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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)
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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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