This document discusses data structures and the evaluation of arithmetic expressions. It covers topics like operands, operators, infix, prefix, and postfix notation. Evaluation of expressions involves understanding operator precedence and using the order of operations. Expressions can be converted between infix, prefix, and postfix notation using stacks. Parentheses are also addressed for infix expressions.

1. Chapter 5-1
Data Structures
Assoc. Prof. Dr. Oğuz FINDIK
2016-2017
KBUZEM
KARABUK UNIVERSITY
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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.
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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
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Evaluation of Expressions

4.  Prefix (Polish Notation)
 <operator><operand><operand>
 İnfix prefix
 4+5 +45
 p/q /pq
 a*b+c +*abc
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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+
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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-
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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]
}
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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.
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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;
}
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Infix to postfix

10.  ((A+B)*C-D)*E
 A+(B*C)
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Infix With parentheses to Postfix