Practice question on B Tree Insertion

Duration: 8 min

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Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Aptitude: Number System, Divisibility Rules, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Partnership, Age Problems, Time and Work, Pipe and Cistern, Speed Time and Distance, Algebra, Arithmetic, Data Interpretation, Sequence and Series (Series), Logarithm, Powers and Exponents (Surds and Indices), Permutation and Combination, Probability, Speed Mathematics and Basic Mathematics, Trigonometry
  2. Logical Reasoning: Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Syllogisms, Inequality, Data Sufficiency, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Venn Diagram, Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Noun, Pronoun, Adjectives, Verb, Adverb, Tenses, Subject Verb Agreement (Verb Noun Agreement), Articles, Preposition, Conjunction, Modals, Determiner, Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  4. Data Structures (Domain Test): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Algorithms (Domain Test): Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms
  6. OOPs (Domain Test): Object Oriented Programming (OOPS)
  7. DBMS (Domain Test): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  8. SQL (Domain Test): SQL
  9. Operating Systems (Domain Test): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Domain Test): 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, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  12. Written English Test: English Writing Ability
  13. Psychometric Test: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video provides a detailed walkthrough of inserting a sequence of integers into an empty B-tree of order 5. The problem statement lists the elements: 5, 10, 12, 13, 14, 1, 2, 4, 20, 18, 19, 17, 16, 15, 25, 23, 24. The instructor defines the order m=5, which dictates that a node can hold a maximum of m-1=4 keys. The core mechanism demonstrated is the split operation: whenever a node accumulates 5 keys, it splits into two nodes, and the middle key is promoted to the parent. This process is repeated until the tree is balanced. The lecture covers multiple levels of splitting, including root splits, to maintain the B-tree properties.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor starts by writing the problem statement on the screen in orange text. He explicitly writes 'm=5' and 'd m-1=4' in red ink to establish the constraints. He begins inserting the first batch of numbers: 5, 10, 12, 13, 14. He draws a single box containing these five numbers. Since the limit is 4, he identifies an overflow. He circles the middle element, 12, and draws an arrow pointing upwards to indicate promotion. He then draws a new root node containing 12. Below it, he draws two child nodes: one containing [5, 10] and the other containing [13, 14]. This establishes the initial two-level structure of the tree.

  2. 2:00 – 5:00 02:00-05:00

    Next, the instructor inserts 1, 2, and 4. He places them into the leftmost leaf node [5, 10], resulting in the sequence [1, 2, 4, 5, 10]. This node now has 5 keys, so he performs a split. He identifies 4 as the middle element and promotes it to the root. The root, previously just 12, now becomes [4, 12]. The children of 4 are [1, 2] and [5, 10]. The instructor then moves to the right side, inserting 20, 18, and 19 into the node [13, 14]. The node becomes [13, 14, 18, 19, 20]. Another split occurs. The middle element 18 is promoted to the root. The root updates to [4, 12, 18]. The children of 18 are [13, 14] and [19, 20].

  3. 5:00 – 7:40 05:00-07:40

    The instructor continues with 17, 16, and 15. He inserts them into the node [13, 14], making it [13, 14, 15, 16, 17]. This triggers a split where 15 is promoted to the root. The root becomes [4, 12, 15, 18]. The children of 15 are [13, 14] and [16, 17]. Then he inserts 25, 23, and 24 into the rightmost node [19, 20]. The node becomes [19, 20, 23, 24, 25]. A split occurs, promoting 23 to the root. The root becomes [4, 12, 15, 18, 23]. This is 5 keys, so the root overflows. He splits the root, promoting 15 to a new single-element root. The final tree has 15 at the top, with left child [4, 12] and right child [18, 23], and their respective subtrees are arranged accordingly.

The video systematically builds a B-tree, illustrating how insertions can cascade upwards. The critical concept is the split rule: a node with m keys splits, promoting the median. This ensures the tree remains balanced. The instructor visually demonstrates each step, drawing boxes for nodes and arrows for pointers, making the abstract concept of B-tree insertion concrete. The final structure shows a balanced tree with a root of 15, ensuring efficient search, insertion, and deletion operations.

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