Team 4
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The document discusses stack applications for conversion and evaluation of expressions. It describes stacks, different types of expressions (infix, postfix, prefix), and algorithms for converting between these types. Examples are provided to demonstrate converting an infix expression to postfix and evaluating a postfix expression step-by-step using a stack. The postfix expression p=abc*/d+ is evaluated, with the steps shown and final result of 3.4.
Team 4
- 1. DATA STRUCTURES STACK APPLICATIONS By Shanthi.S Saradhaswathi.G Thangapriyaa.V.B Sriram.N Ramesh.R Poornachandran.R
- 2. Conversion And Evaluation of Expressions Group - 4
- 3. Conversion And Evaluation of Expressions • Stack A Stack is an ordered list in which all insertions and deletions are made at one end called Top.
- 4. Expressions Expression is a string of operands and operators. Operands are some numeric values and operators are of two types : Unary operators such as ‘+’ and ‘-’. Binary operators such as ‘+’, ‘-’, ‘*’, ‘/’ and exponential.
- 5. Types of Expressions • Infix Expressions • Postfix Expressions • Prefix Expressions
- 6. Infix Expressions • Parenthesis can be used in these expressions. • Infix expressions are the most natural way of representing expressions. Infix expression = Operand1 operator Operand2 Examples: 1) (a+b) 2) (a+b)*(c-d) 3) a+b/c)*(d+f)
- 7. Postfix Expression In postfix expression, there are no parenthesis used. All the corresponding operands come first and then operator can be placed. Postfix Expression = Operand1 operand2 operator Examples: 1) ab+ 2) ab+cd- 3) ab+c/df+*
- 8. Prefix Expression In prefix expression, there are no parentheses used. All the corresponding operators come first and then the operands are arranged. Prefix Expression = Operator Operand1 Operand2 Examples: 1) +ab 2) *+ab-cd 3) */+abc+df
- 9. Conversion of Infix to Postfix Expressions: Eg.: ((a-b)*(a+b)) S.No Input Character Stack Postfix Expressions 1. ( ( 2. ( (( 3. a (( a 4. - ((- a 5. b ((- ab 6. ) ( ab- 7. * (* ab- 8. ( (*( ab- 9. a (*( ab-a 10. + (*(+ ab-a 11. b (*(+ ab-ab 12. ) (* ab-ab+ 13. ) Empty ab-ab+* The postfix expression is ab-ab+*
- 10. Conversion of Postfix to Prefix: Eg.:ABCDE/*-F/G++ Prefix = Operator Operand1 Operand2 Step1: ABCDE/*-F/G++ Step2: ABC(/DE)*-F/G++ Step3: AB(*C/DE)-F/G++ Step4: A(-B*C/DE)F/G++ Step5: A(/-B*C/DEF)G++ Step6: A(+/-B*C/DEFG)+ Step7: +A+/-B*C/DEFG +A+/-B*C/DEFG is the prefix expression.
- 11. Conversion of Postfix to Infix form: Eg.:ABC(DE/*-F/G++ Infix = Operand1 Operator Operand2 Step1: ABCDE/*-F/G++ Step2: ABC/DE*-F/G++ Step3: AB(C*(D/E)-F/G++ Step4: A(-B(C*D/E)))F/G++ Step5: A(((B-(C(D/E)))/F)G++ Step6: A(((B-(C(D/E))/F+G)+ Step7: (A+(B-(C*(D/E)))/F)+G)) (A+(B-(C*(D/E)))/F)+G)) is the infix expression.
- 12. Evaluation of Expressions Algorithm: Add the right paranthesis. Scan the expressions from left to right of each element until the closed parenthesis is encountered. If operand is encountered, then Push to Stack. If operator is encountered, then next two elements from Stack is Poped. Evaluate the expression with the operator . E.g.(b*c). Set the result to the Top of the Stack. Exit.
- 13. Evaluation of Postfix expression p=abc*/d+ Assume a=50, b=10, c=7, d=0 Steps Symbols Scanned Stack 1. ( 2. 50{a} (,50 3. 10{b} (,50,10 4. 7{c} (,50,10,7 5. * (,50,70 6. / (,1.4 7. 2{d} (,1.4,2 8. + (,3.4 9. ) 3.4