TLDR;
This video provides a comprehensive overview of data structures, covering essential concepts and implementations relevant for semester exams. It begins with basic terminology and progresses through arrays, linked lists, stacks, queues, trees, graphs, and hashing. The video emphasises the importance of efficient programming through data structures and algorithms, detailing various data organisation methods and their trade-offs.
- Covers basic to advanced data structures concepts.
- Includes C implementations and practical examples.
- Focuses on exam-oriented content with detailed explanations.
Chapter-0: Introduction [0:00]
The video aims to cover the entire data structures syllabus, focusing on topics important for semester exams. It promises a comprehensive learning experience, even for those with no prior knowledge, and guarantees that 95% of the content will match university exam syllabuses. The presenter encourages viewers to comment with their location to create a virtual map of India in the comment section.
Chapter-1 Introduction: Basic Terminology, Elementary Data Organization, Built in Data Types in C. Abstract Data Types (ADT) [2:30]
Computer science involves solving problems correctly through algorithms, which are then converted into efficient programs. Efficient programs require knowledge of both data structures and algorithms. Data structures organise data in computer memory to optimise time and space usage. The arrangement considers how data is stored and the relationships between data elements. When specifying a data structure, four things are defined: organisation, accessing method, degree of association, and processing method. Data structures are categorised into primitive (built-in) and non-primitive (user-defined), as well as linear (sequential) and non-linear (hierarchical).
Chapter-2 Array: Definition, Single and Multidimensional Arrays, Representation of Arrays: Row Major Order, and Column Major Order, Derivation of Index Formulae for 1-D,2-D,3-D and n-D Array Application of arrays, Sparse Matrices and their representations. [22:10]
An array stores a collection of elements of the same type in contiguous memory locations, accessible via an index. In C, arrays are declared with a data type, name, and size, with default values being garbage. Initialisation assigns values to array elements, which can be modified later. Advantages include efficient storage, random access, and ease of sorting and searching. Disadvantages include fixed size, inefficient insertion/deletion, and homogeneity. Indexing typically starts from zero, with the first index called the lower bound and the last the upper bound. The total number of elements is calculated as (upper bound - lower bound + 1). The size of an array is the number of elements multiplied by the size of each element.
The address of an element at index k in a 1D array is calculated using the formula: Base Address + (k - Lower Bound) * Weight of each element. 2D arrays are organised into rows and columns, stored in memory either in row-major order (left to right, top to bottom) or column-major order (top to bottom, left to right). Formulae are provided for calculating the address of an element in 2D arrays using both row-major and column-major orders. 3D arrays extend this concept, and a general formula is given for n-dimensional arrays. Sparse matrices, which contain mostly zero values, can be efficiently stored using array or linked list representations by only storing non-zero elements.
Chapter-3 Linked lists: Array Implementation and Pointer Implementation of Singly Linked Lists, Doubly Linked List, Circularly Linked List, Operations on a Linked List. Insertion, Deletion, Traversal, Polynomial Representation and Addition Subtraction & Multiplications of Single variable & Two variables Polynomial. [1:06:41]
Linked lists overcome the size limitations of arrays by using non-contiguous memory allocation. A linked list consists of nodes, each containing data and a pointer to the next node. The first node is accessed via a head pointer. Advantages include dynamic size and efficient memory usage, while disadvantages include slower access times and memory overhead due to pointers. Basic operations such as creating a node, traversing, searching, inserting, and deleting are explained with C-style code examples. Variations of linked lists include header linked lists, circularly linked lists, and doubly linked lists, each offering different advantages. Doubly linked lists allow traversal in both directions, improving reliability and flexibility at the cost of increased memory usage. Polynomials can be represented using linked lists, where each node stores a coefficient, exponent, and a pointer to the next term.
Chapter-4 Stack: Abstract Data Type, Primitive Stack operations: Push & Pop, Array and Linked Implementation of Stack in C, Application of stack: Prefix and Postfix Expressions, Evaluation of postfix expression, Iteration and Recursion- Principles of recursion, Tail recursion, Removal of recursion Problem solving using iteration and recursion with examples such as binary search, Fibonacci numbers, and Hanoi towers. Trade offs between iteration and recursion. [1:59:35]
A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle, where insertion (push) and deletion (pop) occur at the same end, known as the top. Stacks can be implemented using arrays (static implementation) or linked lists (dynamic implementation). Key applications include expression parsing, function calls, and undo features. Array implementation involves checking for overflow before pushing and underflow before popping. C code examples illustrate push and pop operations for both array and linked list implementations. Additional functions, such as reversing a string, are also discussed.
The video also covers the conversion and evaluation of prefix, infix, and postfix expressions using stacks. It explains the principles of recursion, including base cases and recursive steps, and compares recursion with iteration, highlighting their trade-offs. Examples such as binary search, Fibonacci numbers, and Hanoi towers are used to illustrate problem-solving using both iteration and recursion.
Chapter-5 Queue: Create, Add, Delete, Full and Empty, Circular queues, Array and linked implementation of queues in C, Dequeue and Priority Queue. [4:00:25]
A queue is a linear data structure that follows the First-In-First-Out (FIFO) principle, where elements are added at the rear and removed from the front. Queues can be implemented using arrays or linked lists. Basic operations include enqueue (add), dequeue (delete), checking if the queue is full or empty. In array implementation, the front and rear pointers are used to manage the queue. Circular queues address the limitations of linear queues by wrapping around to the beginning of the array when the end is reached. C code examples illustrate enqueue and dequeue operations for both array and linked list implementations. Dequeues (double-ended queues) allow insertion and deletion from both ends, while priority queues assign priorities to elements, affecting their order of removal.
Chapter-6 PTree: Basic terminology used with Tree, Binary Trees, Binary Tree Representation: Array Representation and Pointer(Linked List) Representation, Binary Search Tree, Strictly Binary Tree ,Complete Binary Tree . A Extended Binary Trees, Tree Traversal algorithms: Inorder, Preorder and Postorder, Constructing Binary Tree from given Tree Traversal, Operation of Insertion , Deletion, Searching & Modification of data in Binary Search . Threaded Binary trees, Traversing Threaded Binary trees. Huffman coding using Binary Tree. Concept & Basic Operations for AVL Tree , B Tree & Binary Heaps [4:45:05]
A tree is a non-linear data structure representing hierarchical relationships, consisting of a root node and subtrees. Key terminologies include root, edge, parent, child, leaf, internal node, level, height, and path. A binary tree is a tree where each node has at most two children (left and right). Binary trees can be represented using arrays or linked lists. Important types of binary trees include binary search trees (BST), strictly binary trees, complete binary trees, and extended binary trees. Tree traversal algorithms include inorder, preorder, and postorder, each visiting nodes in a specific sequence. Operations on binary search trees include insertion, deletion, searching, and modification. Threaded binary trees use null pointers to facilitate faster traversal. Huffman coding uses binary trees for data compression. The video also touches on AVL trees, B-trees, and binary heaps.
Chapter-7 Graphs: Terminology used with Graph, Data Structure for Graph Representations: Adjacency Matrices, Adjacency List, Adjacency. Graph Traversal: Depth First Search and Breadth First Search. [6:18:06]
A graph is a data structure consisting of vertices (nodes) and edges, representing relationships between data items. Key terminologies include vertices, edges, directed and undirected graphs, weighted graphs, and adjacency. Graphs can be represented using adjacency matrices or adjacency lists. Adjacency matrices use a 2D array to indicate the presence or absence of edges, while adjacency lists use linked lists to store the neighbours of each vertex. Graph traversal algorithms include Depth-First Search (DFS) and Breadth-First Search (BFS), each exploring the graph in a specific manner.
Chapter-8 Hashing: Concept of Searching, Sequential search, Index Sequential Search, Binary Search. Concept of Hashing & Collision resolution Techniques used in Hashing [6:42:46]
Hashing is a technique used to search data in constant time by using a hash function to map keys to specific locations in a hash table. A good hash function should be easy to compute, distribute keys uniformly, and minimise collisions. Common hash functions include the modulo division method, mid-square method, and folding method. Collisions occur when different keys map to the same location, requiring collision resolution techniques such as linear probing, quadratic probing, and chaining. Linear probing involves searching sequentially for an empty slot, while quadratic probing uses a quadratic function to determine the next slot. Chaining involves creating linked lists at each hash table location to store multiple keys.
