EXPRESSION TREE

 EXPRESSION TREE:

Expression Trees

Binary trees are widely used to store algebraic expressions. For example,

consider the algebraic expression given as:

The expression tree is a tree used to represent the various expressions. The tree data structure is used to represent the expressional statements. In this tree, the internal node always denotes the operators.

• The leaf nodes always denote the operands.
• The operations are always performed on these operands.
• The operator present in the depth of the tree is always at the highest priority.i.e least priority operator will on top.
• The operator, which is not much at the depth in the tree, is always at the lowest priority compared to the operators lying at the depth.
• The operand will always present at a depth of the tree; hence it is considered the highest priority among all the operators.

Associativity for operators

• ʌ (power)                                           : Right to Left
• * (multiplication), / (Divison)            :Left to Right
• - (sub), +(Add)                                   : Left to Right

Ex:  Exp = (a – b) + (c * d)

Ex: Given an expression, Exp = ((a + b) – (c * d)) % ((e ^f) / (g – h)), construct the corresponding binary tree.

Ex: Given the binary tree, write down the expression that it represents.

Expression for the above binary tree is 

                 [{(a/b) + (c*d)} ^ {(f % g)/(h – i)}]

solve the expression  a*b /c + e/f  * g + k - x * y