Binary Expression Tree
An Expression Tree is a strictly binary tree in which leaf nodes contain Operands and non-leaf nodes contain Operator root nodes contain the operator that is applied to result of left a and right sub trees. Once we obtain the Expression Tree for a particular expression its conversion into different notations (infix, prefix, and postfix) and evaluation become a matter of Traversing the Expression Tree. The following Figure shows an expression tree for above expression 2*3/(2-1)+5*(4-1)
Expression tree for 2*3/(2-1) +5* (4+1)
A binary expression tree does not contain parenthesis the reason for this is that for evaluating an expression using expression tree structure of tree itself decides order of the operations.
When we run pre-order traversal (visit root left child and then right child) on the Binary Expression Tree we get prefix notation of the expression similarly an post order traversal (visit left child right child and then root) will yield postfix notation, what will we get from an in-order traversal ( visit left child root and then right child) ? well for the expressions which do not contain parenthesis in order traversal will definitely give infix notation of expression but expressions whose infix form requires parenthesis to override conventional precedence of operators cannot be retrieved by simple in order traversal.
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