Introduction to The Design and Analysis of Algorithms

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Introduction to The Design and Analysis of Algorithms


Introduction to The Design and Analysis of Algorithms



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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