Algorithms and Data Structures

Introduction to Algorithms

• What is an Algorithm?
• Characteristics of Algorithms
• Importance of Algorithms in Problem Solving
• Examples of Algorithms in Everyday Life

Complexity Analysis

• Time Complexity
  • Big O Notation
  • Big Theta and Big Omega
• Space Complexity
• Analyzing Algorithms
• Best, Worst, and Average Case Analysis

Basic Data Structures

Arrays

• Definition and Properties
• Operations: Access, Insertion, Deletion
• Dynamic Arrays

Linked Lists

• Singly Linked Lists
• Doubly Linked Lists
• Circular Linked Lists
• Operations and Applications

Stacks

• Definition and Properties
• Stack Operations
• Applications of Stacks

Queues

• Definition and Properties
• Types of Queues: Simple, Circular, Priority
• Queue Operations
• Applications of Queues

Trees

Binary Trees

• Definition and Properties
• Binary Tree Traversals
  • Inorder, Preorder, Postorder
• Binary Search Trees (BST)
  • Operations: Insertion, Deletion, Search
  • Balanced vs. Unbalanced BST

Heaps

• Definition and Properties
• Min-Heaps and Max-Heaps
• Heap Operations
• Applications: Priority Queues

Advanced Trees

• AVL Trees
• Red-Black Trees
• B-Trees and B+ Trees
• Tries and Suffix Trees

Graphs

• Definition and Terminology
• Representations: Adjacency Matrix, Adjacency List
• Graph Traversal Algorithms
  • Depth-First Search (DFS)
  • Breadth-First Search (BFS)
• Shortest Path Algorithms
  • Dijkstra’s Algorithm
  • Bellman-Ford Algorithm
  • A* Algorithm
• Minimum Spanning Tree Algorithms
  • Kruskal’s Algorithm
  • Prim’s Algorithm
• Network Flow Algorithms

Sorting Algorithms

• Bubble Sort
• Selection Sort
• Insertion Sort
• Merge Sort
• Quick Sort
• Heap Sort
• Counting Sort
• Radix Sort
• Bucket Sort
• Comparison of Sorting Algorithms

Searching Algorithms

• Linear Search
• Binary Search
• Interpolation Search
• Exponential Search
• Search in Unsorted and Sorted Data

Hashing

• Hash Functions
• Hash Tables
• Collision Resolution Techniques
  • Chaining
  • Open Addressing: Linear Probing, Quadratic Probing, Double Hashing
• Applications of Hashing

Dynamic Programming

• Principles of Dynamic Programming
• Memoization vs. Tabulation
• Common Dynamic Programming Problems
  • Fibonacci Sequence
  • Knapsack Problem
  • Longest Common Subsequence
  • Matrix Chain Multiplication

Greedy Algorithms

• Principles of Greedy Algorithms
• Common Greedy Problems
  • Activity Selection
  • Huffman Coding
  • Kruskal’s and Prim’s Algorithms Revisited

Divide and Conquer

• Principles of Divide and Conquer
• Common Divide and Conquer Problems
  • Merge Sort and Quick Sort Revisited
  • Binary Search Revisited
  • Closest Pair of Points

Backtracking

• Principles of Backtracking
• Common Backtracking Problems
  • N-Queens Problem
  • Hamiltonian Cycle
  • Subset Sum Problem

Advanced Algorithms

String Algorithms

• Pattern Matching
  • Naive String Matching
  • Knuth-Morris-Pratt (KMP) Algorithm
  • Boyer-Moore Algorithm
• Suffix Arrays and Trees

Computational Geometry

• Convex Hull
• Closest Pair of Points Revisited
• Line Intersection

Number Theoretic Algorithms

• Prime Number Algorithms
• Greatest Common Divisor (GCD)
• Modular Arithmetic
• Cryptographic Algorithms

Parallel and Distributed Algorithms

• Principles of Parallel Algorithms
• Parallel Sorting and Searching
• Distributed Consensus Algorithms
  • Paxos Revisited
  • Raft Revisited

Approximation Algorithms

• Principles of Approximation
• Approximation Algorithms for NP-Hard Problems
  • Traveling Salesman Problem (TSP)
  • Vertex Cover
  • Set Cover

Randomized Algorithms

• Principles of Randomized Algorithms
• Monte Carlo and Las Vegas Algorithms
• Randomized Algorithms for Sorting and Searching
• Applications and Analysis

Machine Learning Algorithms

• Overview of Machine Learning
• Common Machine Learning Algorithms
  • Linear Regression
  • Decision Trees
  • k-Nearest Neighbors (k-NN)
  • Support Vector Machines (SVM)
  • Neural Networks
• Evaluation and Optimization

Case Studies and Applications

• Algorithm Design in Real-World Systems
  • Google’s PageRank
  • Facebook’s Graph Search
  • Amazon’s Recommendation System
• Data Structures in Real-World Applications
  • Twitter’s Timeline
  • Netflix’s Streaming Service

Advanced Topics and Research Directions

• Current Trends in Algorithm Research
• Quantum Algorithms
• Algorithms in Big Data and Cloud Computing
• Open Problems and Future Directions