Arithmetic expression INFIX TO POSTFIX CONVERTION saraswathi ramalingam
Download as PPTX, PDF1 like78 views
The document explains the conversion of arithmetic expressions from infix notation to postfix notation. It details the classification of expressions, the use of a stack for conversion, and provides step-by-step procedures with examples. Key components include handling operators and parentheses while reading the infix expression and building the resulting postfix expression.
Arithmetic expression INFIX TO POSTFIX CONVERTION saraswathi ramalingam
- 1. Arithmetic Expression – INFIX TO POSTFIX SARASWATHI RAMALINGAM SRI AKILANDESWARI WOMENS COLLEGE – WANDIWASH.
- 2. Arithmetic Expression • Arithmetic Expression contains – Operators (+,-,*,/,%,() ) – Operands (a..z) – Ex:- (a*b),(a+b)-c
- 3. Classification of Expression – Depending upon the position of the operators with respect to the position of the operands. – Infix – Prefix – Postfix
- 4. Classification of Expression INFIX PREFIX POSTFIX Operator In between the operands Operator before the operands Operator after the operands Infix notation Prefix notation(Polish notation) Postfix notation(Reverse Polish notation) A+B +AB AB+ A+B*C +A*BC ABC*+ (A+B)*(C-D) *+AB-CD AB+CD-*
- 5. INFIX TO POSTFIX • Conversion of Expression • Evaluation of Postfix Expression
- 6. Conversion of Expression • Steps – Initialize an empty stack. – Read the token from Infix string one at a time from left to right.
- 7. Conversion of Expression – If the scanned character is an operand add it to the Postfix string. – If the scanned character is an operator • if the stack is empty push the character to stack. • If the stack is not empty, compare the precedence of the character with element on top of the stack.
- 8. Conversion of Expression – If the character is a left parentheses, push it on to the stack. – If the character is a right parentheses, • Repeatedly pop the stack and add popped out element in to the string until a left parentheses is encountered. • Remove the left parentheses from the stack and ignore it.
- 9. Conversion of Expression • When top Stack has higher precedence over the scanned character pop the stack else push the scanned character to stack. – (Repeat the step until the operator in the stack has higher precedence than the scanned character) • After all the characters are read and the stack is not empty then pop the stack and add the string.
- 10. Example A+B 1. SYMBOL SCANNED STACK POSTFIX EXPRESSION A A
- 11. 2 SYMBOL SCANNED STACK POSTFIX EXPRESSION A A + + A
- 12. 3 SYMBOL SCANNED STACK POSTFIX EXPRESSION A A + + A B + AB AB+
- 13. Example A+B*C 1. SYMBOL SCANNED STACK POSTFIX EXPRESSION A A
- 14. 2 SYMBOL SCANNED STACK POSTFIX EXPRESSION A A + + A
- 15. 3 SYMBOL SCANNED STACK POSTFIX EXPRESSION A A + + A B + AB
- 16. 4 SYMBOL SCANNED STACK POSTFIX EXPRESSION A A + + A B + AB * +* AB
- 17. 5 SYMBOL SCANNED STACK POSTFIX EXPRESSION A A + + A B + AB * +* AB C +* ABC ABC*+