1.1) What is Tree data structure?

A tree data structure is a hierarchical, non-linear data structure that organizes elements in a tree-like manner. It consists of nodes connected by edges, where each node contains data and can have zero or more child nodes. The topmost node of the tree is called the root, and nodes with no children are called leaves. The path from the root to any node is called a branch, and the length of the branch is the depth or level of the node.

A visual representation of a tree data structure looks like an inverted tree, with the root at the top and the leaves at the bottom. Each node can have multiple children, forming a branching structure.

Visual Representation of a Tree:

         A       <-- Root
       /   \
      B     C
     / \     \
    D   E     F   <-- Leaves

In the above tree:

• Node A is the root node.
• Nodes B and C are child nodes of A, and A is the parent of B and C.
• Nodes D and E are child nodes of B, and B is the parent of D and E.
• Node F is a child node of C, and C is the parent of F.
• Nodes D, E, and F are leaf nodes as they have no children.

Properties of Trees

1. A tree is an acyclic graph, meaning there are no cycles or loops in its structure.
2. Each node in the tree has a unique parent except for the root node, which has no parent.
3. Each node can have zero or more child nodes.
4. A node with no children is called a leaf node, and a node with at least one child is called an internal node.
5. The length of the longest path from the root to any leaf node is called the height (or depth) of the tree.
6. The level of a node refers to the distance from the root. The root node is at level 0, its children at level 1, and so on.

Types of Trees

1. Binary Tree: Each node has at most two children – left child and right child.
2. Binary Search Tree (BST): A binary tree with the left child always having a value less than the parent and the right child having a value greater than the parent. This property allows for efficient searching, insertion, and deletion.
3. AVL Tree: A self-balancing binary search tree where the heights of the two child subtrees of any node differ by at most one.
4. Red-Black Tree: Another self-balancing binary search tree where each node is colored red or black, and the tree adheres to specific properties ensuring balanced operations.
5. N-ary Tree: A tree where each node can have up to N children, instead of being limited to two as in a binary tree.

Tree data structures find extensive use in various applications, including organizing hierarchical data, representing file systems, implementing search algorithms (e.g., binary search), and building efficient data structures like heaps and priority queues. They are a crucial part of computer science and are used to solve numerous real-world problems efficiently.