Application of Stacks (Infix to Postfix) - Part 5

Neso Academy
17 Dec 202108:36

Summary

TLDRIn 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.

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Related Tags
Postfix EvaluationStack AlgorithmC ProgrammingData StructuresPostfix ExpressionsStack OperationsProgramming TutorialInfix to PostfixAlgorithm ExplanationStep-by-Step Guide