Tree Data Structure

Tree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes.

What is Tree Data Structure?

A tree data structure is a hierarchical structure that is used to represent and organize data in a way that is easy to navigate and search. It is a collection of nodes that are connected by edges and has a hierarchical relationship between the nodes. 

The topmost node of the tree is called the root, and the nodes below it are called the child nodes. Each node can have multiple child nodes, and these child nodes can also have their own child nodes, forming a recursive structure.

Terminologies In Tree Data Structure

• Parent Node: The node which is a predecessor of a node is called the parent node of that node. {B} is the parent node of {D, E}.
• Child Node: The node which is the immediate successor of a node is called the child node of that node. Examples: {D, E} are the child nodes of {B}.
• Root Node: The topmost node of a tree or the node which does not have any parent node is called the root node. {A} is the root node of the tree. A non-empty tree must contain exactly one root node and exactly one path from the root to all other nodes of the tree.
• Leaf Node or External Node: The nodes which do not have any child nodes are called leaf nodes. {K, L, M, N, O, P, G} are the leaf nodes of the tree.
• Ancestor of a Node: Any predecessor nodes on the path of the root to that node are called Ancestors of that node. {A,B} are the ancestor nodes of the node {E}
• Descendant: A node x is a descendant of another node y if and only if y is an ancestor of y.
• Sibling: Children of the same parent node are called siblings. {D,E} are called siblings.
• Level of a node: The count of edges on the path from the root node to that node. The root node has level 0.
• Internal node: A node with at least one child is called Internal Node.
• Neighbor of a Node: Parent or child nodes of that node are called neighbors of that node.
• Subtree: Any node of the tree along with its descendant.

Types of Tree Data Structure

• Binary tree: In a binary tree, each node can have a maximum of two children linked to it. Some common types of binary trees include full binary trees, complete binary trees, balanced binary trees, and degenerate or pathological binary trees.
• Ternary Tree: A Ternary Tree is a tree data structure in which each node has at most three child nodes, usually distinguished as “left”, “mid” and “right”.
• N-ary Tree or Generic Tree: Generic trees are a collection of nodes where each node is a data structure that consists of records and a list of references to its children(duplicate references are not allowed). Unlike the linked list, each node stores the address of multiple nodes.

Applications of Tree Data Structure

• File System:  This allows for efficient navigation and organization of files.
• Data Compression: Huffman coding is a popular technique for data compression that involves constructing a binary tree where the leaves represent characters and their frequency of occurrence. The resulting tree is used to encode the data in a way that minimizes the amount of storage required.
• Compiler Design: In compiler design, a syntax tree is used to represent the structure of a program. 
• Database Indexing: B-trees and other tree structures are used in database indexing to efficiently search for and retrieve data. 

Basics of Tree Data Structure

• Introduction to Tree – Data Structure and Algorithm Tutorials
• What is Tree | Tree Definition & Meaning in DSA
• Types of Trees in Data Structures
• Applications of tree data structure
• Applications, Advantages, and Disadvantages of Tree

Basic Operations on Tree Data Structure

1. Height of Tree
2. Height and Depth of Node
3. Level of a Given Node in Tree
4. Search a Node in Tree
5. Find the Parent of a Node
6. Diameter of a Tree
7. Find all Leaf nodes
8. Find Siblings of a Node
9. Find Children of a Node
10. Tree Traversals (Inorder, Preorder and Postorder)

n-ary or Generic Tree

1. Generic Trees(N-ary Trees)
2. What is Generic Tree or N-ary Tree
3. Depth of an N-ary Tree
4. Mirror of n-ary Tree
5. Diameter of an N-ary Tree
6. Level Order Traversal of N-ary Tree
7. Sum of all elements of N-ary Tree
8. Serialize and Deserialize an N-ary Tree

Binary Tree

1. Introduction to Binary Tree – Data Structure and Algorithm Tutorials
2. Properties of Binary Tree
3. Types of Binary Tree
4. Applications, Advantages and Disadvantages of Binary Tree
5. Binary Tree (Array implementation)
6. Level Order Tree Traversal
7. Inorder Traversal of Binary Tree
8. Preorder Traversal of Binary Tree
9. Postorder Traversal of Binary Tree
10. Insertion in a Binary Tree
11. Deletion in a Binary Tree
12. Enumeration of Binary Trees

Binary Search Tree

1. Introduction to Binary Search Tree – Data Structure and Algorithm Tutorials
2. Applications of BST
3. Application, Advantages and Disadvantages of Binary Search Tree
4. Insertion in Binary Search Tree
5. Searching in Binary Search Tree
6. Binary Search Tree (BST) Traversals – Inorder, Preorder, Post Order
7. Deletion in Binary Search Tree

Ternary Search Tree

1. Ternary Search Tree
2. Ternary Search Tree meaning & definition in DSA
3. Ternary Search Tree (Deletion)
4. How to implement text Auto-complete feature using Ternary Search Tree
5. Longest word in ternary search tree

AVL Tree

1. AVL Tree Data Structure
2. What is AVL Tree | AVL Tree meaning
3. Insertion in an AVL Tree
4. Deletion in an AVL Tree
5. Weak AVL or Rank Balanced Trees
6. Insertion, Searching and Deletion in AVL trees containing a parent node pointer
7. AVL with duplicate keys
8. Count greater nodes in AVL tree
9. How to insert Strings into an AVL Tree
10. Minimum number of nodes in an AVL Tree with given height
11. Optimal sequence for AVL tree insertion (without any rotations)
12. Different shapes of AVL possible at height h

B Tree

1. Introduction of B-Tree
2. What is B-Tree? | B-Tree meaning
3. Insert Operation in B-Tree
4. Delete Operation in B-Tree
5. B-Tree Insert without aggressive splitting

B+ Tree

1. Introduction of B+ Tree
2. What is B+ Tree | B+ Tree meaning
3. Insertion in a B+ tree
4. Deletion in B+ Tree

Red-Black Tree

1. Introduction to Red-Black Tree
2. Red-Black Tree Definition & Meaning in DSA
3. Insertion in Red-Black Tree
4. Red-Black Trees | Top-Down Insertion
5. Deletion in Red-Black Tree
6. Applications, Advantages, and Disadvantages of Red-Black Tree

Other types of Trees

• Ternary Tree:
  1. What is Ternary Tree
  2. Create a Doubly Linked List from a Ternary Tree
• Interval Tree:
  1. Interval Tree
  2. Interval Tree using GNU Tree-based container
• 2-3-4 Tree:
  1. 2-3-4 Tree
  2. 2-3 Trees | (Search, Insert, and Deletion)

Trees vs other Data Structures

1. Difference between graph and tree
2. Comparison between Heap and Tree
3. What is the difference between Heap and Red-Black Tree?
4. Difference between Binary Search Tree and Binary Heap
5. Difference between Stack and Tree
6. Difference between an array and a tree

Comparison among different Tree Data Structures

1. Difference between General tree and Binary tree
2. Difference between Binary Tree and Binary Search Tree
3. Difference between Binary tree and B-tree
4. Difference between B tree and B+ tree
5. Difference between Full and Complete Binary Tree
6. Difference between Binary Search Tree and AVL Tree
7. Red Black Tree vs AVL Tree

Problems based on Tree Data Structure

Problems	Difficulty Level	Solve
Height of Binary Tree	Easy	Solve
Determine if two trees are identical	Easy	Solve
Mirror tree	Easy	Solve
Symmetric Tree	Easy	Solve
Diameter of tree	Easy	Solve
Checked for Balanced tree	Easy	Solve
Children Sum Parent	Easy	Solve
Check for BST	Easy	Solve
Array to BST	Easy	Solve
Largest value in each level of binary tree	Easy	Solve
Maximum GCD of siblings of a binary tree	Easy	Solve
Zigzag Tree Traversal	Easy	Solve
Inorder Successor in BST	Easy	Solve
Kth Largest Element in a BST	Easy	Solve
Check if subtree	Medium	Solve
Single Valued Subtree	Medium	Solve
Unique BSTs	Medium	Solve
Inorder Traversal (iterative)	Medium	Solve
Preorder Traversal (iterative)	Medium	Solve
Postorder Traversal(iterative)	Medium	Solve
Vertical Traversal of a Binary Tree	Medium	Solve
Boundary Traversal	Medium	Solve
Construct Binary Tree from Parent array	Medium	Solve
Construct Binary Tree from Preorder and Inorder Traversal	Medium	Solve
Preorder Traversal and BST	Medium	Solve
Construct tree from preorder traversal	Medium	Solve
Minimum distance between two given nodes	Medium	Solve
Maximum sum leaf to root path	Medium	Solve
Odd Even Level Difference	Medium	Solve
Lowest Common Ancestor of a Binary Tree	Medium	Solve
Ancestors in Binary Tree	Medium	Solve
Remove BST keys outside the given range	Medium	Solve
Pair with given target in BST	Medium	Solve
Sum Tree	Medium	Solve
BST to greater sum tree	Medium	Solve
BST to max heap	Medium	Solve
Clone binary tree with random pointer	Medium	Solve
Maximum sum of non adjacent nodes	Medium	Solve
Largest BST in a Binary Tree	Medium	Solve
Extreme nodes in alternate order	Medium	Solve
Connect nodes at same level	Hard	Solve
Nodes at given distance in a Binary Tree	Hard	Solve
Sorted Linked List to BST	Hard	Solve
Binary Tree to Doubly Linked List	Hard	Solve
Maximum sum path between two leaf nodes	Hard	Solve
K-Sum Paths	Hard	Solve
Number of turns in a binary tree	Hard	Solve
Merge two BST’s	Hard	Solve
Fixing two nodes of a BST	Hard	Solve
Burn Binary Tree	Hard	Solve

Quick Links:

• Practice problems on Trees
• Videos on Trees
• Quizzes on Tree