Introduction to Algorithms 2nd Edition by Charles E Leiserson, Ronald L Rivest, Clifford Stein, Thomas H Cormen ISBN 0262032937 9780262032933

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ISBN 10: 0262032937 
ISBN 13: 9780262032933
Author: Charles E Leiserson, Ronald L Rivest, Clifford Stein, Thomas H Cormen

There are books on algorithms that are rigorous but incomplete and others that cover masses of material but lack rigor. Introduction to Algorithms combines rigor and comprehensiveness.

The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

The first edition became the standard reference for professionals and a widely used text in universities worldwide. The second edition features new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming, as well as extensive revisions to virtually every section of the book. In a subtle but important change, loop invariants are introduced early and used throughout the text to prove algorithm correctness. Without changing the mathematical and analytic focus, the authors have moved much of the mathematical foundations material from Part I to an appendix and have included additional motivational material at the beginning.

Introduction to Algorithms 2nd Table of contents:

• Introduction to Algorithms

  • 1.1 What is an Algorithm?
  • 1.2 Importance and Applications of Algorithms
  • 1.3 Analyzing Algorithms: Efficiency and Complexity
  • 1.4 The Role of Algorithms in Computer Science

• Algorithm Design and Problem-Solving Techniques

  • 2.1 Problem-Solving Strategies
  • 2.2 Algorithm Design Paradigms
  • 2.3 Divide and Conquer
  • 2.4 Greedy Algorithms
  • 2.5 Dynamic Programming
  • 2.6 Backtracking

• Complexity Analysis

  • 3.1 Time Complexity: Big O Notation
  • 3.2 Space Complexity
  • 3.3 Worst-case, Best-case, and Average-case Analysis
  • 3.4 Analyzing Recursive Algorithms

• Sorting and Searching Algorithms

  • 4.1 Sorting Algorithms: Bubble Sort, Selection Sort, and Insertion Sort
  • 4.2 Advanced Sorting Algorithms: Merge Sort, Quick Sort, and Heap Sort
  • 4.3 Linear Search vs Binary Search
  • 4.4 Searching Algorithms: Depth-First Search (DFS) and Breadth-First Search (BFS)

• Data Structures and Their Role in Algorithm Design

  • 5.1 Arrays, Linked Lists, and Strings
  • 5.2 Stacks and Queues
  • 5.3 Hash Tables
  • 5.4 Trees: Binary Trees, AVL Trees, and Binary Search Trees (BST)
  • 5.5 Graphs: Representation and Traversal Algorithms

• Divide and Conquer Algorithms

  • 6.1 Understanding Divide and Conquer
  • 6.2 Merge Sort and Quick Sort
  • 6.3 Matrix Multiplication Using Divide and Conquer
  • 6.4 Closest Pair of Points Problem

• Greedy Algorithms

  • 7.1 Introduction to Greedy Algorithms
  • 7.2 The Greedy Choice Property
  • 7.3 Applications of Greedy Algorithms: Activity Selection Problem, Huffman Coding
  • 7.4 Analyzing Greedy Algorithms for Correctness

• Dynamic Programming

  • 8.1 Introduction to Dynamic Programming
  • 8.2 Overlapping Subproblems and Optimal Substructure
  • 8.3 Classic Problems: Fibonacci Sequence, Knapsack Problem
  • 8.4 Memoization and Tabulation Techniques

• Graph Algorithms

  • 9.1 Introduction to Graph Theory
  • 9.2 Graph Representation: Adjacency Matrix and List
  • 9.3 Shortest Path Algorithms: Dijkstra’s and Bellman-Ford
  • 9.4 Minimum Spanning Tree: Prim’s and Kruskal’s Algorithms
  • 9.5 Network Flow Algorithms: Ford-Fulkerson Algorithm

• Backtracking and Branch-and-Bound

  • 10.1 Introduction to Backtracking Algorithms
  • 10.2 Solving Problems Using Backtracking: N-Queens Problem, Sudoku Solver
  • 10.3 Branch-and-Bound Techniques
  • 10.4 The Traveling Salesman Problem

• NP-Completeness

  • 11.1 What is NP-Completeness?
  • 11.2 NP-Complete and NP-Hard Problems
  • 11.3 Cook’s Theorem and Reductions
  • 11.4 Approximation Algorithms and Heuristics

• String Matching and Text Processing

  • 12.1 Naive String Matching
  • 12.2 Rabin-Karp Algorithm
  • 12.3 Knuth-Morris-Pratt (KMP) Algorithm
  • 12.4 Trie Data Structure for String Matching

• Randomized Algorithms

  • 13.1 Introduction to Randomized Algorithms
  • 13.2 Randomized Quicksort
  • 13.3 Monte Carlo and Las Vegas Algorithms
  • 13.4 Applications of Randomized Algorithms

• Advanced Topics in Algorithms

  • 14.1 Approximation Algorithms
  • 14.2 Parallel Algorithms
  • 14.3 Online Algorithms
  • 14.4 MapReduce and Distributed Algorithms

• Applications of Algorithms

  • 15.1 Algorithms in Data Science and Machine Learning
  • 15.2 Algorithms in Network Routing and Security
  • 15.3 Algorithms in Computational Biology and Bioinformatics
  • 15.4 Algorithms in Cryptography

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