Conversion of Infix to Prefix and Postfix with Stack
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The document discusses different notations for mathematical expressions - infix, prefix, and postfix. It explains that infix notation places the operator between operands, prefix puts the operator before operands, and postfix places it after. The document also covers converting between notations using a stack and explains operator precedence with parentheses having highest and addition/subtraction lowest precedence. Examples are given of converting infix expressions to postfix and prefix using a stack.
Conversion of Infix to Prefix and Postfix with Stack
- 1. Conversion of Infix to Prefix and Postfix with Stack
- 2. Infix Notation To add A, B, we write A+B To multiply A, B, we write A*B The operators ('+' ,'*‘ and many more) go in between the operands ('A' and 'B') This is "Infix" notation.
- 3. Prefix Notation Instead of saying "A plus B", we could say "add A,B " and write + A B "Multiply A,B" would be written * A B The operators ('+' ,'*‘ and many more) go in front of the operands ('A' and 'B') This is “Prefix” notation.
- 4. Postfix Notation Another alternative is to put the operators after the operands as in “AB +” and “AB *” The operators ('+' ,’*‘ and many more) go in end of the operands ('A' and 'B') This is “Postfix“ notation.
- 5. Priority/Precedence of Arithmetic Operators:- Highest Precedence ( ) , î or ^. Mid Precedence * , / . Lowest Precedence + , - .
- 6. Conversion of Infix to Postfix with stack A+B*C Symbol Stack Postfix A Empty A + + A B + AB * +* AB C +* ABC + ABC* Empty ABC*+
- 7. (A+B)*C Symbol Stack Postfix ( ( Empty A ( A + (+ A B (+ AB ) Empty AB+ * * AB+ C * AB+C AB+C*
- 8. Conversion of Infix to Prefix with stack (A*B+C)=(C+B*A) Symbol Stack Postfix ( ( Empty C ( C + (+ C B (+ CB * (+* CB A (+* CBA ) (+*) CBA*+ Prefix=+*ABC
- 9. (A/B^C+D) = (D+C^B/A) Symbol Stack Postfix ( ( Empty D ( D + (+ D C (+ DC ^ (+^ DC B (+^ DCB / (+/ DCB^ A (+/ DCB^A ) (+/) DCB^A/+ Prefix:- +/A^BCD