5 1 ^ / + 3 2 - +'?

The result of the postfix expression is 11.

How does the stack behave after processing the final operator in a postfix expression?

After processing the final operator, the stack will contain a single element, which is the final result of the postfix expression.

What should be done once all symbols of a postfix expression have been processed?

Once all symbols have been processed, the remaining symbol in the stack should be popped and printed as the result of the postfix expression.