Data Structures and Algorithms

Transcription

1 Data Structures and Algorithms Course Title: Data Structures and Algorithms Full Marks: Course No: CSC206 Pass Marks: Nature of the Course: Theory + Lab Credit Hrs: 3 Semester: III Course Description: This course includes the basic foundations in of data structures and algorithms. This course covers concepts of various data structures like stack, queue, list, tree and graph. Additionally, the course includes idea of sorting and searching. Course Objectives: To introduce data abstraction and data representation in memory To describe, design and use of elementary data structures such as stack, queue, linked list, tree and graph To discuss decomposition of complex programming problems into manageable subproblems To introduce algorithms and their complexity Detail Syllabus: Unit 1 Introduction to Data Structures & Algorithms Teaching Hours (4) Data types, Data structure and Abstract date type Concept of data type. Basic and user defined data types. Concept of data structure and its uses. Definition and use of ADT. Benefits of using ADTs. Dynamic memory Concept of dynamic memory allocation. 1 hr allocation in C Introduction to Definition of algorithm. What is a good algorithm? 1 hr Algorithms Different structures used in algorithms. Asymptotic notations Time and space complexity. Big Oh (O) notation. 1 hr and common functions Unit 2 Stack Teaching Hours (4) Basic Concept of Concept and example of stack. Stack ADT. Stack 2 hr Stack, Stack as an operations. Different applications: Bracket ADT, Stack matching. Operations, Stack Applications Conversion from infix Basic definitions and examples of prefix, infix, and 2 hr to postfix/prefix postfix expressions. Conversion from one expression, Evaluation expression to another. Using stack to convert an of postfix/prefix infix expression to postfix/prefix. Using stack to expressions evaluate postfix/prefix expression Unit 3 Queue Teaching Hours (4) Basic Concept of Queue, Queue as an Concept of queue. Sequential representation. Queue as and ADT. Different operations. 2 hrs 1 hr

2 ADT, Primitive Operations in Queue Linear Queue, Circular Queue, Priority Queue, Queue Applications Circular queue. Linear vs. Circular queue. Priority queue. Queue applications: print server, operating system scheduler etc. 2 hrs Unit 4 Recursion Teaching Hours (3) Principle of Recursion, Recursion definition. Recursive vs. Iterative 1 hr Comparison between algorithm. Definition and example of tail recursion Recursion and Iteration, Tail Recursion Factorial, Fibonacci Sequence, GCD, Tower of Hanoi(TOH) Example of recursive algorithms (factorial, Fibonacci Sequence, GCD, and Tower of Hanoi algorithms). 2 hrs Applications and Efficiency of Recursion Applications of recursion. Finding efficiency of recursive algorithms. Unit 5 Lists Teaching Hours (8) Basic Concept, List and List concepts. List as an ADT. List operations. 2 hrs ADT, Array Array implementation of lists. Linked list concepts Implementation of Lists, Linked List Types of Linked List: Singly Linked List, Doubly Linked List, Circular Linked List. Singly and doubly linked lists. Circular linked list. 2 hrs Basic operations in Linked List: Node Creation, Node Insertion and Deletion from Beginning, End and Specified Position Inserting and deleting nodes at different positions in a singly and doubly linked list. 3 hrs Stack and Queue as Linked implementation of stack and queue. 1 hr Linked List Unit 6 Sorting Teaching Hours (8) Introduction and Types of sorting: Internal and External sort Concept of sorting. Internal vs. External sort. 4 hrs Comparison Sorting Algorithms: Bubble, Selection and Insertion Sort, Shell Sort Divide and Conquer Sorting: Merge, Quick and Heap Sort Efficiency of Sorting Algorithms Concept of bubble, selection, insertion, and shell sorts Concept of divide and conquer algorithms. Concept of merge, quick, and heap sort Efficiency of all above sorting algorithms. 4 hrs

3 Unit 7 Searching and Hashing Teaching Hours (6) Introduction to Searching, Search Algorithms: Sequential Search, Binary Search Concept of searching. Concept of sequential and binary search 3 hrs Efficiency of Search Efficiency of sequential and binary search Algorithms algorithms. Hashing : Hash Concept of hashing, hash function, and hash table. Function and Hash Concept of hash collision. Choosing a hash 3 hrs Tables, Collision function. Concept of rehashing and chaining. Resolution Techniques Inserting and deleting items in a hash table. Unit 8 Trees and Graphs Teaching Hours (8) Concept and Concept of binary tree. Strictly binary tree. Level 1 hr. Definitions, Basic and depth. Complete and almost complete binary Operations in Binary tree. Operations on binary trees. Binary tree Tree, Tree Height, traversal. Level and Depth Binary Search Tree, Concept of binary search tree. Insertion, deletion, 2 hr. Insertion, Deletion, and search in binary search tree. Traversals, Search in BST AVL tree and Balancing algorithm, Applications of Trees Definition and Representation of Graphs, Graph Traversal, Minimum Spanning Trees: Kruskal and Prims Algorithm Shortest Path Algorithms: Dijksrtra Algorithm Concept and example of balanced binary tree. Balancing algorithm. Tree applications: expression tree and game tree. Concept of graph. Types of graph. Graph representations: adjacency matrix representation and linked representation. Depth-first and breadthfirst traversal. Concept of spanning and minimum spanning trees. Kruskal s and Prim s algorithms for finding minimum spanning tree. Concept of shortest path. Using Dijkstra s algorithm for finding shortest path. Laboratory Works: After completing this course, students should have practical knowledge of data structures, algorithms, and ADTs. The laboratory work includes. Writing programs with dynamic memory allocation and de-allocation. Writing programs to implement stack operations. Writing programs using stack to convert infix expression to postfix/prefix expression and to evaluate postfix/prefix expression. Writing programs to implement queue operations for linear, circular, and priority queue. Writing recursive programs to implement factorial, Fibonacci sequence, GCD, and Tower of Hanoi algorithms. Writing programs to implement list using array and linked list. 2 hr. 3 hr. 1 hr

4 Writing programs for linked list implementation of stack and queue. Writing programs to implement sorting, searching and hashing algorithms. Writing programs to implement Binary Search Trees and AVL Tress. Writing programs to implement searching, spanning tree and shortest path. Text Books: 1. Y Langsam, MJ Augenstein and A.M, Tanenbaum Data Structures using C and C++, Prentice Hall India, Second Edition 2015 Reference Books: 1. Leen Ammeral, Programmes and Data Structures in C, Wiley Professional Computting 2. G.W Rowe, Introduction to Data Structure and Algroithms with C and C++, prentice Hall India 3. R.L Kruse, B.P. Leung, C.L. Tondo, Data Structure and Program Design in C Prentice- Hall India Model Questions Course Title: Data Structure and Algorithms Full Marks: 60 Course No: CSC206 Pass Marks: 24 Semester: III Credit Hrs: 3 Section A Attempt any two questions. (2 10 = 20) 1. Define stack. How is it different from queue? Write a program to implement circular queue. 2. What is linked list? Explain different types of linked lists. Discuss algorithms for inserting and deleting a node at front position of the linked list. 3. Define graph. Discuss Dijkastra s algorithm for finding shortest path in a graph. Section B Attempt any eight questions. (8 5 = 40) 4. What is ADT? How is it different from data type? What are benefits of using ADT? 5. How can you use stack to evaluate a postfix expression? Discuss. 6. Define recursive algorithm. How do you implement recursive GCD algorithm? 7. Hand-test selection-sort algorithm with the data given below: 56, 23, 14, 20, 65, 7, 8, 14, 15, Discuss binary search algorithm. What is time complexity of this algorithm? 9. What are benefits of using hashing? How do you choose a hash function? 10. How do you balance a binary tree? Discus. 11. Discuss depth-first search in a graph with example. 12. Write short notes on: (2 2.5 = 5) a. Big O notation b. Spanning tree

5 Numerical Method Course Title: Numerical Method Full Marks: Course No.: CSC207 Pass Marks: Nature of the Course: Theory + Lab Credit Hrs: 3 Semester: III Course Description: This course contains the concepts of numerical method techniques for solving linear and nonlinear equations, interpolation and regression, differentiation and integration, and partial differential equations. Course Objectives: The main objective of the course is to provide the knowledge of numerical method techniques for mathematical modeling. Course Detail: Unit 1: Solution of Nonlinear Equations (10 Hrs.) o Review of relation between computer programming and Numerical Methods o Errors in numerical calculations truncation, round off, errors in original data, blunders, propagated errors and floating point arithmetic, error in converting values, relative absolute errors o Trial and Error Method o Half-Interval Method bisection method, algorithm, implementation and convergence o Secant Method the method, algorithm, implementation and convergence o Newton's method the method, algorithm, relating Newton s method to other methods, implementation and convergence o Fixed point iteration the method, different rearrangements, algorithm, implementation and its convergence o Newton's method for polynomials the method, synthetic division algorithm and remainder theorem, Horner's method and algorithm, implementation and convergence Unit 2: Interpolation and Approximation (8 Hrs.) o Interpolation definition, application and definition of extrapolation o Lagrange s Interpolation - Lagrange's polynomials, error, algorithms, numerical applications and implementations o Newton's interpolation - divided differences, algorithm for constructing divided difference table, divided difference for a polynomial, error of interpolation, Newton s

6 forward difference interpolation and Newton s backward difference interpolation, differences Vs. divided differences, algorithm and implementation o Cubic Spline interpolation definition, derivation, algorithm, examples illustrating cubic spline interpolation o Introduction to regression, Regression Vs. Interpolation, Least Squares Approximation definition and application, derivation, algorithm and implementation of least square approximation for linear, non- linear and polynomial data Unit 3: Numerical Differentiation and Integration (5 Hrs.) o Numerical Differentiation definition, application, derivatives from divided difference table, error term, algorithm, Derivatives for evenly spaced data, forward difference formula, central difference formula, error terms, Second Order Derivatives, Maxima and minima of tabulated function o Numerical Integration- definition, application, Newton-Cote's quadrature formulas, Trapezoidal rule, Simpson's 1/3 rule, Simpson s 3/8 rule, Composite formulas for trapezoidal and Simpson s rules, algorithms and implementations, Numerical Double Integration, Gaussian integration algorithm, its derivation, Romberg integration formulas, derivation and algorithm, Unit 4: Solution of Linear Algebraic Equations (10 Hrs.) o Review of the existence and uniqueness of solutions of systems of linear equations, and properties of matrices, ill conditioning, types of solution of linear algebraic method o Gaussian elimination method and algorithm, Gaussian elimination with partial pivoting and its algorithm, Gauss-Jordan method and its algorithm, Inverse of matrix using Gauss Jordan method o Matrix factorization Solving system of linear equation using Dolittle algorithm, Cholesky's algorithm o Iterative methods Jacobi method and Gauss Seidel Method, and their algorithms o Eigen values and eigen vectors problems with practical examples, Solving eigen value problems using Lagrangian and power method Unit 5: Solution of Ordinary Differential Equations (7 Hrs.) o Review of differential equations, definition of ordinary differential equations and examples, order and degree, initial value problem

7 o Taylor series method and error terms, Picard s method, Euler's method and its accuracy, Heun's method, Runge-Kutta methods (4 th order method: formula and problem solutions), algorithm and implementations o Solution of the higher order equations definitions and examples of higher order difference equations, solution of system of differential equations, representation of higher order equations into system of equations o Boundary value problems: Definition and examples, shooting method and its algorithm Unit 6: Solution of Partial Differential Equations (5 Hrs.) o Review of partial differential equations, Classification of partial differential equation, Deriving difference equations, Laplacian equation and Poisson's equation and their applications, their solution techniques, algorithms and examples NOTE: o Relations between different related methods, their advantages, disadvantages and comparisions are essential o Each method should be implemented and compared with each other drawing conclusions of their efficiency, accuracy and errors. Laboratory Works: The laboratory exercise should consists of program development and testing of non-linear equations, interpolation, numerical integration and differentation, linear algebraic equations, ordinary and partial differential equations numerical solutions using appropriate languages like C, C++ or Matlab. List topics to be included in Laboratory Exercises: o Solution of non-linear equations using Bisection Method and Secant Method o Solution of non-linear equations using Newton s Raphson Method and Fixed Point Iteration Method o Solution of polynomial using Newton s Method and Horner s Rule to evaluate polynomial

8 o Polynomial interpolation using Lagrange s Interpolation and Newton s Divided Difference Interpolation, Newton s forward and backward difference interpolation o Fitting of linear (straight line, y=ax + b) and non-linear (exponential y=ae bx, quadratic y=ax 2 +bx+c) function using least square method o Derivatives from divided difference table o Integration using Trapezoidal rule, Simpson s 1/3 rule and Simpson s 3/8 rule, Line and Double Integration. o Solution of system of linear equations using Gauss Elimination method and Gauss Jordan Method o Gauss Seidel Method, Jacobi Method and Power Method o Solution of ordinary differential equation using Euler s Method, Heun s Method and 4th order Runge-Kutta Method o Boundary value problems using Shooting Method o Laplacian Equation, Poison s Equation Model Questions: Bachelor/Second Year/Third Semester/Science Computer Science and Information Technology CSc.207 Numerical Method FM:60 PM:24 Time: 3hrs Candidates are required to give their answers in their own words as far as practicable. Assume suitable data if necessary. The figure in the margin indicates full mark. Group A Attempt any TWO questions. (10X2=20) 1. Compare Gauss Elimination method and Gauss Jordan method of solving simultaneous equation. Use Gauss Elimination to solve the following system of equation and also write its algorithm. 2x+3y+4z=5 3x+4y+5z=6 4x+5y+6z=7

9 2. Write an algorithm and a program to compute the interpolation value at a specific point, given a set of data points, using Lagrange interpolation method. 3. Derive Composite Simpson s 1/3 Rule for numerical integration. How does it improve the accuracy of integration? Group B Attempt any EIGHT questions. (5X8=40) 4. Write a program to solve a non linear equation using bisection method. 5. Find the roots of the following equations using Newton s method. log x cos x = 0 6. Estimate the value of ln(3.5) using Newton s backward difference formula, given the following data. x ln Fit a straight line to the following set of data. x y Estimate the first derivative of f(x)=ln x at x=1 using the second order central difference formula. 9. Compare and contrast between Jacobi iterative method and Gauss Seidal method. 10. Explain about boundary value problem with example? Differentiate it with initial value problem. 11. Use the Heun's method to estimate y(0.4) when y (x)=x 2 +y 2 with y(0)=0. Assume h= Solve the Poisson s equation 2 f=2x 2 y 2 over the square domain 0 <= x <= 3 and 0 <= y <= 3 with f=0 on the boundary and h=1.

10 Computer Architecture Course Title: Computer Architecture Full Marks: Course No: CSC208 Pass Marks: Nature of the Course: Theory + Lab Credit Hrs: 3 Course Description: This course includes concepts of instruction set architecture, organization or micro-architecture, and system architecture. The instruction set architecture includes programmer s abstraction of computer. The micro-architecture consist internal representation of computers at register and functional unit level. The system architecture includes organization of computers at the cache and bus level.. Course Objectives Discuss representation of data and algorithms used to perform operations on data Demonstrate different operations in terms of Micro-operations Explain architecture of basic computer and micro-programmed control unit Understand and memory and I/O organization of a typical computer system Demonstrate benefits of pipelined systems Course Contents: Unit Unit 1: Data Representation (4 Hrs.) 1.1 Data Representation: Binary Representation, BCD, Alphanumeric Representation, Complements ((r-1) s Complement and r s complement), Fixed Point representation, Representing Negative Numbers, Floating Point Representation, Arithmetic with Complements (Subtraction of Unsigned Numbers, Addition and Subtraction of Signed Numbers) Overflow, Detecting Overflow 1.2 Other Binary Codes: Gray Code, self Complementing Code, Weighted Code (2421 and 8421 codes), Excess-3 Code, EBCDIC 1.3 Error Detection Codes: Parity Bit, Odd Parity, Even parity, Parity Generator & Checker Teaching Hour 2 Hour 1 Hour 1 Hour

11 Unit 2: Register Transfer and Microoperations (5) 2.1 Register Transfer Language: Microoperation, Register Transfer Language, Register Transfer, Control Function 2.2 Arithmetic Microoperations: List of Arithmetic Microoperations, Binary Adder, Binary Adder-subtractor, Binary Incrementer, Arithmetic Circuit 0.5 Hour 2 Hour 2.3 Logic Microoperations: List of Logic Microoperations, Hardware Implementation, Applications of Logic Microoperations. 1.5 Hour 2.1 Shift Microoperations: Logical Shift, Circular shift, Arithmetic Shift, Hardware Implementation of Shifter. 1 Hour Unit 3: Basic Computer Organization and Design (8) 3.1 Basic Concepts: Instruction Code, Operation Code, Concept of Instruction Format, Stored Program Concept. 0.5 Hour 3.2 Basic Computer Registers and Memory: List of Registers, Memory of Basic Computer, Common Bus System for Basic Computer. 1 Hour 3.3 Basic Computer Instructions: Instruction Format, Instruction Set Completeness, Control Unit of Basic Computer, Control Timing Signals 1.5 Hour 3.4 Instruction Cycle of Basic Computer: Fetch and Decode, Determining Type of Instruction, Memory Reference Instructions, Input-Output Instructions, IO Interrupt, Program Interrupt, Interrupt Cycle. 4 Hour 3.5 Description and Flowchart of Basic Computer 1 Hour

12 Unit 4: Microprogrammed Control (4) 4.1 Introduction: Hardwired and Microprogrammed Control Unit, Control Word, Microprogram, Control Memory, Control Address Register, Sequencer, 4.2 Address Sequencing: Conditional Branch, Mapping of Instructions, Subroutines, Microinstruction Format, Symbolic Microinstructions 4.3 Design of Control Unit: Decoding, Microprogram Sequencer. 0.5 Hour 2 Hour 1.5 Hour Unit 5: Central Processing Unit (4) 5.1 Introduction: Major Components of CPU, CPU Organizations (Accumulator Based Organization, General Register Organization, Stack Based Organization) 5.2 CPU Instructions: Instruction Formats, Addressing Modes, Types of Instructions (on the basis of numbers of addresses, on the basis of type of operation: data transfer instructions, data manipulation instructions, program control instructions), Program Control, Subroutine Call and Return, Types of Interrupt 5.3 RISC and CISC: RISC vs CISC, Pros and Cons of RISC and CISC, Overlapped Register Windows 0.5 Hour 2.5 Hour Unit 6: Pipelining (6) 6.1 Introduction: Parallel Processing, Multiple Functional Units, Flynn s Classification 6.2 Pipelining: Concept and Demonstration with Example, Speedup Equation, Floating Point addition and Subtraction with Pipelining 1 Hour 0.5 Hour 1.5 Hour

13 6.3 Instruction Level Pipelining: Review of Instruction Cycle, Three & Four-Segment Instruction Pipeline, Pipeline Conflicts and Solutions (Resource Hazards, Data Hazards, Branch Hazards) 3 Hour 6.4 Vector Processing: Concept and Applications, Vector Operations, Matrix Multiplication 1 Hour Unit 7: Computer Arithmetic (6) 7.1 Addition and Subtraction: Addition and Subtraction with Signed Magnitude Data (Algorithm and Hardware Implementation), Addition and Subtraction with Signed 2 s Complement Data (Algorithm and Hardware Implementation) 7.2 Multiplication and Division: Multiplication of Signed Magnitude Data, Booth Multiplication (Algorithm and Hardware Implementation), Restoring and Non-restoring Division Algorithm, Divide Overflow (Algorithm and Hardware Implementation). Unit 8: Input Output Organization (4) 8.1 Input-Output Interface: Why IO Interface?, I/O Bus and Interface Modules, I/O vs Memory Bus, Isolated vs Memory- Mapped I/O 8.2 Asynchronous Data Transfer: Strobe, Handshaking 8.3 Modes of Transfer: Programmed I/O, Interrupt-Initiated I/O, Direct memory Access 8.4 Priority Interrupt: Polling, Daisy-Chaining, Parallel Priority Interrupt 8.5 DMA and IOP: Direct Memory Access, Input-Output Processor, DMA vs IOP Unit 9: Memory Organization (4) 9.1 Introduction: Memory Hierarchy, Main Memory, RAM and ROM Chips, Memory address Map, Memory Connection to 2 Hour 4 Hour 1 Hour 0.5 Hour 0.5 Hour 1 Hour 1 Hour 1 Hour

14 CPU, Auxiliary Memory (Review of magnetic Disk, Magnetic Tape) 9.2 Associative Memory: Hardware Organization, Match Logic, Read Operation, Write Operation 9.3 Cache Memory: Locality of Reference, Hit & Miss Ratio, Mapping, Write Policies 1.5 Hour 1.5 Hour Text Book M. Morris Mano, Computer System Architecture, Prentice-Hall of India, Pvt. Ltd., Third edition, 2007 References William Stallings, Computer Organization and Architecture, Prentice-Hall of India, Pvt. Ltd., Seventh edition, Vincent P. Heuring and Harry F. Jordan, Computer System Design and Architecture, Prentice-Hall of India, Pvt. Ltd., Second edition, Laboratory Work Student should be able to implement and simulate the algorithms by using high level languages like C/Matlab and/or VHDL/Verilog. Laboratory work must include following exercises: 1 Laboratory work for familiarizing with the syntax, data types, and operators of Verilog/VHDL 2 Design of n-bit 2 s complement adder/subtractor 3 Design of Overflow detector in signed number addition 4 Design of parity generator and parity checker 5 Design of encoder and decoders 6 Design of multiplexer 7 Design of registers and memory 8 Memory Mapping 9 Design of control unit 10 Design of ALU

15 11 Design of CPU 12 Simulation of 5 stage or 4 stage or 3 stage pipelining 13 Simulation of addition and subtraction of signed 2 s complement data 14 Simulation of multiplication and division algorithms Model Questions Long Answer Questions 1 What is meant by instruction set completeness? Is instruction set of basic computer complete? Discuss instruction cycle of basic computer with suitable flowchart. 2 What is the concept behind pipelining? Discuss different types of pipeline conflicts and their possible solutions briefly 3 Multiply (-13) x (+40) using Booth multiplication algorithm. Short Answer Questions 4 What is overflow? Explain overflow detection process with signed and unsigned number addition with suitable example. 5 Write down different arithmetic Microoperations and design a 4-bit binary addersubtractor. 6 What is the purpose and advantage of common bus system? Explain common bust system of basic computer. 7 What is meant by address sequencing? Draw diagram of address sequencer and Explain in detail about mapping of instruction. 8 Consider that we are provided with following memory content. What will be the value loaded in AC if addressing mode is direct, indirect, immediate, PC-relative and index relative.

16 9 Define priority interrupt. Explain Daisy-chaining method of handling interrupt priority. 10 What is cache mapping? Explain direct mapping with suitable example. 11 What is space-time diagram? Discuss pipeline speedup equation with suitable example 12 Write short notes on a) Excess-3 code b) Input-output processor

17 Course Title: Computer Graphics Course no: CSC209 Nature of the Course: Theory + Lab Semester: III Full Marks: Pass Marks: Credit Hrs: 3 Course Description: The course coversconcepts of graphics hardware, software, and applications,data structures for representing 2D and 3D geometric objects, drawing algorithms for graphical objects, techniques for representing and manipulating geometric objects, illumination and lighting models, and concept of virtual reality. Course Objectives: The objective of this course is to understand the theoretical foundation as wellas the practical applications of 2D and 3D graphics. Detail Syllabus Chapter / Units Teaching Teaching Methodology Hours Unit 1: Introduction of Computer Graphics Class Lecture 3 Hours 1.1 A Brief Overview of Computer Graphics, Areas of applications 1.2 Graphics Hardware: Display Technology, Architecture of Raster-Scan Displays, Interlaced refresh procedure, refresh buffer, frame buffer, Vector Displays, Display Processors, Hard copy devices. Input Devices 1.3 Graphics Software: Software standards, Coordinate Representations, PHIGS Workstations, Need of machine independent graphics language 1.4 Human visual system: basic of how we perceived the world, strength and weakness of the human visual system 1.5 Color models: RGB, CMYK, HVS, XYZ 2. Scan Conversion Algorithm Class Lecture 6 Hours 2.1 Scan Converting a Point and a straight Line: DDA Line + Lab Session Algorithm, Bresenham s Line Algorithm 2.2 Scan Converting Circle and Ellipse :Mid Point Circle and Ellipse Algorithm 2.3 Area Filling: Scan Line Polygon fill Algorithm,Insideoutside Test,Scan line fill of Curved Boundary area, Boundary-fill and Flood-fill algorithm 1

18 3.Two-Dimensional Geometric Transformations Class Lecture 5 Hours 3.1 Two-Dimensional translation, Rotation,Scaling, Reflection + Lab Session and Shearing 3.2 Homogeneous Coordinate and 2D Composite Transformations. Transformation between Co-ordinate Systems 3.3 Two Dimensional Viewing: Viewing pipeline,window to viewport coordinate transformation 3.4 Clipping: Point,Lines(Cohen Sutherland line clipping,liang-barskylineclipping),polygon Clipping(Sutherland Hodgeman polygon clipping) 4. Three-Dimensional Geometric Transformation Class Lecture 5 Hours 4.1 Three-Dimensional translation, Rotation,Scaling, + Lab Session Reflection and Shearing 4.2 Three-Dimensional Composite Transformations 4.3 Three-Dimensional Viewing: Viewing pipeline, world to screen viewing transformation, Projection concepts(orthographic, parallel,perspective projections) 5. 3D Objects Representation Class Lecture 7 Hours 5.1 Representing Surfaces: Boundary and Space partitioning + Lab Session Polygon Surface: Polygon tables, Surface normal and Spatial orientation of surfaces, Plane equations, Polygon meshes Wireframe Representation Blobby Objects 5.2 Representing Curves: Parametric Cubic Curves, Spline Representation,Cubic spline interpolation, Hermite Curves,Bezier and B-spline Curve and surface, Fractals and its applications 5.3 Quadric Surface: Sphere and Ellipsoid 6. Solid Modeling Class Lecture 4 Hours 6.1 Solids and solid modeling, boundary point, interior point, closure 6.2 Sweep,Boundary and Spatial-Partitioning Representation 2

19 6.3 Binary Space Partition Trees (BSP) 6.4 Octree Representation 7. Visible Surface Detections Class Lecture 5 Hours 7.1 Visible surface and hidden surface, Coherence for visibility + Lab Session 7.2 Image Space and Object Space Techniques 7.3 Back Face Detection, Depth Buffer (Z-buffer), A-Buffer and Scan-Line Algorithms 7.4 Depth Sorting Method (Painter s Algorithm) 7.5 BSP tree Method, Octree and Ray Tracing 8. Illumination Models and Surface Rendering Techniques Class Lecture 5 Hours 8.1 Defining Realism, Image Synthesis Validation, challenges in computing light, optics model 8.2 Basic Illumination Models:Ambientlight, Diffuse reflection,specular reflection and Phong model 8.3 Intensity attenuation and Color consideration,transparency,shadows 8.4 Polygon Rendering Methods : Constant intensity shading, Gouraud shading, Phong Shading and Fast Phong Shading, Real time vs offline rendering 9. Introduction to Virtual Reality Class Lecture 2 Hours 9.1 Concept of Virtual reality 9.2 Virtual Reality Components of VR System, Types of VR System, 3D Position Trackers, Navigation and Manipulation Interfaces 9.3 Visual computation in virtual reality 9.4 Augmented Reality 9.5 Application of VR 10. Introduction to OpenGL Class Lecture 3 Hours 10.1Introduction, Callback functions, Color commands, + Lab Session Drawings pixels, lines, polygons using OpenGL, OpenGL and Direct X APIs - key differences, Viewing, Lighting and reflectance model 3

20 Text Books: 1. Donald Hearne and M.Pauline Baker, Computer Graphics, C Versions. Prentice Hall Reference Books: 1. J.D. Foley, S.K. Feiner and J.F. Hughes, Computer Graphics Principles and Practises (Second Edition in C) 2. R.K. Maurya, Computer Graphics with Virtual Reality, Wiley India 3. F.S. Hill, Stephen M.Kelley, Computer Graphics using Open GL Prentice Hall Laboratory Works: Students should be able to write program on the most of the contents listed in syllabus, using any known programming language (C, C++) in previous semester. Majorly, students should on computer graphics primitives like line, circle and ellipse drawing algorithm to hidden surface removal techniques. After completing the basic lab session the students must be able to design some project works like game, 3D rotation, screen saver etc. Some sample lab sessions can be as following:- Unit 2 : Scan Conversions Algorithm (10 Hours) Study of Fundamental Graphics Functions Implementation of Line drawing algorithms: DDA Algorithm, Bresenham's Algorithm Implementation of Circle drawing algorithms: Bresenham's Algorithm, Mid-Point Algorithm Unit 3 : Two-Dimensional Geometric Transformations ( 4 Hours) Simulation of 2D transformation, Rotation and Scaling Write a program to implement Cohen Sutherland line clipping algorithm Unit 4 : Three-Dimensional Geometric Transformation (12 Hours) Write a program to perform shear transformation on a rectangle Write a program to perform 2D Transformation on a line Write a program to draw a car using in build graphics function and translate it from bottom left corner to right bottom corner of screen Write a program to draw a cube using in build library function and perform 3D transformations o Translations in x, y, z directions o Rotation by angle 450 about z axis, rotation by 600 about y-axis in succession. o Scaling in x-direction by a factor of 2, scaling in y- direction by a factor of 3 4

21 Unit 5 : 3D Objects Representation ( 4 Hours) Implementation of polygon tables. Write a program to draw Bezier curve, sphere Unit 7 : Visible Surface Detections (10 Hours) Back face detection:- Implementation of Depth Buffer, A Buffer, Scan-Line algorithm Implementation of rotation of 3D cube. Unit 10 : Introduction to OpenGL (5 Hours) Event driven programming Point, Line and Polygon Drawing 3D objects 5

22 Model Question Tribhuvan University Institute of Science and Technology Course Title: Computer Graphics Full Marks: 60 Course No: CSC 209 Pass Marks: 24 Level: B. Sc CSIT Second Year/ Third Semester Time: 3 Hrs Section A Long Answer Questions Attempt any TWO questions [ 2 10 = 20] 1. Explain the working details of DDA algorithm? Explain. Digitize a line with end points A(6,12) and B(10,5) using Bresenham s line drawing algorithm. [5 + 5] 2. How can polygons be clipped? Why is Phong shading also called Normal Vector Interpolation scheme? Explain. [5 + 5] 3. Given a window bordered by (1,2) at the lower left and (16,12) at the upper right, give the screen coordinates of a triangle with vertices (3,2), (10,7.5) and (5,5) when mapped into a viewport with corners (100,100) and (400,200). Provide accurate illustrations of the window, viewport, and the untransformed and transformed triangles with your answer. [10] Section B Short Answer Questions Attempt any EIGHT questions [8 5 = 40] 4. How to animate a two dimensional figure using transformations? Explain with example. [5] 5. Remember in screen coordinates y increases as you go down. [5] 6. What are the key issues prevalent in producing a Virtual reality scene? Describe the Binary Space Partition tree. [2 + 3] 7. How can a polygon surface be filled using the Flood fill approach? Explain. [5] 8. What is the significance of vanishing points in Perspective Projection? Explain. [5] 9. Explain ambient light, diffuse reflection and specular reflection with examples. [5] 10. Compute the midpoint of the Bezier Curve with control points p0 = (0,0,1), p1 = (1,0,1) and p2 = (1,2,0). [5] 11. How does a polygon can be created in OpenGL? Illustrate with an example. [5] 12. How does a video controller and a frame buffer jointly collaborate to produce graphical display on the screen, in case of a Raster Display? [5] 13. Write short notes on (Any TWO) [ ] a. Polygon Tables b. Augmented Reality c. Painter s algorithm 6

23 Syllabus for Statistics (B.Sc. CSIT) program Tribhuvan University Institute of Science & Technology(IOST) Level: B.Sc. Full Marks: Course Title: Statistics II Pass Marks: Course Code: STA 210 Credit Hrs : 3 Nature of the Course: Theory and Practical Course objectives: To impart the theoretical as well as practical knowledge of estimation, testing of hypothesis, application of parametric and non-parametric statistical tests, design of experiments, multiple regression analysis, and basic concept of stochastic process with special focus to data/problems related with computer science and information technology. 1. Sampling Distribution and Estimation [6] Sampling distribution of mean and proportion; Concept of Central Limit Theorem; Concept of inferential Statistics; point estimation; Properties of a Good estimator: unbiasedness, consistency, efficiency and sufficiency; Methods of estimation: Maximum likelihood estimation, Method of moments; Interval estimation: Confidence interval and confidence coefficient, confidence limits, confidence interval of mean for normal population. Confidence interval for proportion; Determination of sample size, relationship of sample size with desired level of error. Problems and illustrative examples related to computer Science and IT 2. Testing of hypothesis [8] Types of statistical hypotheses null and alternative hypothesis, type I and type II errors, level of significance, critical value and critical region, power of the test, concept of p-value and use of p - value in decision making, steps used in testing of hypothesis, one sample tests for mean of normal population (for known and unknown variance), test for single proportion, test for difference between two means and two proportions, paired sample t-test; Linkage between confidence interval and testing of hypothesis; Assumptions for applying independent t-test, paired t-test; Test of equality of two variances Problems and illustrative examples related to computer Science and IT 3. Non parametric test [8] Parametric vs. non-parametric test; Needs of applying non-parametric tests; One-sample test: Run test, Binomial test, Kolmogorov Smirnov test; Two independent sample test: Median test, Kolmogorov-Smirnov test, Wilcoxon Mann Whitney test, Chi-square test; Paired-sample test: 1

24 Wilcoxon signed rank test; Cochran s Q test; Friedman two way analysis of variance test; Kruskal Wallis test. Problems and illustrative examples related to computer Science and IT 4. Multiple correlation and regression [6] Multiple and partial correlation; Introduction of multiple linear regression; Least square estimation of parameters; Properties of least square estimators; Matrix approach to multiple linear regression; Hypothesis testing of multiple regression(upto two independent variables): Test of significance of regression, test of individual regression coefficient; Model adequacy test: Residual analysis, influential observation, multicollinearity; Coefficient of determination, Adjusted R 2, and their interpretations. Problems and illustrative examples related to computer Science and IT 5. Design of experiment [10] Basic terminologies of experimental design; Basic principles of experimental designs; Completely Randomized Design (CRD): Statistical analysis of CRD, ANOVA table, Advantages and disadvantages, concept of multiple comparisons; Randomized Block Design (RBD): Statistical analysis of RBD for one observation per experimental unit, ANOVA table, Efficiency of RBD relative to CRD, Estimations of missing value (one observation only), Advantages and disadvantages; Latin Square Design (LSD): Statistical analysis of m x m LSD for one observation per experimental unit, ANOVA table, Estimation of missing value in LSD (one observation only), Efficiency of LSD relative to RBD, Advantage and disadvantages. Problems and illustrative examples related to computer Science and IT 6. Stochastic Process [7] Definition and classification; Markov Process: Markov chain, Matrix approach, Steady- State distribution; Counting process: Binomial process, Poisson process; Simulation of stochastic process; Queuing system: Main component of queuing system, Little s law; Bernoulli single server queuing process: system with limited capacity; M/M/1 system: Evaluating the system performance. 2

25 Practical (Computational Statistics): [15] Practical problems to be covered in the Computerized Statistics laboratory: Practical problems S. No. Title of the practical problems (Using any statistical software such as SPSS, STATA etc. whichever convenient). Sampling distribution, random number generation, and computation of 1 sample size No. of practical problems 1 2 Methods of estimation(including interval estimation) 1 3 Parametric tests (covering most of the tests) 3 4 Non-parametric test(covering most of the tests) 3 5 Partial correlation 1 6 Multiple regression 1 7 Design of Experiments 3 Stochastic process 2 Total number of practical problems 15 Text Books: 1. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, & Keying Ye(2012). Probability & Statistics for Engineers & Scientists. 9 th Ed., Printice Hall. 2. Michael Baron (2013). Probability and Statistics for Computer Scientists. 2 nd Ed., CRC Press, Taylor & Francis Group, A Chapman & Hall Book. Reference Books: 1. Douglas C. Montgomery & George C. Runger(2003). Applied Statistics and Probability for Engineers. 3 rd Ed., John Willey and Sons, Inc. 2. Sidney Siegel, & N. John Castellan, Jr. Nonparametric Statistics for the Behavioral Sciences, 2 nd Ed., McGraw Hill International Editions. 3

26 Tribhuvan University Institute of Science and Technology Model Question Bachelor Level/Second Year/Third Semester/Science Full Marks: 60 Computer Science and Information Technology STA 210 Pass Marks: 24 (Statistics II) Time : 3 Hours Candidates are required to give their answers in their own words as far as practicable. All notations have the usual meanings. Group A Attempt any Two questions (2 10 = 20) 1. Suppose a population of 4 computers with their lifetimes 3, 5, 7 & 9 years. Comment on the population distribution. Assuming that you sample with replacement, select all possible samples of n = 2, and construct sampling distribution of mean and compare the population distribution and sampling distribution of mean. Compare population mean versus mean of all sample means, and population variance versus variance of sample means and comment on them with the support of theoretical consideration if any. 2. A computer manager is keenly interested to know how efficiency of her new computer program depends on the size of incoming data and data structure. Efficiency will be measured by the number of processed requests per hour. Data structure may be measured on how many tables were used to arrange each data set. All the information was put together as follows. Data size(gigabytes) Number of tables Processed requests Identify which one is dependent variable? Fit the appropriate multiple regression model and provide problem specific interpretations of the fitted regression coefficients. 3. State and explain the mathematical model for randomized complete block design. Explain all the steps to be adopted to carry out the analysis, and finally prepare the ANOVA table. Group B Attempt any Eight questions (8 5 = 40) 4. In order to ensure efficient usage of a server, it is necessary to estimate the mean number of concurrent users. According to records, the average number of concurrent users at 100 randomly selected times is 37.7, with a sample standard deviation of 9.2. At the 1% level of significance, do these data provide considerable evidence that the mean number of concurrent users is greater than 35? Draw your conclusion based on your result. 1

27 5. A sample of 250 items from lot A contains 10 defective items, and a sample of 300 items from lot B is found to contain 18 defective items. At a significance level α = 0.05, is there a significant difference between the quality of the two lots? 6. Modern servers and anti-spam filters attempt to identify spam s and direct them to a junk folder. There are various ways to detect spam, and research still continues. In this regard, an information security officer tries to confirm that the chance for an to be spam depends on whether it contains images or not. The following data were collected on n = 1000 random messages. Image containing status Spam status With images No images Total Spam No spam Total Assess whether being spam and containing images are independent factors at 1% level of significance. 7. Two computer makers, A and B, compete for a certain market. Their users rank the quality of computers on a 4-point scale as Not satisfied, Satisfied, Good quality, and Excellent quality, will recommend to others. The following counts were observed: Computer maker Not satisfied Satisfied Good quality Excellent quality A B Is there a significant difference in customer satisfaction of the computers produced by A and by B using Mann-Whitney U test at 5% level of significance. 8. Define queuing systems with suitable examples. Also explain the main components of queuing systems in brief. 9. In some town, each day is either sunny or rainy. A sunny day is followed by another sunny day with probability 0.7, whereas a rainy day is followed by a sunny day with probability 0.4. Weather conditions in this problem represent a homogeneous Markov chain with 2 states: state 1 = sunny and state 2 = rainy. Transition probability matrix of sunny and rainy days is given below. P Compute the probability of sunny days and rainy days using the steady-state equation for this Markov chain. 2

28 10. Consider a completely randomized design with 4 treatments with 7 observations in each. For the ANOVA summary table below, fill in all the missing results. Also indicate your statistical decision. Source Degrees of freedom Sum of Squares Mean Sum of Squares F-ratio Treatments? SSA =? 70 F =? Error? SSE = 590? Total? SST =? 11. Following are the scores obtained by 10 university staffs on the computer proficiency skills before training and after training. It was assumed that the proficiency of computer skills is expected to be increased after training. Staffs Score 1 Before training After training Test at 5% level of significance whether the training is effective to improve the computer proficiency skills applying appropriate statistical test. Assume that the given score follows normal distribution. 12. Write short notes on the following. a) Concept of Latin Square Design b) Multiple correlation 3