Insertion in B-Tree

Duration: 7 min

This video lesson is available to enrolled students.

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Module outline

  1. About Course: UPPSC Course Overview
  2. Interview Preparation & Guidance: Interview Preparation
  3. Paper 1 | General Hindi: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, वर्णमाला, समास, संधि, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material)
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  7. Paper 1 | Cyber Security: Society, Law & Ethics, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  8. Paper 1 | Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design
  9. Paper 1 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  10. Paper 1 | Design and Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  11. Paper 1 | Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  12. Paper 1 | Discrete Structures and Theory of Logic: Permutation and Combination, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  13. Paper 1 | Software Project Management: Software Project Management
  14. Paper 2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Security
  15. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  16. Paper 2 | Artificial Intelligence & High Performance Computing: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Natural Language Processing, Emerging Tech Trends
  17. Paper 2 | Image Processing: Digital Image Fundamentals, Image Enhancement, Image Restoration, Color Image Processing, Image Compression
  18. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  19. Paper 2 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  20. Paper 2 | Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, Java
  21. Paper 2 | Soft Computing: Fuzzy Sets, Artificial Neural Networks, Genetic Algorithms
  22. Paper 2 | Distributed System: Distributed Systems
  23. UPPSC Live Class Recordings: UPPSC Polytechnic Lecturer 2025 (CS)
  24. Previous Year Papers:
  25. Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture provides a detailed explanation of B-trees, starting with formal definitions and rules for a B-tree of order m. It covers constraints on the number of children and keys for root, internal, and leaf nodes, emphasizing that all leaves must be on the same level. The instructor then transitions to a practical demonstration, solving a problem where a sequence of numbers is inserted into an empty B-tree of order 3. The lecture visually traces the insertion process, highlighting node splitting and key promotion mechanisms required to maintain the tree's balance and structural properties. This combination of theory and practice helps students understand the dynamic nature of B-trees.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The session begins with a slide defining a B-tree of order m. The instructor reads out the properties: the root has at least zero and at most m child nodes, while internal nodes (except the root) have at least ceil(m/2) and at most m child nodes. The slide includes three tables labeled "Root", "Internal except Root", and "Leaf", detailing the MAX and MIN values for CHILD and DATA. For instance, the Root table shows MAX CHILD as m and MIN CHILD as 0, while the Internal table shows MIN CHILD as ceil(m/2). The instructor emphasizes that the number of keys in a node is one less than the number of child nodes and that these keys partition the subtrees. He also notes that all leaf nodes are on the same level, making the tree perfectly balanced.

  2. 2:00 – 5:00 02:00-05:00

    The problem statement appears: "Consider the following elements 5, 10, 12, 13, 14, 1, 2, 3, 4 insert them into an empty b-tree of order = 3." The instructor starts drawing the tree. He inserts 5, 10, and 12 into a single node. Since the order is 3, the maximum number of keys is 2. The node {5, 10, 12} overflows. He splits the node, promoting the middle key 10 to become the root. The resulting tree has root 10, with left child 5 and right child 12. He then inserts 13 into the right child, resulting in the node {12, 13}. He draws the tree structure with 10 at the top and 5, 12 below it.

  3. 5:00 – 7:22 05:00-07:22

    The instructor continues by inserting 14. The right child becomes {12, 13, 14}, causing an overflow. He splits this node, promoting 13 to the root. The root now contains {10, 13}. The children are 5, 12, and 14. Next, he inserts 1, 2, 3, and 4. He inserts 1 into the left child {5}, making it {1, 5}. Then 2 is inserted, making it {1, 2, 5}, which overflows. He splits, promoting 2 to the root. The root becomes {2, 10, 13}, which overflows. He splits the root, promoting 10 to a new root. The tree structure evolves with a root of 10, left child 2, and right child 13. Finally, he inserts 3 and 4, resulting in a final tree with root 10, left child 2, 4, and right child 13. The leaves are 1, 3, 5 under the left child and 12, 14 under the right child. He draws the final tree structure clearly showing the hierarchy. He also writes down the sequence of elements being inserted to keep track.

The lecture successfully connects theoretical B-tree definitions with practical insertion algorithms. By working through a specific example with order 3, the instructor demonstrates how the tree dynamically adjusts to new data through splitting and promotion. This visual approach clarifies complex concepts like maintaining balance and handling node overflows, providing a clear understanding of B-tree mechanics for students. The step-by-step drawing allows viewers to follow the logic of key movement and node creation, reinforcing the rules presented at the beginning of the session.

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