A tree is a hierarchical data structure that consists of nodes connected by edges. Each tree has a root node at the top, and each node can have zero or more child nodes. Unlike graphs, trees have no cycles - there's exactly one path between any two nodes. Trees are everywhere in computer science: file systems, organization charts, decision-making algorithms, and even in how your browser displays this webpage (the DOM tree)!
Understanding these key terms is essential for working with trees:
The topmost node in the tree. It has no parent and is the starting point of the tree.
A node that has one or more child nodes connected below it.
A node that has a parent node connected above it.
A node with no children. These are the endpoints of the tree.
The distance (number of edges) from the root to a specific node.
The maximum depth of the tree - the longest path from root to any leaf.
A tree formed by a node and all its descendants.
Nodes that share the same parent.
There are three main ways to visit every node in a tree (using binary trees as an example):
Use: Gets values in sorted order for BST
Use: Copy tree, prefix expressions
Use: Delete tree, postfix expressions
Your computer organizes folders and files in a tree structure
Company hierarchies with managers and employees
AI and machine learning classification trees
Representing possible moves in chess, tic-tac-toe, etc.
Web pages are structured as a tree of elements
B-trees enable fast data retrieval
Mathematical expressions represented as trees
Trie trees for efficient word suggestions
Trees provide logarithmic time complexity for many operations when balanced. Instead of checking every item in a list (O(n)), a balanced binary search tree can find an item in O(log n) time. This means searching through 1,000,000 items requires only about 20 comparisons!
Example: Finding a file on your computer with 100,000 files would take ages if you checked each one sequentially. But with a tree structure organized alphabetically, you can navigate: Computer → Documents → Projects → 2024 → MyFile.txt in just a few steps.
Test your understanding by building efficient folder structures!
Play Folder Tree Builder Game →