Binary trees trip up a lot of students — not because the ideas are deep, but because textbooks bury the logic under dense theory before you ever see a clear example. This guide cuts straight to what you need.

**Binary Trees & Binary Search Trees** covers the full arc of the topic: what a tree is and why it beats a plain linked list for certain problems, how to walk every node using pre-order, in-order, post-order, and level-order traversals, and how the BST property turns a tree into a fast lookup structure. From there it walks through the three core BST operations — search, insert, and delete — tracing each algorithm step by step, including the three deletion cases and the in-order successor trick that always confuses students. The final section explains why balance is the difference between O(log n) performance and an O(n) disaster, and previews self-balancing trees so you know where the subject goes next.

This is a data structures study guide built for high school students in AP Computer Science and early college CS1 or CS2 courses. It is short by design: no filler, no padding, just the concepts, the vocabulary, worked traces, and the intuition you need to walk into an exam with confidence.

If BST insert, delete, and traversal are on your next test, start here.

• 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

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.