book

Introduction to Algorithms

by Cuantum Technologies LLC

June 2024

Intermediate to advanced

294 pages

6h 34m

English

Packt Publishing

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Introduction to the BookWho Should Read This BookHow to Use This Book
1.1 What is an Algorithm?1.1.1 Characteristics of a Good Algorithm1.1.2 How Algorithms are Used1.1.3 Brief Summary and Some Points for Further Reflection1.2 Importance of Algorithms in Computer Science1.2.1 Algorithms Power Our Digital World1.2.2 Algorithms Drive Efficiency1.2.3 Algorithms Form the Basis of Advanced Fields1.2.4 The Future Implications and Advancements in Algorithms1.3 Fundamentals of Computational Thinking1.3.1 Decomposition1.3.2 Pattern Recognition1.3.3 Abstraction1.3.4 Algorithmic Thinking1.3.5 Debugging and Iteration1.4 Practice ProblemsProblem 1: Password GeneratorProblem 2: Calendar EventsProblem 3: Building a PyramidProblem 4: Text Compression
2.1 Understanding Pseudocode2.1.1 Flexibility of Pseudocode2.2 Understanding Flowcharts2.3 Translating Real-World Problems into Pseudocode2.4 Practice ProblemsProblem 1Problem 2Problem 3
3.1 Understanding Time Complexity3.1.1 Big O notation3.1.2 Difference between the best-case, average-case, and worst-case time complexity3.2 Understanding Space Complexity3.2.1 Caching/Memoization3.3 Introduction to Big O Notation3.3.1 What is Big O Notation?3.3.2 Common Types of Time Complexities3.3.3 Asymptotic Analysis3.4 Practice ProblemsLinear Search:Sum of Elements:Find Duplicate:Bubble Sort:

4.1 Divide and Conquer Algorithms4.2 Greedy Algorithms4.2.1 What is a Greedy Algorithm?4.2.2 Coin Change Problem4.3 Dynamic Programming Algorithms4.4 Recursive Algorithms4.4.1 Tail Recursion4.5 Practice ProblemsProblem 1: Binary Search (Divide and Conquer)Problem 2: Coin Change (Greedy Algorithm)Problem 3: Fibonacci Series (Dynamic Programming)Problem 4: Sum of Natural Numbers (Recursive Algorithm)Problem 5: QuickSort (Divide and Conquer)Problem 6: Implementing a Stack using Recursion (Recursive Algorithm)
5.1 Linear Search5.1.1 Limitations of Linear Search5.2: Binary Search5.3 Hashing and Hash Tables5.3.1 Collisions5.4 Practice ProblemsProblem 1: Linear SearchProblem 2: Binary SearchProblem 3: HashingProblem 4: Binary Search vs Linear Search
6.1 Bubble Sort6.1.1 When and Why to Use or Not to Use Bubble Sort6.2 Selection Sort6.3 Insertion Sort6.4 Quick Sort6.5 Merge Sort6.6 Heap Sort6.7 Practice Problems1. Implement Bubble Sort2. Analyze Quick Sort's Worst Case3. Merge Sort with Linked Lists4. Heapify an Array5. Stability in Sorting
7.1 Introduction to Graph Theory7.2 Depth-First Search7.3 Breadth-First Search7.3.1 BFS Time Complexity7.4 Dijkstra's Algorithm7.5 A* Search7.5.1 Heuristics in A*7.5.2 Time and Space Complexity7.5.3 Optimality of A Search7.5.4 Real-world Applications of A Search*7.5.5 Variations of A Search*7.5.6 Complexity of A Search*7.6 Practice ProblemsProblem 1: DFS in Maze SolvingProblem 2: Shortest Path in a Grid with BFS
8.1 Arrays8.1.1 Properties and Common Uses of Arrays8.2 Linked Lists8.2.1 Other Types of Linked Lists8.3 Stacks and Queues8.3.1. Stacks8.3.2 Queues8.3.3 Priority Queues and Dequeues8.4 Trees and Graphs8.4.1 Trees8.4.2 Graphs8.4.3 Going Deeper8.5 Practice ProblemsProblem 1: Arrays - Maximum Subarray SumProblem 2: Linked Lists - Reverse a Linked ListProblem 3: Stacks - Valid ParenthesesProblem 4: Trees - Maximum Depth of Binary Tree
9.1 Recursion9.2 Iterative Approaches9.2.1 Iterative Factorial Calculation9.2.2 The Tail Recursion Optimization9.3 Backtracking9.4 Branch and Bound9.4.1 Working Principle of Branch and Bound9.4.2 The Travelling Salesman Problem9.5 Practical Problems1. Recursion: Fibonacci Series2. Iterative Approach: Factorial3. Backtracking: N-Queens Problem4. Branch and Bound: Travelling Salesman Problem
10.1 Algorithms in Databases10.2 Algorithms in Artificial Intelligence10.2.1 Machine Learning Algorithms10.2.2 Search Algorithms10.2.3 How Algorithms Can Power NLP in AI10.2.4 Role of Algorithms in Machine Learning10.3 Algorithms in Network Routing10.3.1 Dijkstra’s Algorithm10.3.2 Bellman-Ford Algorithm10.3.3 Link State Routing Protocol (LSRP)10.4 Practice ProblemsProblem 1: Algorithms in DatabasesProblem 2: Algorithms in Artificial IntelligenceProblem 3: Algorithms in Network Routing

Content preview from Introduction to Algorithms

Chapter 7 Summary

In this chapter, we've discovered the rich and complex field of graph theory and its applied branch, graph algorithms. We've started with an introduction to graphs, describing them as mathematical structures consisting of nodes, also known as vertices, and edges connecting these nodes. Graphs are ubiquitous in computer science and other fields, as they can represent a myriad of structures and problems: social networks, web pages, biological networks, transportation networks, and so much more.

After grounding ourselves in the fundamentals of graph theory, we plunged into the realm of specific graph algorithms. We began with the Depth-First Search (DFS), a simple yet powerful strategy for traversing or searching tree or graph ...