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Computer Sotware and Inormation Technology Engineering CSE IT

Design and Analysis of Algorithms - CS6402






Introduction to The Design and Analysis of Algorithms by Anany Levitin

Chapter 1 Introduction

-> Introduction to the Design and Analysis of Algorithms
-> What Is an Algorithm?
-> Fundamentals of Algorithmic Problem Solving
-> Ascertaining the Capabilities of the Computational Device
-> Algorithm Design Techniques
-> Designing an Algorithm and Data Structures
-> Methods of Specifying an Algorithm
-> Proving an Algorithm’s Correctness
-> Analyzing an Algorithm
-> Coding an Algorithm
-> Important Problem Types in Algorithms Analysis
-> Fundamental Data Structures

Chapter 2 Fundamentals of the Analysis of Algorithm Eficiency

-> The Analysis Framework
-> Asymptotic Notations and Basic Efficiency Classes
-> Mathematical Analysis of Non recursive Algorithms
-> Mathematical Analysis of Recursive Algorithms
-> Example: Computing the nth Fibonacci Number
-> Empirical Analysis of Algorithms
-> Algorithm Visualization

Chapter 3 Brute Force and Exhaustive Search

-> Brute Force and Exhaustive Search
-> Selection Sort and Bubble Sort
-> Sequential Search and Brute-Force String Matching
-> Closest-Pair and Convex-Hull Problems by Brute Force
-> Exhaustive Search
-> Depth-First Search and Breadth-First Search

Chapter 4 Decrease and Conquer

-> Decrease and Conquer
-> Insertion Sort
-> Topological Sorting
-> Algorithms for Generating Combinatorial Objects
-> Decrease by a Constant Factor Algorithms
-> Variable Size Decrease Algorithms

Chapter 5 Divide and Conquer

-> Divide and Conquer
-> Mergesort
-> Quicksort
-> Binary Tree Traversals and Related Properties
-> Multiplication of Large Integers
-> Strassen’s Matrix Multiplication
-> The Closest Pair Problem by Divide and Conquer
-> Convex Hull Problems by Divide and Conquer

Chapter 6 Transform and Conquer

-> Transform and Conquer
-> Presorting
-> Gaussian Elimination
-> Balanced Search Trees: AVL Trees and 2-3 Trees
-> Heaps and Heapsort
-> Horner’s Rule and Binary Exponentiation
-> Problem Reduction

Chapter 7 Space and Time Trade Offs

-> Space and Time Trade-Offs
-> Sorting by Counting
-> Input Enhancement in String Matching: Horspool’s and Boyer-Moore Algorithm
-> Open and Closed Hashing
-> B-Trees Algorithms

Chapter 8 Dynamic Programming

-> Dynamic Programming
-> Dynamic Programming: Three Basic Examples
-> The Knapsack Problem and Memory Functions
-> Optimal Binary Search Trees
-> Warshall’s and Floyd’s Algorithms

Chapter 9 Greedy Technique

-> Greedy Technique
-> Prim’s Algorithm
-> Kruskal’s Algorithm
-> Dijkstra’s Algorithm
-> Huffman Trees and Codes

Chapter 10 Iterative Improvement

-> Iterative Improvement
-> The Simplex Method
-> The Iterative Maximum-Flow Problem
-> Maximum Matching in Bipartite Graphs
-> The Stable Marriage Problem

Chapter 11 Limitations of Algorithm Power

-> Limitations of Algorithm Power
-> Lower-Bound Arguments
-> Decision Trees algorithms
-> P , NP , and NP-Complete Problems
-> Challenges of Numerical Algorithms

Chapter 12 Coping with the Limitations of Algorithm Power

-> Coping with the Limitations of Algorithm Power
-> Backtracking
-> Branch-and-Bound
-> Approximation Algorithms for NP -Hard Problems
-> Approximation Algorithms for the Traveling Salesman Problem
-> Approximation Algorithms for the Knapsack Problem
-> Algorithms for Solving Nonlinear Equations

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