Posted by :
Shubham Pandey
Friday, February 5

## Polish notation

The grate polish mathematician came up with a new technique for representation and calculation of arithmetic expression where operator will be before or after the operand called polish notation.Normal expression A+B

Prefix +AB

Postfix AB+

Infix A+N

#### Example questions --

convert the following expression to prefix & postfix{[(A+B)/C] *(D-E)}

#### Prefix

We have to solve above expression according to the priory of operatorsFirst we solve the brackets

#### ={[(+AB)/C]*(-DE)}

#### ={[/+ABC]*(-DE)}

#### ={*/+ABC-DE}

Prefix expression is */+ABC-DE

#### Postfix

#### ={[(AB+)/C]*(DE-)}

#### ={[AB+C/]*(DE-)}

#### ={AB+CD/DE-*}

#### =AB+CD/DE-*

postfix expression is AB+CD/DE-*

#### Algorithms for converting infix to postfix using stack

- Add a unique symbol # into stack and add it in the end of array infix. A*(B+C^D)-E^F #
- Scan the symbol of array infix one by one from left to right.
- Symbol is left parenthesis '(' then add it to the array.
- Symbol is operand then add it to array postfix.
- Symbol is operator then pop the operator which have same priority or higher priority then operator which occurred .
- Add the pop operator to array.
- Add the scaned symbole into stack.
- Symbol is right parenthesis ')' then pop all the operator from the stack.
- Symbol is # then pop all the symbol from stack & add them to array except #.
- You ave done it .

#### For example .

Infix expression is A*(B+C^D)-E^F

A*(B+C^D)-E^F #

Symbole | Stack | Postfix expression |

A | A | |

* | * | A |

( | *( | A |

B | *(+ | AB |

+ | *(+ | AB |

C | *(+ | ABC |

^ | *(+^ | ABC |

D | *(+^ | ABCD |

) | * | ABCD^+ |

- | - | ABCD^+* |

E | - | ABCD^+*E |

^ | -^ | ABCD^+*E |

F | -^ | ABCD^+*EF |

* | -* | ABCD^+*EF^ |

( | -*( | ABCD^+*EF^ |

G | -*( | ABCD^+*EF^G |

/ | -*(/ | ABCD^+*EF^G |

H | -*(/ | ABCD^+*EF^GH |

) | -* | ABCD^+*EF^GH/ |

# | ABCD^+*EF^GH/*- |

#### We would like an interactive session. Comment your question below.

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## Cheers !!

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