Reverse polish notation, Operations with big numbers Ivelin Rachev Telerik Corporation “Baba Tonka” High School of Mathematics

1. Priority of Operations  Left and Right associatively 2. Reverse Polish notation  Getting reverse polish notation  Calculating reverse polish notation 3. Big Numbers  Comparing  Adding  Subtracting  Multiplying 2

Solve the equations!

 Operations have strict priority Functions “(“ and “)” “*” and “/” “+” and “–”

LEFT ASSOCIATIVE The left operation takes priority! 7-3+2=(7-3)+2=6 5 When operations have the same priority it matters whether they are left or right associative RIGHT ASSOCIATIVE The right operation takes priority! 7-3+2=7-(3+2)=2

6 Equation written in reverse polish notation has the operations, functions etc. written after the operands. (suffixed) There are no “(“ and “)” in Reverse Polish notation! 5+3*(2-1)-1*4 → * * - Infixed Suffixed

 Add a zero before each empirical operator.  While there are symbols to be read:  Read a symbol  If it is a number add it to the stack  If it is an operator:  While the top operator of the stack has lower priority to the current operator or it is left associated and has the same or lower priority pop it out of the stack and add it the suffixed equation.  Push the current operator into the stack.  If it is a left parenthesis put it in the stack. 7

 If it is a right parenthesis:  Until the token at the top of the stack is a left parenthesis, pop operators off the stack onto the suffixed equation.  Pop the left parenthesis from the stack, but not onto the suffixed equation.  If the stack runs out without finding a left parenthesis, then there are mismatched parentheses 8

 When there are no more symbols to read:  While there are still operator tokens in the stack:  If the operator token on the top of the stack is a parenthesis, then there are mismatched parentheses.  Pop the operator onto the suffixed equation. 9

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 Read through the suffixed equation:  When you reach an  When you reach an operation do it using the values in your stack and push the answer back in the stack  The only remaining value in your stack is your answer to the equation. 11

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How to?

 Big Numbers are usually represented using a data structure and an logical variable for signed big numbers.

 Criteria in comparing big numbers:  By positivity and negativity.  By Length.  By each individual digit.  Note that negative numbers are ordered in reverse order by absolute value. 15

16  We fallow the same steps as in real life when we add and extract. The maximum that can be transferred is 1.  Multiplying is just adding numbers and moving them rightwards

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