![ 2*3+4*5-6=>23*45*+6- (postfix)
evaluatePostfix(exp){
create a Stack S
for i<-0 to length(exp)-1
{
if (exp[i] is operand)
push(exp[i])
else if (exp[i] is operator){
op2<-pop()
op1<-pop()
temp<perform(op1,op2,exp[i])
push(temp)
}
} return S[top]
}
7
Evaluation of Postfix with Stack](https://image.slidesharecdn.com/datastructureweeky5-1-171015115604/85/Data-structure-week-y-5-1-7-320.jpg)
![ A+B*C-D*E
InfixToPostfix(exp){
create a Stack S
String temp<-empty String
for i<-0 to length(exp)-1{
if exp[i] is operand
temp <-temp+exp[i]
else if exp[i] is operator
while(!S.empty()&&HasHigherPrecedence(s.top(),exp[i])){
temp <-temp + s.pop();
}
s.push(exp[i])
}
while(!s.empty()) temp<-temp+s.pop();
Return 1;
}
9
Infix to postfix](https://image.slidesharecdn.com/datastructureweeky5-1-171015115604/85/Data-structure-week-y-5-1-9-320.jpg)
Data structure week y 5 1
- 1. Chapter 5-1 Data Structures Assoc. Prof. Dr. Oğuz FINDIK 2016-2017 KBUZEM KARABUK UNIVERSITY 1
- 2. İf we look at the arithmetic expressions, we encounter operand, operator and parenthesis. 2+3 , (p*q), 2+5*6 For evaluting this expressions, we should parse and them calculate. <operand><operator><operand> (infix) Operand: Any object that operation is performed. Operator: In mathematics and sometimes in computer programming, an operator is a character that represents an action, as for example x is an arithmetic operator that represents multiplication. 2 Evaluation of Expressions
- 3. For example 2+3*5-1*4 To evaluate this expressions you should know precedence of operator. Order of operations 1. Parentheses {()} 2. Exponents 2^3^2 (right to left) 3. Multiplication and division (left to right) 4. Addition and subtraction (left to right) 2*6/3+5-2+8/4*2 3 Evaluation of Expressions
- 4. Prefix (Polish Notation) <operator><operand><operand> İnfix prefix 4+5 +45 p/q /pq a*b+c +*abc 4 Evaluation of Expressions
- 5. Postfix (Reverse Polish Notation) <operand><operand><operator> İnfix prefix postfix 4+5 +45 45+ p/q /pq pq/ a*b+c +*abc ab*c+ 5 Evaluation of Expressions
- 6. a*b+c*d-2 First step we should add parentheses {(a*b)+(c*d)}-2 Next step is that operator will place to end of expression {(ab*)+(cd*)}-2 {ab*cd*+}-2 ab*cd*+2- 6 Evaluation of prefix and postfix
- 7. 2*3+4*5-6=>23*45*+6- (postfix) evaluatePostfix(exp){ create a Stack S for i<-0 to length(exp)-1 { if (exp[i] is operand) push(exp[i]) else if (exp[i] is operator){ op2<-pop() op1<-pop() temp<perform(op1,op2,exp[i]) push(temp) } } return S[top] } 7 Evaluation of Postfix with Stack
- 8. 2*3+4*5-6=>-+*23*456 (prefix) This algorithm is same with postfix algorithm. But this algorithm starts from end of expression. 8 Evaluation of Prefix with Stack
- 9. A+B*C-D*E InfixToPostfix(exp){ create a Stack S String temp<-empty String for i<-0 to length(exp)-1{ if exp[i] is operand temp <-temp+exp[i] else if exp[i] is operator while(!S.empty()&&HasHigherPrecedence(s.top(),exp[i])){ temp <-temp + s.pop(); } s.push(exp[i]) } while(!s.empty()) temp<-temp+s.pop(); Return 1; } 9 Infix to postfix
- 10. ((A+B)*C-D)*E A+(B*C) 10 Infix With parentheses to Postfix