BST Practice Question

Duration: 7 min

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Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Aptitude: Ratio and Proportion (Ratios), Data Interpretation, Mixture and Alligation, Permutation and Combination, Number System, Sequence and Series (Series), Speed Time and Distance, Speed Mathematics and Basic Mathematics, Algebra, Percentage, Profit and Loss, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Time and Work, Mensuration and Geometry, Partnership
  2. Reasoning Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Seating Arrangements, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Directions (Direction Test), Ranking, Order and Sequence, Syllogisms, Blood Relations, Puzzle Solving (Puzzles), Inequality, Machine Input-Output
  3. English Language: Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, 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), Sentence Construction, Pronoun, Preposition, Conjunction, Adverb, Verb, Modals, Articles, Determiner, Interjection
  4. General Awareness: Evolution of Indian Banking (Banking & Financial Awareness), GK- Current Affairs, Static General Knowledge, Indian Economy
  5. C Concepts + MCQs (IT Specialist): C Programming by Yash Sir, C Language Core
  6. Java (IT Specialist): Java
  7. Python (IT Specialist): Python for Placements by Yash Sir, Python Basics
  8. OOPs (IT Specialist): Object Oriented Programming (OOPS)
  9. DBMS (IT Specialist): 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
  10. SQL (IT Specialist): SQL
  11. Software Engineering (IT Specialist): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Data Structure (IT Specialist): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  13. Operating System (IT Specialist): 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
  14. Compiler Design (IT Specialist): 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
  15. Computer Architecture (IT Specialist): Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Multiprocessors, Programming the Basic Computer
  16. Data Communication & Networking (IT Specialist): 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
  17. Descriptive Test (Main Exam): English Writing Ability
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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