Unit I - Evaluation of expression

Evalauation of Expression, Infix, Postfix Expression

1. Evaluation of Expression Dr. R. Khanchana Assistant Professor Department of Computer Science Sri Ramakrishna College of Arts and Science for Women

2. Evaluation of Expression An expression is made up of operands, operators and delimiters.  Operands - A,B,C,D,E ( these are all one letter variables) Operators **,+,*,-, /, = A  = 4,  B  =  C  = 2,  D  =  E  = 3 Output ?

3. Evaluation of Expression

4. Basic Operator Types Basic arithmetic operators: Plus, minus, times, divide, and exponentiation (+,-,*,/,**) Other arithmetic operators Unary plus, unary minus and  mod, ceil , and  floor . Relational operators Relational operators is one of the two constants:  true  or  false ( Boolean)

5. Priority of arithmetic, Boolean and relational operators

6. Precedence of Operator Operator Associativity (),{},[] ^ - Right to Left * / - Left to Right + - - Left to Right

7. Order of Evaluation Scenario 1 A  = 4,  B  =  C  = 2,  D  =  E  = 3, 4/(2 ** 2) + (3 * 3) - (4 * 2) = (4/4) + 9 - 8 = 2. Scenario 2 (4/2) ** (2 + 3) * (3 - 4) * 2 = (4/2) ** 5* -1 * 2 = (2**5)* -2 = 32* -2 = -64.

8. Infix & Postfix Notation If  e  is an expression with operators and operands, the conventional way of writing  e  is called  infix , because the operators come  in- between the operands. The  postfix  form of an expression calls for each operator to appear  after  its operands. Example Infix:  A * B/C   Postfix:  AB  *  C /

9. Infix to Postfix Conversion  It is simple to describe an algorithm for producing postfix from infix: 1) Fully parenthesize the expression 2) Move all operators so that they replace their corresponding right parentheses 3) Delete all parentheses. Example : A/B  **  C  +  D  *  E  -  A  *  C   when fully parenthesized yields The arrows point from an operator to its corresponding right parenthesis. Performing steps 2 and 3 gives ABC  ** /  DE  * +  AC  * -

10. Infix & Postfix Expression Infix:  A / B  **  C  +  D  *  E  -  A  *  C Postfix:  ABC  ** / DE  * +  AC  * - Operation Postfix --------- ------- T 1 = B **C AT 1 /DE * + AC * - T 2 = A/T 1 T 2 DE * + AC * - T 3 = D * E T 2 T 3 + AC * - T 4 = T 2 + T 3 T 4 AC * - T 5 = A * C T 4 T 5 - T 6 = T 4 - T 5 T 6

11. Steps for Postfix Expression Using Stack Start reading from left to right and push the operands into the stack If an operator occurs pop the last two operands from stack and then perform the repeated operation (Operand 2) Operator (Operand 1) Example 23*51/+ Pop 3 and 2 Push (2*3) Pop 5 and 1 Push (5/1) Push (6 +5)

12. Procedure -Expression Evaluation

13. STACK Implementation A  +  B  *  C  to yield  ABC  * + our algorithm should perform the following sequence of stacking

14. STACK Implementation Animated Video https://www.youtube.com/watch?v=TeM6DdvSxvQ

15. Assignment Another example,  A  * ( B  +  C ) *  D  has the postfix form  ABC  + *  D  *

16. Assignment Results A  * ( B  +  C ) * 

17. Priorities of Operators for Producing Postfix

18. Postfix conversion with Stack EXAMPLE 1

19. Postfix conversion with Stack EXAMPLE 2 - - -

20. Postfix conversion with Stack ( A+B)*C – (D*E) Ch Stack Postfix Expression ( ( A A + + A ( B + AB ( ) ) AB+ + ( * * AB+ C * AB+ - - AB+* Ch Stack Postfix Expression ( ( AB+* - D ( AB+*D _ * * AB+*D ( - E * AB+* DE ( - ) ) AB+*DE*- * ( _ EXAMPLE Vs Assignment

21. Procedure Postfix

22. Quiz https://quizizz.com/admin/quiz/5f14103a219aa5001b718cf1