Binary Trees

A binary tree is a special type of tree in which each node can have at most two children.

These children are usually called:

• The left child

• The right child

This may seem like a small restriction, but binary trees are one of the most important data structures in computer science.

Why binary trees are important

Binary trees are easier to study than general trees because every node follows the same simple rule: it can have zero, one, or two children. This regular structure makes them easier to understand, analyze, and work with. Because of this, binary trees are widely used in recursion, searching, sorting, and decision-making algorithms.

They also serve as the foundation for several essential data structures. Binary search trees organize values so they can be searched efficiently. Heaps use a binary tree structure to support priority queues. Expression trees represent formulas and programming language expressions.

Another reason binary trees are important is that many algorithms divide a problem into two smaller subproblems. The left and right subtrees provide a direct structural mapping for this decomposition. This is why binary trees are commonly used in algorithms, technical interviews, and real-world systems.

Example

Here’s a simple example of a binary tree:

In this tree, $10$ is the root. Its left child is $5$, and its right child is $15$. Node $5$ has two children, while Node $15$ has only one. This shows that a node in a binary tree may have ...