BST Practice Question

Duration: 7 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
  3. Paper-1 & 2 | Data Interpretation: Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Analogy, Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement, Logical Sequence Of Words, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: Selection Decision Table (Decision Making)
  7. Paper-1 | General Science: Physics, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: State Wise GK, GK- Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, Artificial Intelligence
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing
  22. Paper 2 | Pedagogy: Child Development, Theories, Concept of Pedagogy, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Psychology, Curriculum Framework & Reforms, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment addresses a binary search tree (BST) practice question: how many distinct BSTs can be constructed with 3 distinct keys. The instructor presents the multiple-choice options (4, 5, 6, or 9), then works through a concrete example using keys 1, 2, and 3. By systematically enumerating all possible insertion sequences (permutations) and drawing the resulting tree structures, the instructor demonstrates that each permutation yields a unique BST shape. The six distinct trees are numbered and displayed, leading to the answer c) 6. In the final segment, the instructor begins introducing a more general combinatorial approach using a root node K with left and right subtrees, writing partial calculations such as 1*1=1 and 2*1=2, suggesting a recursive counting method for larger N.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The slide displays the question 'Q how many distinct BST can be constructed with 3 distinct keys?' in orange text, with answer options a) 4, b) 5, c) 6, d) 9. Red hand-drawn underlines emphasize key terms: 'distinct', 'BST can be constructed', and '3 distinct keys'. The instructor then writes 'Example -> N = 3' and the key set '1,2,3', beginning to draw the first BST structure by placing node 1 as root, then adding node 2 as a right child, and node 3 as a right child of 2, forming a right-leaning chain.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues drawing additional BST structures for different insertion sequences. The first tree (1,2,3) is a right-skewed chain tagged with circled '1'. The second tree (1,3,2) shows root 1 with right child 3 and left child 2 beneath it, tagged '2'. A balanced tree for sequence 2,1,3 is drawn with root 2 and children 1 (left) and 3 (right). A right-skewed tree for 3,1,2 and a left-skewed tree for 3,2,1 are also drawn. Numbered labels from 1 to 6 appear below each tree, confirming six distinct configurations and supporting answer option c) 6.

  3. 5:00 – 7:29 05:00-07:29

    The board now shows all six hand-drawn BSTs grouped by root: sequences 1,2,3 and 1,3,2 under root 1; 2,1,3 and 2,3,1 under root 2 with children 1 and 3; and 3,1,2 and 3,2,1 under root 3. A bottom-left diagram introduces a general node 'K' branching to two circles, one labeled 'No of possible combination structures.' The instructor writes partial calculations including a crossed-out '1 * 2', then '1 * 1 = 1' and '2 * 1 = 2', hinting at a recursive formula for counting BSTs by multiplying left and right subtree possibilities. The segment ends before the full general solution is completed.

The core teaching objective is to connect permutation-based enumeration with BST structure uniqueness. The instructor uses N=3 as a tractable example: all 6 permutations of keys {1,2,3} produce distinct tree shapes because BST insertion order determines structure. This concrete demonstration validates the answer c) 6 and builds intuition for why the count equals the number of permutations for small N. The transition to a general method via node K with left/right subtree multiplication suggests the Catalan number recurrence C(n) = sum_{i=0}^{n-1} C(i)*C(n-1-i), though this is only partially developed in the sampled frames. Students should note that for N=3, the six trees correspond exactly to 3! = 6 permutations, but this equivalence does not hold for larger N where different insertion sequences can yield the same shape.

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