Basic Ideas of Tree Data Structures

Tree data structures are like special diagrams made up of points connected by lines. Here are some important parts to know:

• Node: This is like a box that holds data and connects to other boxes (nodes).
• Root: This is the top box in the tree. It doesn’t have a parent box.
• Leaf: These are the boxes at the end of the branches, which don’t connect to any other boxes.
• Height: This measures the longest path from the root to a leaf.

Different Types of Trees

1. Binary Tree: In this tree, each box can have up to two children (one on the left and one on the right). So, the most boxes you can find at a certain level (called depth $d$) is $2^d$. In a perfect binary tree, if the height is $h$, you can find a total of $n = 2^{h+1} - 1$ boxes.

2. Binary Search Tree (BST): This is a special type of binary tree. In a BST, boxes on the left side only contain values that are less than the parent box. The boxes on the right contain values that are more.

How to Navigate Trees

There are different ways to move through a tree and get or change its data:

• Pre-order: First, visit the root box, then go to the left boxes, and finally visit the right boxes.
• In-order: Start by visiting the left boxes, then the root box, and then the right boxes. This method is often used in BSTs to give sorted results.
• Post-order: Visit the left boxes, then the right boxes, and finally the root box.

These ways of navigating are very important. They help us find and change information in trees easily and quickly.