Reverse Polish Expressions Some general observations about what they are and how they relate to infix expressions. These 9 slides provide details about exactly what operations are performed on stacks to both evaluate RPN expressions (which you DO NOT have to do in lab - but should know about), and transform infix expressions to postfix (which you DO have to do for lab).

Postfix notation Given the standard infix notation: 7*5-3 The RPN expression is: 75*3- We made it like this by placing operators last (after the operands)

Evaluating RPN expressions RPN expressions are best evaluated using a stack. Stacks are LIFO (last in first out)

Evaluation example Expression: 7 5 * empty top pop 7*5 35 pop push 35 3 push 35-3 pop push 32 pop 010 push

Operator placement It makes a big difference how operators are placed: 7*5-3 = 32 RPN: 75*3- = 32 RPN: 753*- = -8 same as infix 7-(5*3) RPN: 75-3* = 6 same as infix (7-5)*3

Converting infix expressions To convert an infix expression to a postfix expression means building a stack of operators. The operators have priority levels highest: */, next highest: +-, lowest (

Converting infix to postfix Expression: 7 * empty top -1 ** 00,-1 pop - check priority push - 3 pop -1,00 push 75 * -

Another example: 6*7*8*9-3 Expression: 6*7*8*9-3 empty top 0 ** 12 pop * check priority push * pop 210 push 6789***3- *** * * pop * * * - 0

Things to notice In the previous example, the subtraction operator could not be pushed on to the stack until all operators of higher priority had been popped off. THE END