Summary
Binary trees are everywhere in programming, even if you don't realize it. Your file system is a tree. HTML DOM is a tree. Organization charts are trees. Any time you have hierarchical data where each element has a parent and potentially children, you're working with tree structures. Understanding binary trees—where each node has at most two children—is fundamental to working with these structures effectively.
What makes binary trees interesting isn't just their structure, but how you navigate them. Tree traversal—the process of visiting each node in a specific order—determines what you can do with trees. Different traversal methods serve different purposes. Want to copy a directory structure? You need one type of traversal. Want to evaluate a mathematical expression? You need another. The structure is the same, but the order you visit nodes changes everything.
I've interviewed dozens of developers who could define what a binary tree is but struggled to explain when you'd use preorder versus postorder traversal. The theory is important, but understanding the practical applications makes the difference between knowing about trees and actually using them to solve problems.
This guide walks through binary trees from the ground up—what they are, why they matter, and how different traversal methods work. We'll focus on the intuition behind each approach, not just the mechanics, so you can recognize when to reach for these tools in your own work.
What Makes a Binary Tree
A binary tree is a data structure where each node has a value and references to up to two child nodes—conventionally called left and right. The top node is the root. Nodes with no children are leaves. It's a simple concept that models hierarchical relationships naturally.
Binary Search Trees (BSTs) add an ordering constraint: left children are smaller than their parent, right children are larger. This property makes BSTs incredibly efficient for searching—you can eliminate half the remaining tree with each comparison. That's why binary search trees power databases, implement sorted collections, and underpin countless algorithms.
But not all binary trees are search trees. Expression trees represent mathematical formulas. Parse trees represent code syntax. These trees don't need the ordering property—they just need the hierarchical structure to model relationships between elements.
Inorder Traversal: Left-Root-Right
Inorder traversal visits nodes in this sequence: left subtree, current node, right subtree. For binary search trees, this visits nodes in sorted order—smallest to largest. That's why it's called "inorder"—you visit elements in their sorted order.
The implementation is elegantly recursive. Visit the left subtree inorder, process the current node, then visit the right subtree inorder. The recursion handles all the backtracking for you. When you need sorted output from a BST, inorder traversal is your tool.
I use inorder traversal most often for validation—checking if a tree is actually a valid binary search tree. If inorder traversal produces sorted values, you have a valid BST. If not, something's wrong with your tree structure or insertion logic.
Preorder Traversal: Root-Left-Right
Preorder traversal visits the current node first, then the left subtree, then the right subtree. This might seem arbitrary, but it's perfect for creating copies of trees or serializing tree structures. You process parents before children, which is exactly what you need for reconstruction.
Think about copying a directory structure. You need to create each directory before you can create its subdirectories. That's preorder traversal—handle the parent, then handle the children. Expression trees use preorder traversal to generate prefix notation, where operators come before operands.
Preorder is also used in tree serialization. If you need to save a tree to disk or send it over a network, preorder traversal captures the structure in a way that's easy to reconstruct. Process the node, save its value, then recursively handle its children.
Postorder Traversal: Left-Right-Root
Postorder traversal processes children before parents—left subtree, right subtree, then the current node. This seems backwards until you realize when you need it: any time you can't process a parent until you've processed its children.
Deleting a tree uses postorder traversal. You can't delete a node until you've deleted its children, otherwise you lose references to those children. Evaluating expression trees uses postorder—you need the results of subexpressions before you can compute the parent operation. Calculating directory sizes uses postorder—you need to know the size of subdirectories before you can calculate a directory's total size.
The pattern is consistent: when child results feed into parent processing, you need postorder traversal. It's less common than inorder or preorder, but when you need it, nothing else works.
Level-Order Traversal: Breadth-First
Level-order traversal visits nodes level by level—all depth-0 nodes, then all depth-1 nodes, and so on. Unlike the other traversals, this isn't naturally recursive. You need a queue to track which nodes to visit next.
Level-order traversal is perfect when you care about distance from the root. Finding the shortest path in a tree? Level-order. Pretty-printing a tree structure? Level-order. Any problem where "closest to root" or "minimum depth" matters uses this approach.
Concluding Remarks
Binary trees aren't complicated data structures—they're just nodes with two pointers. What makes them powerful is choosing the right traversal method for your problem. Need sorted output from a BST? Inorder. Copying a structure? Preorder. Processing children before parents? Postorder. Working with distance from root? Level-order.
The key insight is that traversal order changes what you can accomplish. The same tree structure supports different operations just by changing how you visit nodes. That's why understanding traversals isn't just academic—it's practical knowledge that shapes how you approach hierarchical data in real systems.