Applications of stack: There are a number of applications of stacks such as;

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1 The Infix, Prefix, Postfix Notation: pplications of stack: There are a number of applications of stacks such as; To print charactersstring in reverse order. Check the parentheses in the expression. To evaluate the arithmetic expressions such as, infix, prefix and postfix. rithmetic expression: n expression is defined as a number of operands or data items combined using several operators. There are basically three types of notations for an expression; Infix notation Prefix notation Postfix notation Infix notation: It is most common notation in which, the operator is written or placed inbetween the two operands. or eg. The expression to add two numbers and B is written in infix notation as, B Operands Operator In this example, the operator is placed inbetween the operands and B. The reason why this notation is called infix. Prefix Notation: It is also called Polish notation, named after in the honor of the mathematician Jan Lukasiewicz, refers to the notation in which the operator is placed before the operand as, B s the operator is placed before the operands and B, this notation is called prefix pre means before. Postfix Notation: In the postfix notation the operators are written after the operands, so it is called the postfix notation post means after, it is also known as suffix notation or reverse polish notation. The above postfix if written in postfix notation looks like follows; B By: Surya Bam Page

2 Notation Conversions: Let us take an expression BC which is given in infix notation. To evaluate this expression for values,, for, B, C respectively we must follow certain rule in order to have right result. or eg. BC = = =!!!!!!!! Is this the right result? No, this is because the multiplication is to be done before addition, because it has higher precedence over addition. This means that for an expression to be calculated we must have the knowledge of precedence of operators. Operator Precedence: Operator Symbol Precedence Exponential $ Highest MultiplicationDivision, Next highest dditionsubstraction, Lowest Conversion from infix to postfix expression: lgorithm POSTIX Q, P Suppose Q is an arithmetic expression written in infix notation. This algorithm finds the equivalent postfix expression P. Step: Push onto STCK and add to the end of Q. Step: Scan Q from left to right and repeat step to for each element of Q, until the STCK is empty. Step: If an operand is encountered, push it to STCK. Step: If a left parenthesis is encountered, push it to STCK. Step: If an operator X is encountered, then a Repeatedly pop from STCK and add to P each operator Top of Stack which has same precedence as or higher precedence than X. b dd X to STCK. Step: If a right parentheses is encountered, then; a Repeatedly pop from STCK and add to P each operator top of stack until a left parentheses is encountered. b Remove the left parentheses from stack [Do not add it to P] By: Surya Bam Page

3 [End of if] [End of step loop]. Step: Exit. Note: In the Infix to postfix conversion expression algorithm x means any mathematical operator such as,,,,$. Example: BCD$E. S.N. Symbol Scan STCK P Postfix Expression B C D $ E $ $ B B B BC BC BCD BCD BCDE BCDE$ BCDE$ Required postfix expression P = BCDE$ Evaluating a postfix expression: lgorithm for evaluating postfix expression: Let P is an expression written in postfix notation. STCK=empty stack. Scan P from left to right and repeat step and for each symbol in P until end of expression. If an operand is encountered, push it on STCK. If an operator x encountered then; a Operand = pop STCK. b Operand = pop STCK. c Value= operand x operand. By: Surya Bam Page

4 d Push value on STCK. Return the value at top of the STCK. Exit. Tracing of algorithm P= 8$ S.N. Symbol Scan Operand Operand Value STCK $ 8 9 9,,,,,,,8,,8,,,,, 9 9, Conversion from Infix to Prefix: lgorithm for Infix to prefix: Step : Scan character at a time from right to left. Step : Repeat until there is data. a If Push into opstack. b If operand push into prestack. c If operator if stack is empty push it into opstack. Else repeat while prece tos char >= prece scan char and push to prestack. pop and push to prestack. push scanchar to opstack. By: Surya Bam Page

5 d if found pop and push to prestack until the matching is found and ignore cancel both. Step : pop and push to prestack until stack is empty. Step : pop and display from prestack until stack is empty. Example; BCDE S.N. Scan symbol Prefix stack Opstack E D C B E E ED ED ED ED ED ED EDC EDC EDCB EDCB EDCB EDCB EDCB EDCB Hence, the required prefix expression is BCDE Evaluation of prefix expression: lgorithm Read prefix string from right to left until there is a data. Repeat; If char is operand add to prestack If char is operator operand = pop prestack. By: Surya Bam Page

6 operand = pop prestack. result= value after applying operator between operand and operand. push the result into prestack. pop prestack get required value. Tracing $ S.N. Scan Symbol Operand Operand Value Prestack $,,,,,,,,,,,,,,,,,,,,,, Homework Q. Convert the following infix expression into postfix expression. BC BC$E BCD$E Q. Evaluate the following postfix expressions BCBC$ BCCB Where, =, B=, C=. Q. Convert the following infix expression into prefix expression. B$CD BCDE$G BCD By: Surya Bam Page

7 Q. Evaluate the following prefix expression a $BCD b BCDE where, =, B=, C=, D=, E=, = By: Surya Bam Page