INFIX, PREFIX,

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INFIX, PREFIX, POSTFIXEXPRESSIONS

• Saurav Karmakar
• Spring 2007

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Infix Notation

• We usually write algebraic expressions like this
• a b
• This is called infix notation, because the
  operator () is inside the expression
• A problem is that we need parentheses or
  precedence rules to handle more complicated
  expressions
• For Example
• a b c (a b) c ?
• a (b c) ?

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Infix, Postfix, Prefix notation

• There is no reason we cant place the operator
  somewhere else.
• How ?
• Infix notation a b
• Prefix notation a b
• Postfix notation a b

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Other Names

• Prefix notation was introduced by the Polish
  logician Lukasiewicz, and is sometimes called
  Polish notation.
• Postfix notation is sometimes called reverse
  Polish notation or RPN.

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Why ?

• Question Why would anyone ever want to use
  anything so unnatural, when infix seems to work
  just fine?
• Answer With postfix and prefix notations,
  parentheses are no longer needed!

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Example

• infix postfix prefix
• (a b) c a b c a b c
• a (b c) a b c a b c
• Infix form ltidentifiergt ltoperatorgt ltidentifiergt
• Postfix form ltidentifiergt ltidentifiergt
  ltoperatorgt
• Prefix form ltoperatorgt ltidentifiergt ltidentifiergt

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Convert from Infix to Prefix and Postfix
(Practice)

• x
• x y
• (x y) - z
• w ((x y) - z)
• (2 a) / ((a b) (a - c))

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Convert from Postfix to Infix (Practice)

• 3 r -
• 1 3 r -
• s t 1 3 r -
• v w x y z -