Stack_Expression_Evaluation_Presentation.pptx

stack expression evaluation

1. Application of Stack in Expression Evaluation Presentation by: Your Name

2. Introduction • Expression evaluation is a key task in compilers, calculators, and interpreters. • Stack plays a vital role in handling operators and operands. • It helps evaluate expressions in different notations: - Infix (A + B) - Prefix (+ A B) - Postfix (A B +)

3. Why Use a Stack? • Provides LIFO (Last In, First Out) structure. • Useful for: - Managing operator precedence - Handling parentheses in infix expressions - Converting between notations - Evaluating postfix/prefix expressions efficiently

4. Expression Notations 1. Infix → Operators between operands (A + B) 2. Prefix → Operators before operands (+ A B) 3. Postfix → Operators after operands (A B +) 👉 Stack is essential for conversion & evaluation of these forms.

5. Infix to Postfix Conversion (using Stack) Algorithm: 1. Scan expression left to right 2. If operand → add to result 3. If operator → push to stack (consider precedence) 4. If '(' → push to stack 5. If ')' → pop until '(' 6. Pop remaining operators

6. Example: Infix to Postfix Expression: (A + B) * C Steps: - Infix: (A + B) * C - Postfix: A B + C * (Stack manages operators and parentheses)

7. Postfix Evaluation using Stack Algorithm: 1. Scan expression left to right 2. If operand → push to stack 3. If operator → pop operands, apply operator, push result 4. Final result = top of stack

8. Example: Postfix Evaluation Expression: A B + C * 1. Push A, Push B → '+' → A + B 2. Push C → '*' → (A + B) * C Result obtained from stack.

9. Real-Life Applications • Compilers: Parsing and evaluating arithmetic expressions • Calculators: Internal evaluation of user input • Expression Solvers: Used in interpreters and query engines

10. Conclusion • Stacks simplify expression evaluation • Handle operator precedence and parentheses effectively • Widely applied in compilers, interpreters, and calculators