Expression Trees

Expression trees are a type of binary tree used to represent arithmetic expressions. In an expression tree, each node represents an operator or operand, and the tree's structure reflects the order of operations within the expression. These trees provide a structured way to evaluate and manipulate arithmetic expressions.

Node Structure

In an expression tree, each node can be either an operator or an operand. The operator nodes represent arithmetic operations such as addition, subtraction, multiplication, and division. The operand nodes represent the numeric values or variables in the expression.

The node structure typically contains three fields:

Value/Label: The value or label associated with the node. For operator nodes, this represents the operator symbol (+, -, *, /). For operand nodes, it represents the numeric value or variable name.
Left Child: A reference to the left child node, which represents the left operand or subexpression.
Right Child: A reference to the right child node, which represents the right operand or subexpression.

for example the tree for the infix notation would be:

expression tree.svg

Constructing an Expression Tree

To construct an expression tree from an arithmetic expression, we typically use one of two approaches: prefix notation (also known as Polish notation) or postfix notation (also known as Reverse Polish notation).