Evaluation of expression Using Stack

Duration: 4 min

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  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
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  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture focuses on the application of stacks in computer science, specifically for evaluating arithmetic expressions in postfix notation. The instructor, Sanchit Jain Sir from Knowledge Gate, presents a specific problem from the GATE 2015 exam. The problem asks to evaluate the postfix expression `10 5 + 60 6 / * 8 -`. The solution involves using a stack to store operands and performing operations as operators are encountered. The instructor systematically walks through the expression, pushing numbers onto the stack and performing calculations when an operator appears, ultimately arriving at the correct answer among the provided choices.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a title slide indicating a 'Break' and the topic 'Application of Stack: Arithmetic Expression Evaluation'. The instructor introduces a GATE 2015 question asking for the result of the postfix expression `10 5 + 60 6 / * 8 -`, with options (A) 284, (B) 213, (C) 142, and (D) 71. He writes the expression on the board and begins the evaluation process. He draws a stack diagram and pushes the first two operands, 10 and 5. Upon encountering the `+` operator, he pops 5 and 10, calculates their sum (15), and pushes the result back onto the stack. Next, he pushes the operands 60 and 6. When the `/` operator is encountered, he pops 6 and 60, performs the division (60 divided by 6 equals 10), and pushes the result 10 onto the stack. At this point, the stack contains 15 and 10, ready for the next operation.

  2. 2:00 – 4:27 02:00-04:27

    Continuing from the previous state, the instructor encounters the `*` operator. He pops the top two elements, 10 and 15, and multiplies them (15 * 10 = 150), pushing the result 150 back onto the stack. He then pushes the next operand, 8, onto the stack. Finally, he encounters the `-` operator. He pops 8 and 150, subtracting 8 from 150 to get the final result of 142. The instructor marks option (C) 142 as the correct answer, completing the step-by-step demonstration of postfix expression evaluation using a stack. He emphasizes the visual representation of the stack growing and shrinking as operations are performed.

This lecture segment effectively demonstrates the practical application of the stack data structure in parsing and evaluating mathematical expressions. By breaking down the GATE 2015 problem, the instructor illustrates the Last-In-First-Out (LIFO) nature of stacks, where operands are stored until an operator triggers a calculation. The example emphasizes the correct order of operands for non-commutative operations like subtraction and division, ensuring students understand how postfix notation simplifies expression evaluation without parentheses. The visual board work reinforces the abstract concept of stack operations.

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