BST Practice Question

Duration: 13 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 solves a binary search tree (BST) counting problem by introducing Catalan numbers. It begins with the example of 3 distinct keys, showing that there are 5 possible BST structures. The main question asks how many distinct BSTs can be created from 4 distinct keys, with options (A) 4, (B) 14, (C) 24, and (D) 42. The instructor introduces the Catalan number formula in both recursive form, C_n = sum_{i=0}^{n-1} C_i * C_{n-i-1}, and closed form, (2n choose n)/(n+1) or (2n)!/((n+1)! * n!). A table is built for f(N) where N represents the number of keys: f(0)=1, f(1)=1, f(2)=2, and f(3)=5. For N=4, the instructor considers each key (1, 2, 3, or 4) as the root and multiplies the number of left-subtree combinations by right-subtree combinations: C_0*C_3 + C_1*C_2 + C_2*C_1 + C_3*C_0 = 5 + 2 + 2 + 5 = 14. Option (B) 14 is circled as the correct answer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a practice question asking how many distinct BSTs can be constructed with 3 distinct keys, displaying the 5 possible tree structures for N=3. It then transitions to the main question: 'How many distinct binary search trees can be created out of 4 distinct keys?' with options (A) 4, (B) 14, (C) 24, and (D) 42. The instructor writes 'Formula of catalan number' in red, showing the recurrence c_n = sum_{i=0}^{n-1} c_i * c_{n-i-1} and the closed form (2n choose n)/(n+1). A two-column table headed 'N' and 'f(n)' is drawn, with the row N=0 entered as f(0)=1.

  2. 2:00 – 5:00 02:00-05:00

    The instructor builds the table step by step, writing N=1 with f(1)=1=C_1 and continuing to calculate values for increasing N. The closed-form formula C_n = (2n)!/((n+1)! * n!) is displayed on the right side of the screen. For N=3, the instructor draws explicit BST structures using keys 1, 2, and 3 to visualize why f(3)=5. The recursive formula C_n = sum_{i=0}^{n-1} C_i * C_{n-i-1} is written alongside the table, connecting the manual enumeration to the general Catalan number recurrence.

  3. 5:00 – 10:00 05:00-10:00

    The instructor calculates f(2)=2 and confirms f(3)=5 by summing products of left and right subtree combinations. For N=4, the instructor lists all possible roots (1, 2, 3, and 4) and draws tree diagrams for each root choice. The breakdown shows that choosing key 1 as root gives C_0*C_3 combinations, key 2 gives C_1*C_2, key 3 gives C_2*C_1, and key 4 gives C_3*C_0. The table now shows f(0)=1, f(1)=1, f(2)=2, and f(3)=5, with the Catalan recurrence C_n = sum C_i * C_{n-1-i} displayed on the right.

  4. 10:00 – 12:58 10:00-12:58

    The final calculation sums the products for N=4: C_0*C_3 + C_1*C_2 + C_2*C_1 + C_3*C_0 = 5 + 2 + 2 + 5 = 14. The instructor writes f(4)=14 in the table and circles option (B) 14 as the correct answer. The completed whiteboard shows the full table from N=0 to N=4, four BST structures drawn at the bottom corresponding to roots 1 through 4, and the Catalan number formula C_n = sum_{i=0}^{n-1} C_i * C_{n-i-1} on the right side, verifying that the recursive counting matches the closed-form Catalan number.

The central concept is that the number of distinct BSTs with n keys equals the nth Catalan number. The teaching flow moves from a concrete example (N=3, five trees) to the general formula. The recursive method works by choosing each key as root: if key i is root, the left subtree has (i-1) keys and the right subtree has (n-i) keys, contributing C_{i-1} * C_{n-i} combinations. Summing over all roots gives the recurrence. The closed form (2n)!/((n+1)! * n!) provides a direct calculation. For N=4, the answer 14 is verified both by the recurrence and by explicit enumeration of root cases. Key exam takeaway: recognize BST counting problems as Catalan number applications, and be able to compute small values (1, 1, 2, 5, 14) from the recurrence.

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