DAG Practice Question 3

Duration: 6 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): 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
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow 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
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment focuses on constructing a Directed Acyclic Graph (DAG) from a complex arithmetic expression to optimize storage by identifying and sharing common sub-expressions. The instructor presents the problem: (a+b+c)*(a+b)+(a+b+c)*(a+b)+(a+b+c), asking students to determine the total number of nodes and edges in the resulting DAG. The teaching flow moves from analyzing the expression to breaking it down into components, identifying repeated terms like (a+b+c) and (a+b), and then systematically drawing the graph structure. The process emphasizes merging identical subtrees to minimize redundancy, contrasting with a standard expression tree where such terms would be duplicated. The session concludes by counting the final graph elements, establishing 8 nodes and 10 edges as the solution.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem by writing the arithmetic expression (a+b+c)*(a+b)+(a+b+c)*(a+b)+(a+b+c) on the board. He underlines the repeated sub-expression (a+b+c) to highlight optimization opportunities, explicitly stating that a DAG will be constructed for this expression. The visible text on screen asks for the total number of nodes and edges in the DAG, setting the objective for the lesson. The instructor begins breaking down the expression into manageable parts, focusing on operator precedence and grouping to prepare for graph construction.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to draw the DAG structure, starting with leaf nodes for variables a, b, and c. He connects these to addition operator nodes, demonstrating how the sub-expression (a+b+c) is formed. He then highlights the term (a+b) as another common sub-expression that can be shared within the graph. The instructor draws green arrows to trace connections, showing how nodes for (a+b+c) and (a+b) are reused rather than duplicated across the three main terms of the original expression. This visual mapping correlates specific parts of the formula with their corresponding nodes in the diagram.

  3. 5:00 – 5:37 05:00-05:37

    The instructor finalizes the graph construction and performs a count of the total elements. He points to shared sub-expressions in the completed graph to verify that no nodes were unnecessarily duplicated. The final solution is written on the board as 8 nodes and 10 edges, concluding the problem-solving process. This count represents the optimized structure where common terms like (a+b+c) and (a+b) are represented by single nodes with multiple incoming edges from different operators, demonstrating the efficiency of DAGs over standard expression trees.

The core educational value of this session lies in understanding how Directed Acyclic Graphs optimize arithmetic expression representation. Unlike a binary tree where every operation creates new nodes, a DAG allows multiple parents to point to the same child node. In this specific example, the term (a+b+c) appears three times in the expression but is represented by a single node structure in the DAG. Similarly, (a+b) appears twice and shares a node. The instructor's method of underlining repeated terms before drawing the graph serves as a heuristic for students to identify optimization candidates. The final count of 8 nodes and 10 edges is derived by summing the unique variable nodes (a, b, c), the unique operator nodes for additions and multiplications, and accounting for the shared edges that connect these components without duplication. This technique is fundamental in compiler design for intermediate code generation and optimization.

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