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Design and Analysis of Algorithms
Practical project ideas and implementations for hands-on learning
BRUTE FORCE AND EXHAUSTIVE SEARCH
Brute Force and Exhaustive Search
Closest-Pair and Convex-Hull Problems by Brute Force
Depth-First Search and Breadth-First Search
Exhaustive Search
Selection Sort and Bubble Sort
Sequential Search and Brute-Force String Matching
COPING WITH THE LIMITATIONS OF ALGORITHM POWER
Algorithms for Solving Nonlinear Equations
Approximation Algorithms for NP-Hard Problems
Approximation Algorithms for the Knapsack Problem
Approximation Algorithms for the Traveling Salesman Problem
Backtracking
Branch-and-Bound
Coping with the Limitations of Algorithm Power
DECREASE AND CONQUER
Algorithms for Generating Combinatorial Objects
Decrease and Conquer
Decrease by a Constant Factor Algorithms
Insertion Sort
Topological Sorting
Variable Size Decrease Algorithms
DIVIDE AND CONQUER
Binary Tree Traversals and Related Properties
Convex Hull Problems by Divide and Conquer
Divide and Conquer
Mergesort
Multiplication of Large Integers
Quicksort
Strassen’s Matrix Multiplication
The Closest Pair Problem by Divide and Conquer
DYNAMIC PROGRAMMING
Dynamic Programming
Dynamic Programming: Three Basic Examples
Optimal Binary Search Trees
The Knapsack Problem and Memory Functions
Warshall’s and Floyd’s Algorithms
FUNDAMENTALS OF THE ANALYSIS OF ALGORITHM EFFICIENCY
Algorithm Visualization
Asymptotic Notations and Basic Efficiency Classes
Computing the nth Fibonacci Number
Empirical Analysis of Algorithms
Mathematical Analysis of Nonrecursive Algorithms
Mathematical Analysis of Recursive Algorithms
The Analysis Framework
GREEDY TECHNIQUE
Dijkstra’s Algorithm
Greedy Technique
Huffman Trees and Codes
Kruskal’s Algorithm
Prim’s Algorithm
INTRODUCTION
Algorithm Design Techniques
Analyzing an Algorithm
Ascertaining the Capabilities of the Computational Device
Coding an Algorithm
Designing an Algorithm and Data Structures
Fundamental Data Structures
Fundamentals of Algorithmic Problem Solving
Introduction to the Design and Analysis of Algorithms
Methods of Specifying an Algorithm
Proving an Algorithm’s Correctness
What Is an Algorithm?
ITERATIVE IMPROVEMENT
Iterative Improvement
Maximum Matching in Bipartite Graphs
The Iterative Maximum-Flow Problem
The Simplex Method
The Stable Marriage Problem
LIMITATIONS OF ALGORITHM POWER
Challenges of Numerical Algorithms
Decision Trees Algorithms
Limitations of Algorithm Power
Lower-Bound Arguments
P, NP, and NP-Complete Problems
SPACE AND TIME TRADE-OFFS
B-Trees Algorithms
Input Enhancement in String Matching: Horspool’s and Boyer-Moore Algorithms
Open and Closed Hashing
Sorting by Counting
Space and Time Trade-Offs
TRANSFORM AND CONQUER
Balanced Search Trees: AVL Trees and 2–3 Trees
Gaussian Elimination
Heaps and Heapsort
Horner’s Rule and Binary Exponentiation
Presorting
Problem Reduction
Transform and Conquer