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Analysis & Design of Algorithms

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Course Name        MCA (Master of Computer Application)

Subject Code       MC0080 (Analysis & Design of Algorithms)

Get Questions        PART - A    PART - B    PART - C

Analysis & Design of Algorithms Syllabus.

Part 1 Elementary Algorithms
Introduction; Notation for expressing algorithms; Role and Notation for comments; Example of an Algorithm; Problems and Instances; Characteristics of an Algorithm; Building Blocks of Algorithms; Procedure and Recursion; Recursion; Outline of Algorithmics.

Part 2 Mathematical Functions & Notations
Introduction; Functions & Notations; Modular Arithmetic / Mod function; Mathematical Expectation in average case analysis; Mathematical Expectation; Concept of Efficiency of an Algorithm; Well known Asymptotic Functions & Notations; The  Notation; The Notation ; The Notation ; The Notation ; Analysis of Algorithms – Simple Examples; Analysis of First – Averages; Well known Sorting Algorithms; Divide and Conquer Technique; Recursive Constructs; Average – Case and Amortized Analysis; Sorting in Linear Time; Medians and Order Statistics.

Part 3 Elementary Data Structures
Introduction; Stacks and queues; Linked lists; Hash tables; Collision resolution by chaining; Binary Search Trees; Red-Black Trees; Rotations; Insertion; Augmenting Data Structures; Determining the rank of an element; Maintaining subtree sizes; How to augment a data structure; Divide-and-Conquer; Integer Multiplication; Binary Search; Sorting; Quick Sort; Matrix Multiplication; Splay tree; Zig Step

Part 4 B – Trees
Introduction; Properties of B – Trees; The height of a B – Tree; Binomial trees; Binomial Heaps; Fibonacci Heaps; Data Structures for Disjoint Set

Part 5 Graph Algorithms
Introduction; NIM/Marienbad Game; Traversing Trees; Depth-First Search; Breadth-First
Search; Best First Search & Minimax Principle; Topological Sort

Part 6 Dynamic Programming
Introduction; The Problem of Making Change; The Principle of Optimality; Chained Matrix Multiplication; Matrix Multiplication using Dynamic Programming

Part 7 Greedy Techniques
Introduction; Some Examples; Formalization of Greedy Technique; Minimum Spanning Tree; Prim‘s Algorithm; Kruskal‘s Algorithm; Djikstra‘s Algorithm

Part 8 Models for Executing Algorithms – : FA
Introduction; Regular Expressions; Regular Languages; Finite Automata

Part 9 Models for Executing Algorithms – II: PDFA & CFG
Introduction; Formal Language & Grammar; Chomsky Classification for Grammar; Context Free Grammar (CFG); Pushdown Automata (PDA)

Part 10 Models for Executing Algorithms – III: TM
Introduction; Prelude to Formal Definition; Turing Machine: Formal Definition and Examples; Instantaneous Description and Transition Diagrams; Some Formal Definitions; Observations; Turing Machine as a Computer of Function

Part 11 Algorithmically Unsolvable Problems
Introduction; Decidable and Undecidable Problems; The Halting Problem; Reduction to Another Undecidable Problem; Undecidability of Post Correspondence Problem; Undecidable Problems for Context Free Languages; Other Undecidable Problems

Part 12 Complexity of Algorithms
Introduction; Notations for the Growth Rates of Functions; Classification of Problems; Reduction, NP-Complete and NP-Hard Problems; Establishing NP-Completeness of Problem
 

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