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Computer Sotware and Inormation Technology Engineering CSE IT
Design and Analysis of Algorithms
 CS6402
INTRODUCTION
BRUTE FORCE AND DIVIDE
DYNAMIC PROGRAMMING AND GREEDY TECHNIQUE
ITERATIVE IMPROVEMENT
COPING WITH THE LIMITATIONS OF ALGORITHM POWER
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
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Methods of Specifying an Algorithm
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Proving an Algorithm’s Correctness
:
Analyzing an Algorithm
:
Coding an Algorithm
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Important Problem Types in Algorithms Analysis
:
Fundamental Data Structures
Chapter 2 Fundamentals of the Analysis of Algorithm Eficiency
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The Analysis Framework
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Asymptotic Notations and Basic Efficiency Classes
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Mathematical Analysis of Non recursive Algorithms
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Mathematical Analysis of Recursive Algorithms
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Example: Computing the nth Fibonacci Number
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Empirical Analysis of Algorithms
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Algorithm Visualization
Chapter 3 Brute Force and Exhaustive Search
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Brute Force and Exhaustive Search
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Selection Sort and Bubble Sort
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Sequential Search and BruteForce String Matching
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ClosestPair and ConvexHull Problems by Brute Force
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Exhaustive Search
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DepthFirst Search and BreadthFirst Search
Chapter 4 Decrease and Conquer
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Decrease and Conquer
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Insertion Sort
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Topological Sorting
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Algorithms for Generating Combinatorial Objects
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Decrease by a Constant Factor Algorithms
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Variable Size Decrease Algorithms
Chapter 5 Divide and Conquer
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Divide and Conquer
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Mergesort
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Quicksort
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Binary Tree Traversals and Related Properties
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Multiplication of Large Integers
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Strassen’s Matrix Multiplication
:
The Closest Pair Problem by Divide and Conquer
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Convex Hull Problems by Divide and Conquer
Chapter 6 Transform and Conquer
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Transform and Conquer
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Presorting
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Gaussian Elimination
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Balanced Search Trees: AVL Trees and 23 Trees
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Heaps and Heapsort
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Horner’s Rule and Binary Exponentiation
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Problem Reduction
Chapter 7 Space and Time Trade Offs
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Space and Time TradeOffs
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Sorting by Counting
:
Input Enhancement in String Matching: Horspool’s and BoyerMoore Algorithm
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Open and Closed Hashing
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BTrees Algorithms
Chapter 8 Dynamic Programming
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Dynamic Programming
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Dynamic Programming: Three Basic Examples
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The Knapsack Problem and Memory Functions
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Optimal Binary Search Trees
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Warshall’s and Floyd’s Algorithms
Chapter 9 Greedy Technique
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Greedy Technique
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Prim’s Algorithm
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Kruskal’s Algorithm
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Dijkstra’s Algorithm
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Huffman Trees and Codes
Chapter 10 Iterative Improvement
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Iterative Improvement
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The Simplex Method
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The Iterative MaximumFlow Problem
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Maximum Matching in Bipartite Graphs
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The Stable Marriage Problem
Chapter 11 Limitations of Algorithm Power
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Limitations of Algorithm Power
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LowerBound Arguments
:
Decision Trees algorithms
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P , NP , and NPComplete Problems
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Challenges of Numerical Algorithms
Chapter 12 Coping with the Limitations of Algorithm Power
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Coping with the Limitations of Algorithm Power
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Backtracking
:
BranchandBound
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Approximation Algorithms for NP Hard Problems
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Approximation Algorithms for the Traveling Salesman Problem
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Approximation Algorithms for the Knapsack Problem
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Algorithms for Solving Nonlinear Equations