Expression evaluation
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This document discusses different notations for representing mathematical expressions: infix, prefix, and postfix. In infix notation, operators are placed between operands (e.g. A + B). In prefix notation, operators come before operands (e.g. + A B). In postfix notation, operators follow operands (e.g. A B +). It notes that infix notation requires parentheses to determine the order of operations, while prefix and postfix notations do not. The document then provides a step-by-step example of converting an infix expression to postfix notation using a stack.
![Infix to Postfix
( ( A + B ) * ( C - E ) ) / ( F + G ) )
stack: (
output: []](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-19-320.jpg)
![Infix to Postfix
( A + B ) * ( C - E ) ) / ( F + G ) )
stack: ( (
output: []](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-20-320.jpg)
![Infix to Postfix
A + B ) * ( C - E ) ) / ( F + G ) )
stack: ( ( (
output: []](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-22-320.jpg)
![Infix to Postfix
+ B ) * ( C - E ) ) / ( F + G ) )
stack: ( ( (
output: [A]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-24-320.jpg)
![Infix to Postfix
B ) * ( C - E ) ) / ( F + G ) )
stack: ( ( ( +
output: [A]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-26-320.jpg)
![Infix to Postfix
) * ( C - E ) ) / ( F + G ) )
stack: ( ( ( +
output: [A B]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-27-320.jpg)
![Infix to Postfix
* ( C - E ) ) / ( F + G ) )
stack: ( (
output: [A B + ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-29-320.jpg)
![Infix to Postfix
( C - E ) ) / ( F + G ) )
stack: ( ( *
output: [A B + ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-30-320.jpg)
![Infix to Postfix
C - E ) ) / ( F + G ) )
stack: ( ( * (
output: [A B + ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-31-320.jpg)
![Infix to Postfix
- E ) ) / ( F + G ) )
stack: ( ( * (
output: [A B + C ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-32-320.jpg)
![Infix to Postfix
E ) ) / ( F + G ) )
stack: ( ( * ( -
output: [A B + C ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-33-320.jpg)
![Infix to Postfix
) ) / ( F + G ) )
stack: ( ( * ( -
output: [A B + C E ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-34-320.jpg)
![Infix to Postfix
) / ( F + G ) )
stack: ( ( *
output: [A B + C E - ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-35-320.jpg)
![Infix to Postfix
/ ( F + G ) )
stack: (
output: [A B + C E - * ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-36-320.jpg)
![Infix to Postfix
( F + G ) )
stack: ( /
output: [A B + C E - * ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-37-320.jpg)
![Infix to Postfix
F + G ) )
stack: ( / (
output: [A B + C E - * ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-38-320.jpg)
![Infix to Postfix
+ G ) )
stack: ( / (
output: [A B + C E - * F ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-39-320.jpg)
![Infix to Postfix
G ) )
stack: ( / ( +
output: [A B + C E - * F ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-40-320.jpg)
![Infix to Postfix
) )
stack: ( / ( +
output: [A B + C E - * F G ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-41-320.jpg)
![Infix to Postfix
)
stack: ( /
output: [A B + C E - * F G + ]](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-42-320.jpg)
![Infix to Postfix
stack: <empty>
output: [A B + C E - * F G + / ]
Done!!!](https://image.slidesharecdn.com/expressionevaluation-150601112933-lva1-app6891/85/Expression-evaluation-43-320.jpg)
Expression evaluation
- 4. Content
- 6. Infix Notation To add A, B, we write A+B To multiply A, B, we write A*B The operators ('+' and '*') go in between the operands ('A' and 'B') This is "Infix" notation.
- 7. Prefix Notation Instead of saying "A plus B", we could say "add A,B " and write + A B "Multiply A,B" would be written * A B This is Prefix notation.
- 8. Postfix Notation Another alternative is to put the operators after the operands as in A B + and A B * This is Postfix notation.
- 9. The terms infix, prefix, and postfix tell us whether the operators go between, before, or after the operands.
- 10. Parentheses Evaluate 2+3*5. + First: (2+3)*5 = 5*5 = 25 * First: 2+(3*5) = 2+15 = 17 Infix notation requires Parentheses.
- 11. What about Prefix Notation? + 2 * 3 5 = = + 2 * 3 5 = + 2 15 = 17 * + 2 3 5 = = * + 2 3 5 = * 5 5 = 25 No parentheses needed!
- 12. Postfix Notation 2 3 5 * + = = 2 3 5 * + = 2 15 + = 17 2 3 + 5 * = = 2 3 + 5 * = 5 5 * = 25 No parentheses needed here either!
- 13. Conclusion: Infix is the only notation that requires parentheses.
- 14. Why all this At our level, we cannot evaluate an infix expression, but we can turn an infix evaluation into a prefix or postfix expression and then evaluate them.
- 15. What we did We took infix expression and turned them into postfix expression.
- 16. Simple way to convert Infix Postfix......
- 17. Now we want show how we can convert Infix to Postfix using stack.
- 18. Now we will see a little bit complex Example which contain parentheses.
- 19. Infix to Postfix ( ( A + B ) * ( C - E ) ) / ( F + G ) ) stack: ( output: []
- 20. Infix to Postfix ( A + B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( output: []
- 22. Infix to Postfix A + B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( output: []
- 24. Infix to Postfix + B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( output: [A]
- 26. Infix to Postfix B ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( + output: [A]
- 27. Infix to Postfix ) * ( C - E ) ) / ( F + G ) ) stack: ( ( ( + output: [A B]
- 29. Infix to Postfix * ( C - E ) ) / ( F + G ) ) stack: ( ( output: [A B + ]
- 30. Infix to Postfix ( C - E ) ) / ( F + G ) ) stack: ( ( * output: [A B + ]
- 31. Infix to Postfix C - E ) ) / ( F + G ) ) stack: ( ( * ( output: [A B + ]
- 32. Infix to Postfix - E ) ) / ( F + G ) ) stack: ( ( * ( output: [A B + C ]
- 33. Infix to Postfix E ) ) / ( F + G ) ) stack: ( ( * ( - output: [A B + C ]
- 34. Infix to Postfix ) ) / ( F + G ) ) stack: ( ( * ( - output: [A B + C E ]
- 35. Infix to Postfix ) / ( F + G ) ) stack: ( ( * output: [A B + C E - ]
- 36. Infix to Postfix / ( F + G ) ) stack: ( output: [A B + C E - * ]
- 37. Infix to Postfix ( F + G ) ) stack: ( / output: [A B + C E - * ]
- 38. Infix to Postfix F + G ) ) stack: ( / ( output: [A B + C E - * ]
- 39. Infix to Postfix + G ) ) stack: ( / ( output: [A B + C E - * F ]
- 40. Infix to Postfix G ) ) stack: ( / ( + output: [A B + C E - * F ]
- 41. Infix to Postfix ) ) stack: ( / ( + output: [A B + C E - * F G ]
- 42. Infix to Postfix ) stack: ( / output: [A B + C E - * F G + ]
- 43. Infix to Postfix stack: <empty> output: [A B + C E - * F G + / ] Done!!!
- 46. Thank’s to all THE END By Mahadi
Editor's Notes
- #9: &quot;A,B are multiplied&quot; &quot;A,B are added&quot;