DAG Practice Questions

Duration: 22 min

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Module outline

  1. About Course: UPPSC Course Overview
  2. Interview Preparation & Guidance: Interview Preparation
  3. Paper 1 | General 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, वर्णमाला, समास, संधि, 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), शब्द-भंडार, वर्ण-विचार, हिन्दी की ध्वनि और स्वनिम व्यवस्था, प्राचीन और मध्यकालीन भारतीय आर्यभाषाएँ, काव्य के लक्षण, हेतु और प्रयोजन, अशुद्धि-शोधन, शब्द-रचना, शब्द-भेद, हिन्दी की रूप रचना, रूप-रचना, हिन्दी शब्द रचना, हिन्दी साहित्येतिहास दर्शन, भक्तिकालीन काव्यधाराएँ, भारतीय काव्यशास्त्र की परंपरा, भारतीय नवजागरण और स्वाधीनता आंदोलन, अन्य गद्य विधाएँ एवं प्रवासी साहित्य, निर्धारित उपन्यासों का तुलनात्मक अध्ययन, गोदान, हिन्दी कहानी का विकास, स्वातंत्र्योत्तर और नयी कहानी, हिन्दी निबंध का विकास, शुक्लोत्तर निबंध, द्विवेदी और शुक्ल युग के निबंध, हिन्दी की संवैधानिक स्थिति, आधुनिक भारतीय आर्यभाषाएँ और हिन्दी का उद्भव, हिन्दी भाषा प्रयोग के विविध रूप, रीतिकाल, जीवनी, द्विवेदी युग और छायावाद, रीति, वक्रोक्ति और औचित्य सिद्धान्त, शब्दशक्ति और ध्वनि सिद्धान्त, रस सिद्धान्त और साधारणीकरण, उत्तर आधुनिकतावाद, लोहिया दर्शन, हिन्दी उपन्यास का विकास, हिन्दी नवजागरण, अंबेडकर दर्शन, आदिकाल, प्रयोगवाद और नयी कविता, छायावादी काव्य: प्रसाद और निराला, प्रगतिवाद से समकालीन कविता, निर्गुण भक्ति काव्य, द्विवेदीयुगीन काव्य, रीतिकालीन काव्य, आरंभिक हिन्दी उपन्यास, स्वातंत्र्योत्तर उपन्यास, आत्मकथा, स्वाधीनता-पूर्व प्रेमचंदोत्तर उपन्यास, निर्धारित कहानियों का तुलनात्मक अध्ययन, साठोत्तरी नाटक, प्रसाद और प्रसादोत्तर युग के नाटक, भारतेन्दु युगीन नाटक, स्वातंत्र्योत्तर नाटक, भारतेन्दु युगीन निबंध, संस्मरण और रेखाचित्र, व्यंग्य, एक साहित्यिक की डायरी, संस्कृति के चार अध्याय, सगुण भक्ति काव्य, हिन्दी नाटक, एकांकी और रंगमंच, आधुनिक गद्य और हिन्दी नवजागरण, अलंकार सिद्धान्त, हिन्दी आलोचना का विकास, भक्ति आंदोलन, कल्पना, बिम्ब, प्रतीक, मिथक और फंतासी, नयी कविता का विस्तार और साठोत्तरी कविता, उत्तर-छायावादी और प्रगतिवादी काव्य, काव्यगुण और काव्यदोष, प्लेटो, अरस्तू और पाश्चात्य परंपरा, मार्क्सवाद, स्वच्छन्दतावादी काव्यशास्त्र, आधुनिक पाश्चात्य आलोचना, भाषा और भाषा परिवार, देवनागरी लिपि
  4. Paper 2 | General Studies: State Wise GK, Polity, Geography, History, GK- Current Affairs
  5. Paper 1 | Programming Language: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
  6. Paper 1 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, ORDBMS, NoSQL
  7. Paper 1 | Cyber Security: Society, Law & Ethics, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  8. Paper 1 | Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design
  9. Paper 1 | 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, Network Security
  10. Paper 1 | Design and Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  11. Paper 1 | Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  12. Paper 1 | Discrete Structures and Theory of Logic: Permutation and Combination, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  13. Paper 1 | Software Project Management: Software Project Management
  14. Paper 2 | Operating Systems: 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, Security
  15. 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, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  16. Paper 2 | Artificial Intelligence & High Performance Computing: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Natural Language Processing, Emerging Tech Trends
  17. Paper 2 | Image Processing: Digital Image Fundamentals, Image Enhancement, Image Restoration, Color Image Processing, Image Compression
  18. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  19. Paper 2 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  20. Paper 2 | Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, Java
  21. Paper 2 | Soft Computing: Fuzzy Sets, Artificial Neural Networks, Genetic Algorithms
  22. Paper 2 | Distributed System: Distributed Systems
  23. UPPSC Live Class Recordings: UPPSC Polytechnic Lecturer 2025 (CS)
  24. Previous Year Papers:
  25. Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture focuses on constructing Directed Acyclic Graphs (DAGs) from three-address code to optimize intermediate representations in compiler design. The instructor systematically works through multiple examples, demonstrating how to identify common subexpressions and merge redundant nodes. The core methodology involves processing each assignment statement sequentially, creating operator nodes for operations like addition and subtraction, and leaf nodes for variables. A critical rule applied is that if a subexpression has already been computed, the existing node is reused rather than creating a new one. The instructor counts the total nodes in each resulting graph to answer specific exam-style questions. Key concepts include variable renaming, operator precedence handling within the DAG structure, and the distinction between leaves (operands) and internal nodes (operators). The progression moves from simple addition chains to more complex expressions involving subtraction and variable reassignments, illustrating how the graph structure evolves with each instruction.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The session begins with the introduction of a problem involving three-address code where the objective is to construct a Directed Acyclic Graph (DAG) and determine the total number of nodes. The instructor presents the code sequence: `a = a + c`, `b = a + d`, `c = a + b`, and `d = b * d`. He explicitly numbers the lines of code to facilitate step-by-step analysis. The visible text on screen asks, 'What is the total number of nodes in the DAG?' This sets the stage for a methodical construction process where each statement is mapped to graph nodes.

  2. 2:00 – 5:00 02:00-05:00

    The instructor initiates the DAG construction by processing the first statement `a = a + c`. He draws an addition node with children representing variables 'a' and 'c'. Moving to the second statement `b = a + d`, he prepares to extend the graph. The visual evidence shows him writing out the second statement on the board while referencing the first. He begins combining expressions, noting that `a + c` is a common subexpression if it appears again. The teaching cue emphasizes mapping code statements directly to graph nodes, starting with the leaves and moving up to operators.

  3. 5:00 – 10:00 05:00-10:00

    The analysis continues with the third instruction `c = a + b`. The instructor expands this expression into sub-expressions to visualize the tree structure before merging common parts. He draws nodes for variables `a`, `c`, and `d` along with the addition operator. The process involves tracing the flow of values through the graph, ensuring that if a variable is reassigned (like `a` in line 4), the graph reflects this change. The instructor points to line 4 `a = a + c` and expands the expression, culminating in a count of the total nodes required for this specific code sequence.

  4. 10:00 – 15:00 10:00-15:00

    A new problem is introduced with a different code sequence: `1 a = b + c`, `2 c = a + d`, `3 d = b + c`, `4 e = d - b`, `5 a = e + b`. The instructor systematically processes each line, starting with `a = b + c` to create the initial addition node. He highlights how `b + c` is reused in the third instruction, demonstrating the optimization benefit of DAGs. By substituting variables and tracing dependencies, he draws the graph structure with nodes for `b`, `c`, and the addition operator. The visual progression shows him writing out expanded forms to clarify variable dependencies before finalizing the node count.

  5. 15:00 – 20:00 15:00-20:00

    The instructor solves the second problem by determining that the total number of nodes in the constructed DAG is 6. He analyzes the statements to identify common subexpressions like `b + c` and simplifies expressions to reduce node count. The teaching cues focus on tracing variable dependencies through the code sequence and identifying redundant calculations. He points to the DAG while explaining the third instruction `d = b + c`, showing how the existing node for `b + c` is reused. This section reinforces the rule that identical subexpressions share a single node in the graph.

  6. 20:00 – 22:23 20:00-22:23

    The final example involves the code sequence `1 a = e + c`, `2 b = e + d`, `3 c = a - b`, `4 a = a + c`, `5 d = b - f`. The instructor simplifies expressions by substituting previous calculations, such as replacing 'a' and 'b' in the third instruction. He identifies common subexpressions to minimize nodes, ultimately concluding that there are 4 distinct nodes in the final DAG structure. The visible text confirms the question asks for the total number of nodes. This concludes the lecture with a clear demonstration of how variable reassignment and subtraction operations are handled in DAG construction.

The lecture provides a comprehensive guide to constructing Directed Acyclic Graphs (DAGs) from three-address code, a fundamental technique in compiler optimization. The instructor demonstrates that the primary goal is to identify and merge common subexpressions, thereby reducing the total number of nodes in the graph. The methodology is consistent across all examples: process instructions sequentially, create operator nodes for arithmetic operations, and reuse existing operand or operation nodes whenever a subexpression is repeated. Key observations include the handling of variable reassignments, where new edges are added to reflect updated values without necessarily creating duplicate operator nodes if the expression remains identical. The instructor emphasizes counting the final nodes as a metric for optimization efficiency. By working through multiple distinct code sequences, including those with addition, subtraction, and multiplication, the lecture establishes a clear pattern for students to apply in exam scenarios. The visual evidence of board writing and node counting serves as a practical reference for constructing these graphs manually.

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