Programming The derivation of algorithms 1st Edition by Kaldewaij ISBN 0132041081 9780132041089

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ISBN 10: 0132041081
ISBN 13: 9780132041089
Author: Kaldewaij 

Programming The derivation of algorithms 1st Edition Table of contents:

Part I: Foundations of Algorithm Design

2. The Concept of an Algorithm

   • Defining Algorithms: Structure and Properties
   • Algorithms in the Context of Problem Solving
   • Types of Algorithms: Exact vs. Approximate Solutions
   • Formalizing Algorithm Specifications

3. Basic Techniques for Deriving Algorithms

   • Top-Down and Bottom-Up Design Approaches
   • Stepwise Refinement in Algorithm Development
   • Using Pseudocode and Flowcharts
   • Proof of Correctness: Induction and Other Techniques

4. Problem Decomposition and Divide-and-Conquer

   • The Importance of Decomposition in Problem Solving
   • Divide-and-Conquer Algorithms: Theory and Examples
   • Recursion and the Role of Recursive Algorithms
   • Analyzing Divide-and-Conquer Algorithms

Part II: Algorithm Design Methods

5. Iterative Methods and Loops

   • Iteration as a Tool for Algorithm Derivation
   • Using Loops and Recursion for Problem Solving
   • Convergence and Termination Conditions in Iterative Algorithms
   • Example Problems: Sorting, Searching, and Counting

6. Greedy Algorithms

   • The Greedy Strategy for Algorithm Design
   • Characterizing Greedy Algorithms: Feasibility and Optimality
   • Classic Examples of Greedy Algorithms
   • Limitations and Application Scope of Greedy Methods

7. Dynamic Programming

   • Understanding Dynamic Programming Concepts
   • Overlapping Subproblems and Optimal Substructure
   • Examples of Dynamic Programming Algorithms
   • Analyzing Time Complexity of Dynamic Programming Solutions

8. Backtracking and Brute Force Algorithms

   • The Backtracking Approach: Exploring Possible Solutions
   • Brute Force Algorithms: Simplicity vs. Efficiency
   • Common Problems Solved by Backtracking
   • Optimizing Brute Force Methods

Part III: Advanced Topics in Algorithm Derivation

9. Graph Algorithms

   • Representing Graphs and Their Applications
   • Traversal Algorithms: Depth-First and Breadth-First Search
   • Shortest Path Algorithms: Dijkstra and Bellman-Ford
   • Network Flow Algorithms and Their Applications

10. Randomized Algorithms

    • Introduction to Randomized Algorithms
    • The Role of Probability in Algorithm Design
    • Monte Carlo and Las Vegas Algorithms
    • Analyzing the Effectiveness of Randomization in Algorithms

11. Approximation Algorithms

    • When Exact Solutions Are Infeasible
    • Design and Analysis of Approximation Algorithms
    • Performance Guarantees and Approximability
    • Applications of Approximation Algorithms in NP-Hard Problems

Part IV: Analyzing and Refining Algorithms

12. Time Complexity and Efficiency

    • Understanding Time Complexity and Big-O Notation
    • Best, Worst, and Average Case Analysis
    • Techniques for Improving Algorithm Efficiency
    • Case Studies: Optimizing Algorithms for Practical Use

13. Space Complexity and Memory Management

    • The Importance of Space Complexity
    • Memory Management in Algorithm Derivation
    • Trade-offs Between Time and Space Efficiency
    • Techniques for Optimizing Space Complexity

14. Correctness and Formal Verification

    • Proving the Correctness of Algorithms
    • Formal Methods and Verification Techniques
    • Inductive Proofs and Invariants
    • The Role of Testing and Debugging in Algorithm Development

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