Basic Terms for Trees in Computer Science

Understanding trees is important for computer science students, especially when studying data structures. Here are some basic terms you need to know about trees:

1. Tree: This is a special type of data structure. It looks like a family tree, with one main starting point called the root, and branches that spread out to other points called nodes. In a tree, you don’t go in circles.

2. Node: A node is a basic part of a tree. It holds data, like information about a person in a family tree. Each node can connect to none, one, or more other nodes.

3. Edge: An edge is the link between two nodes. If a tree has $n$ nodes, there will be $n-1$ edges.

4. Root: The root is the starting point of a tree. A good tree will always have just one root.

5. Leaf: A leaf is a node that does not have any children. In a well-balanced tree, leaves can make up about half of all the nodes.

6. Height: The height of a tree is the length of the longest path from the root to a leaf. If a tree has a height of $h$, the most leaves it can have is $2^h$.

7. Depth: Depth shows how deep a node is in the tree. The root is at depth $0$, and every other node gets a number that tells how far away it is from the root.

8. Binary Tree: This kind of tree allows each node to have up to two children. At a height of $h$, it can have a total of $2^h - 1$ nodes.

9. Balanced Trees: These trees keep their height short, which helps speed up operations. They typically work in logarithmic time, written as $O(\log n)$.

10. Traversal Methods: These are ways to go through the tree. The main methods are in-order, pre-order, and post-order. They are important for handling tree data effectively.