Makrehchi M. Efficient Algorithm Design: Unlock the Power of Algorithms to Optimize Computer Programming

Packt Publishing Pvt. Ltd., 2024. — 873 p.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, Ph.D., 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 learning 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.Who this book is for?What this book covers.To get the most out of this book.
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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.Mathematical Induction and Loop Invariant for Algorithm Correctness.
Mathematical induction.
Loop invariants for the correctness of algorithms.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.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.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? The intuition behind Akra-Bazzi.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.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.References and further reading.
Symbiotic Relationship between Sort and Search.
Striking the right balance between sorting and searching.
The symbiotic link between sorting and searching.
The efficiency dilemma – to organize or not?
Think like a computer scientist.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.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.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.References and further reading.
Linear Data Structures.
Lists.
Arrays.
Linked lists.
Skip lists.
Insertion in skip lists.
Search in skip lists.
Stacks.
Queue.
Deque.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.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.