Summary of "Tree in Data Structures | Learn Coding"
Summary of “Tree in Data Structures | Learn Coding”
This video provides a comprehensive introduction to trees in data structures and algorithms, covering definitions, terminology, types, implementations, and key algorithms like searching and sorting, with a focus on binary trees and their subtypes.
Main Ideas and Concepts
1. What is a Tree?
- A tree is a non-linear hierarchical data structure consisting of nodes connected by edges.
- Nodes are not stored sequentially but in a hierarchical form.
- The root node is the starting point of the tree.
- Nodes are divided into left and right subtrees.
- Trees represent data in a hierarchical structure resembling a natural tree (branches and leaves).
2. Basic Terminology
- Node: Basic data element.
- Root: The top-most node where the tree starts.
- Child (Successor): Nodes directly connected below a node.
- Parent (Predecessor): Node directly above a node.
- Ancestor: All nodes in the path from root to a node.
- Sibling: Nodes sharing the same parent.
- Leaf (Terminal) Node: Node with no children.
- Non-terminal Node: Node with one or more children.
- Edge: Connection between two nodes.
- Branch (Path): Sequence of nodes from root to a leaf.
- Degree: Number of children of a node.
- Level: Depth of a node from the root, root is level 0.
3. Types of Trees
- General Tree: No limit on the number of children per node.
- Binary Tree: Each node has at most two children (left and right).
Types of Binary Trees
- Full Binary Tree: Every node has 0 or 2 children.
- Perfect Binary Tree: All internal nodes have two children and all leaves are at the same level.
- Complete Binary Tree: All levels are fully filled except possibly the last, which is filled from left to right.
- Degenerate (Skewed) Tree: Each internal node has only one child (can be left or right skewed).
- Expanded Binary Tree: A full binary tree formed by adding dummy nodes to make all nodes have two children.
- Binary Search Tree (BST): Left subtree nodes are smaller, right subtree nodes are greater than the root node.
- Heap Tree: A complete binary tree where each parent node is greater than or equal to its children (max-heap) or smaller (min-heap).
4. Tree Implementations
-
Linked List Implementation:
- Each node contains three parts:
- Data (value)
- Pointer to left child
- Pointer to right child
- Addresses of child nodes are stored in left and right pointers.
- Each node contains three parts:
-
Array Implementation:
- Root node stored at index 1 (1-based indexing).
- Left child of node at index k is at index 2k.
- Right child of node at index k is at index 2k + 1.
- Simple way to represent complete binary trees.
5. Binary Search Tree (BST) Construction
- Insert nodes by comparing values:
- Smaller values go to the left subtree.
- Larger values go to the right subtree.
- Steps to insert elements and maintain BST property are explained with examples.
6. BST Algorithms
- Sorting: Use in-order traversal to get elements in sorted order.
- Searching: Start from root, compare target with current node:
- If equal, found.
- If less, search left subtree.
- If greater, search right subtree.
- If reach null, element not found.
7. Heap Tree
- Complete binary tree satisfying heap property:
- Parent node is greater than or equal to children (max-heap).
- Children nodes are smaller than parent.
- Steps to create a heap tree by inserting elements and performing “heapify” operations.
- Algorithm to sort using heap tree by repeatedly removing root and restructuring the heap.
Methodologies and Algorithms
Binary Tree Implementation Using Linked List
- Each node contains:
- Data part (stores node value)
- Left pointer (address of left child)
- Right pointer (address of right child)
- Store root node first.
- For each node:
- Store addresses of left and right children.
- If no child, store null.
Binary Tree Implementation Using Array
- Root node at index 1.
- For node at index k:
- Left child at 2k.
- Right child at 2k + 1.
- Fill array according to these positions.
- If node missing, leave corresponding array position empty or null.
Binary Search Tree Construction Algorithm
- Start with first element as root.
- For each new element:
- Compare with current node.
- If smaller, go left; if left is null, insert here.
- If greater, go right; if right is null, insert here.
- Repeat until all elements inserted.
BST Sorting Algorithm (In-order Traversal)
- Traverse left subtree.
- Visit node (add to output).
- Traverse right subtree.
- Result is sorted array of elements.
BST Searching Algorithm
- Start at root.
- If root is null, element not found.
- If element equals root, found.
- If element < root, search left subtree.
- If element > root, search right subtree.
- Repeat until found or null reached.
Heap Tree Construction and Sorting Algorithm
- Insert elements maintaining complete tree property.
- After insertion, perform “heapify” to maintain heap property (parent ≥ children).
- For sorting:
- Remove root (max element).
- Replace root with last node.
- Heapify to restore heap.
- Repeat until tree is empty.
- Extracted elements form sorted array.
Speakers/Sources
- The video features a single instructor/narrator who explains the concepts step-by-step with examples and demonstrations.
- No other speakers or external sources are explicitly mentioned.
Summary
This video is a detailed tutorial on trees in data structures, explaining fundamental concepts, terminology, types (with emphasis on binary trees and their subtypes), implementations (linked list and array), and key algorithms for binary search trees and heap trees. It is designed for learners preparing for exams and interviews, providing clear examples and stepwise instructions for creating, searching, and sorting trees.
Category
Educational
