Makrehchi M. Efficient Algorithm Design. Unlock the power of algorithms...2024
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Description:
Textbook in PDF format
Master advanced algorithm design techniques to tackle complex programming challenges and optimize application performance
Key FeaturesDevelop advanced algorithm design skills to solve modern computational problems
Learn state-of-the-art techniques to deepen your understanding of complex algorithms
Apply your skills to real-world scenarios, enhancing your expertise in today's tech landscape
Book DescriptionEfficient Algorithm Design redefines algorithms, tracing the evolution of computer science as a discipline bridging natural science and mathematics. Author Masoud Makrehchi, PhD, with his extensive experience in delivering publications and presentations, explores the duality of computers as mortal hardware and immortal algorithms.
The book guides you through essential aspects of algorithm design and analysis, including proving correctness and the importance of repetition and loops. This groundwork sets the stage for exploring algorithm complexity, with practical exercises in design and analysis using sorting and search as examples. Each chapter delves into critical topics such as recursion and dynamic programming, reinforced with practical examples and exercises that link theory with real-world applications. What sets this book apart is its focus on the practical application of algorithm design and analysis, equipping you to solve real programming challenges effectively.
By the end of this book, you’ll have a deep understanding of algorithmic foundations and gain proficiency in designing efficient algorithms, empowering you to develop more robust and optimized software solutions.
What you will learnGain skills in advanced algorithm design for better problem-solving
Understand algorithm correctness and complexity for robust software
Apply theoretical concepts to real-world scenarios for practical solutions
Master sorting and search algorithms, understanding their synergy
Explore recursion and recurrence for complex algorithmic structures
Leverage dynamic programming to optimize algorithms
Grasp the impact of data structures on algorithm efficiency and design
Who this book is forIf you’re a software engineer, computer scientist, or a student in a related field looking to deepen your understanding of algorithm design and analysis, this book is tailored for you. A foundation in programming and a grasp of basic mathematical concepts is recommended. It's an ideal resource for those already familiar with the basics of algorithms who want to explore more advanced topics. Data scientists and AI developers will find this book invaluable for enhancing their algorithmic approaches in practical applications.
Efficient Algorithm Design
Contributors
About the author
About the reviewer
Preface
Who this book is for
What this book covers
To get the most out of this book
Download the example code files
Conventions used
Get in touch
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Download a free PDF copy of this book
Foundations of Algorithm Analysis
Introduction to Algorithm Analysis
Understanding algorithms and problem-solving
The rationale for algorithm analysis
The dual dimensions of algorithm analysis – efficiency and correctness
Summary
Mathematical Induction and Loop Invariant for Algorithm Correctness
Mathematical induction
Loop invariants for the correctness of algorithms
Summary
References and further reading
Rate of Growth for Complexity Analysis
Unpacking the rate of growth in algorithms
Constant growth
Sub-linear growth
Linear growth
Non-linear growth
Asymptotic notations
Simplification rules in asymptotic notation
Asymptotic bounds
Asymptotic upper bound (O notation)
Asymptotic lower bound (-notation)
Asymptotic tight bound (-notation)
Confronting the unsolvable NP-hard problems
Complexities of NP, NP-complete, and NP-hard
Summary
References and further reading
Recursion and Recurrence Functions
Recursive algorithms
The basics of recursion
Types of recursion
Recurrence functions
Subtractive recurrence functions
Divide-and-conquer recurrence functions
Unfolding recurrence functions
Summary
References and further reading
Solving Recurrence Functions
The substitution method
Iteration approach or unrolling the recurrence
Guessing and induction approach
Variable change approach
Recursion tree as a visualization technique
The master theorem
Case 1 – dominance of recursive calls or leaf-heavy recursion trees
Case 2 – balanced growth or balanced recursion trees
Case 3 – dominance of non-recursive work or root-heavy recursion trees
Modified master theorem to solve subtracting recurrence functions
Master theorem limitations
Alternative approaches
Beyond the master theorem – the Akra-Bazzi method
Why does it work? Intuition behind Akra-Bazzi
Summary
References and further reading
Deep Dive in Algorithms
Sorting Algorithms
The taxonomy of sorting algorithms
Comparison
Recursion
Adaptability
Inversion
Memory usage
Iterative sorting algorithms
Bubble sort
Selection sort
Insertion sort
Recursive sorting algorithms
Merge sort
Quick sort
Non-comparison-based sorting
Counting sort
Radix sort
Bucket sort
Summary
References and further reading
Search Algorithms
Properties of search algorithms
Linear-time and logarithmic search algorithms
Linear or sequential search
Sub-linear search
Hashing
Hash functions
Constant time search using hashing
Summary
References and further reading
Symbiotic Relationship between Sort and Search
Striking the right balance between sorting and searching
Symbiotic link between sorting and searching
The efficiency dilemma – to organize or not?
Think like a computer scientist
Summary
References and further reading
Randomized Algorithms
A review of probabilistic algorithms
Non-deterministic algorithms
Analysis of randomized algorithms
Monty Hall problem
Birthday paradox
Hiring secretary problem
Case studies
Optimal selection in an online dating app
Finding the closest parking spot
Summary
References and further reading
Dynamic Programming
Dynamic programming versus divide-and-conquer
Optimal substructure
Overlapping subproblems
Exploring dynamic programming
Top-down versus bottom-up approaches for dynamic programming
Solving the 0/1 knapsack problem using dynamic programming
Limitations of dynamic programming
Greedy algorithms – an introduction
Traveling salesman problem
Heuristics and their role in greedy algorithms
Summary
References and further reading
Fundamental Data Structures
Landscape of Data Structures
Taxonomy of data structures
Physical versus logical data structures
Primitive versus composite data structures
Linear versus non-linear data structures
Static versus dynamic memory allocation
Sequential versus random access
Abstract data types
Dictionaries
Insertion
Search
Update
Deletion
Summary
References and further reading
Linear Data Structures
Lists
Arrays
Linked lists
Skip lists
Insertion in skip lists
Search in skip lists
Stacks
Queue
Deque
Summary
References and further reading
Non-Linear Data Structures
Introduction to non-linear data structures
Graphs
Graphs representation
Traversing graphs
Trees
Different types of trees and their properties
Tree representation
BSTs
Heaps
Heap operations
Heapsort
Summary
References and further reading
Next Steps
Tomorrow’s Algorithms
Learning from the past
Scalability
Context awareness
Moral responsibility
Moral consciousness in software practice
Final words
References and further reading
Index