Binary Expression Tree Example

Binary expression tree example.

A binary expression tree represents an arithmetic expression as operators and operands. Every operator has two children, and each leaf is a value or variable. The top node is the operation performed last, so the tree preserves grouping and precedence without relying on a line of text. This example is useful for explaining parsers, compiler coursework and recursive evaluation. To evaluate the tree, calculate the left and right subtrees first, then apply the operator at their parent node.

Type OrganigrammeNorme Reingold-Tilford tidy treeMoteur schematex-orgchartMis à jour 24/09/2026

La demande

“Create a binary expression tree for (a × b) + (c − (d ÷ (e + f))), with + as the root, × on the left and − on the right.”

Essayez ensuiteChange the right expression to c ÷ d.Add parentheses around the full expression in the title.

Ce que contient ce dessin

Comprenez les décisions qui le sous-tendent.

01Operator root

Put the outermost addition at the root.

02Binary operands

Give every operator a left and right child.

03Precedence

Group multiplication and subtraction before addition.

Use this tree to explain parsing and expression evaluation.

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FAQ

Questions fréquentes

What are the leaves in an expression tree?

Leaves are operands such as numbers, variables or constants.

Why use a binary tree for an expression?

Binary operators naturally have a left operand and a right operand.

How is the root chosen?

It is the outermost operation, performed after its two subexpressions.