BST Practice Question

Duration: 13 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: 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, संधि, समास, 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), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep, Artificial Intelligence, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), कंप्यूटर नेटवर्क / Computer Networks
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory, Number System & Place Value, Factors, Multiples, Divisibility, HCF & LCM, Mensuration — Perimeter, Area, Surface Area, Volume, Data Handling, Graphs & Probability, Coordinates & Graphs, Higher Mathematics — Trigonometry, Quadratics, Polynomials, Progressions, Statistics, Logarithms, समतल क्षेत्रमिति / Plane Mensuration, प्रतिचयन / Sampling
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
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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