BST Practice Question

Duration: 7 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. 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
  9. Paper 2 | Operating System: 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
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: 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, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
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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