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Computer Science

Binary Trees and Binary Search Trees

A High School & College Primer

You have a data structures exam coming up, or your CS class just hit trees and suddenly nothing makes sense. Binary trees look simple in a diagram and then fall apart the moment you try to write an insert function or explain why deletion has three cases. This guide exists to fix that — fast.

**TLDR: Binary Trees and Binary Search Trees** covers everything a high school or early-college student needs to walk into an AP Computer Science class, a first data structures course, or a coding interview prep session with real confidence. You will learn how a binary tree is structured and why it beats arrays for certain problems, how to trace pre-order, in-order, post-order, and level-order traversals step by step, what the BST property is and why it makes searching fast, and exactly how search, insert, and delete work — including the tricky three-case deletion and the in-order successor. The final section explains why a BST study guide for data structures students has to talk about balance: an unbalanced tree quietly turns your O(log n) lookups into O(n) crawls.

The book is short on purpose. Each section leads with the one thing you need to know, backs it with worked examples and real code, and calls out the misconceptions students get wrong most often. No filler, no padding, no 400-page textbook weight.

If you need to understand binary trees and BSTs clearly and quickly, pick this up and start reading today.

What you'll learn
  • Define a binary tree and a binary search tree, and distinguish the two
  • Identify and use core terminology: root, leaf, height, depth, subtree, parent, child
  • Perform pre-order, in-order, post-order, and level-order traversals by hand
  • Implement and trace search, insert, and delete operations on a BST
  • Reason about why BST operations are O(log n) when balanced and O(n) when skewed
  • Recognize when a balanced tree (like an AVL or red-black tree) is needed
What's inside
  1. 1. What Is a Binary Tree?
    Introduces the binary tree data structure, its vocabulary, and how it differs from arrays and linked lists.
  2. 2. Tree Traversals: Visiting Every Node
    Walks through pre-order, in-order, post-order, and level-order traversals with recursive code and worked examples.
  3. 3. From Binary Tree to Binary Search Tree
    Defines the BST property and explains how ordering turns a tree into a fast lookup structure.
  4. 4. BST Operations: Search, Insert, Delete
    Covers the three core BST algorithms with traces, including the three cases of deletion and the in-order successor.
  5. 5. Why Balance Matters: Big-O and Skewed Trees
    Explains why BST operations are O(log n) when balanced and O(n) when skewed, and previews self-balancing trees.
Published by Solid State Press
Binary Trees and Binary Search Trees cover
TLDR STUDY GUIDES

Binary Trees and Binary Search Trees

A High School & College Primer
Solid State Press

Binary Trees and Binary Search Trees

A High School & College Primer

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you're a high school student working through an AP Computer Science course and drowning in data structures, a college freshman in your first data structures course looking for a short primer that cuts to the essentials, or a self-taught programmer who needs binary search trees explained for beginners without the textbook bloat — this guide is for you.

This data structures study guide for high school and early college covers everything you need: what a binary tree is and how nodes connect, tree traversal in inorder, preorder, and postorder order, and every core BST insert, delete, and search operation with worked examples. It closes with a binary tree big-O complexity breakdown so you understand exactly when a BST is fast and when it falls apart. About 15 pages, no filler.

Read it straight through once, then go back and work each example yourself before you check the solution. Finish with the practice problems at the end to confirm you've got it.

Contents

  1. 1 What Is a Binary Tree?
  2. 2 Tree Traversals: Visiting Every Node
  3. 3 From Binary Tree to Binary Search Tree
  4. 4 BST Operations: Search, Insert, Delete
  5. 5 Why Balance Matters: Big-O and Skewed Trees
Chapter 1

What Is a Binary Tree?

A node is the fundamental building block: a container that holds a value and links to other nodes. In a binary tree, each node holds at most two links — one to a left child and one to a right child. That two-link constraint is the entire structural rule. Everything else flows from it.

This is worth pausing on. An array stores data in a straight line, indexed by position. A linked list strings nodes together in a single chain — each node points to the next one only. A binary tree branches. From any node you can go two directions, and those two directions can each branch again, giving you a structure that fans out like an upside-down tree.

The vocabulary you need

Every binary tree has exactly one root: the node at the top, the one with no node above it. Every other node is reachable from the root by following child links downward. If node A links to node B, then A is the parent of B, and B is a child of A. A node can have zero, one, or two children — but never more than two (that's what makes it binary).

A node with zero children is called a leaf. It's a dead end. A node with one or two children is an internal node.

The connection between a parent and a child is called an edge. Edges are the links themselves — in most diagrams and code, they show up as arrows or pointers. A tree with $n$ nodes always has exactly $n - 1$ edges. (You can convince yourself of this: every node except the root has exactly one parent, so there's one edge per non-root node.)

A subtree is any node together with all the nodes below it. If you pick any node in a tree and mentally snip the edge connecting it to its parent, what's left hanging is a subtree. Subtrees matter because most tree algorithms are recursive: you solve a problem on the left subtree, solve it on the right subtree, then combine.

Depth measures how far a node is from the root. The root is at depth 0. Its children are at depth 1. Their children are at depth 2. In general, a node's depth equals the number of edges on the path from the root down to that node.

Keep reading

You've read the first half of Chapter 1. The complete book covers 5 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon