Here are 100 chapter titles for Arrays, progressing from beginner to advanced, tailored for competitive programming:
I. Foundational Concepts (20 Chapters)
- Introduction to Data Structures: Arrays
- What are Arrays? (Static vs. Dynamic)
- Declaring and Initializing Arrays in C++/Java/Python
- Accessing Array Elements (Indexing)
- Basic Array Operations: Traversal, Insertion, Deletion
- Linear Search in Arrays
- Binary Search in Sorted Arrays
- Two-Pointer Technique Basics
- Array Manipulation: Shifting and Rotating
- Finding the Largest/Smallest Element
- Sum and Average of Array Elements
- Frequency Counting in Arrays
- Duplicate Element Detection
- Removing Duplicates from an Array
- Sorting Arrays (Basic Algorithms: Bubble Sort, Insertion Sort)
- Introduction to Array Problems in Competitive Programming
- Arrays vs. Linked Lists: Choosing the Right Data Structure
- Memory Allocation and Arrays
- Multi-Dimensional Arrays (2D Arrays)
- Basic 2D Array Operations: Traversal, Input/Output
II. Intermediate Techniques (30 Chapters)
- Prefix Sum Technique
- Suffix Sum Technique
- Sliding Window Technique
- Kadane's Algorithm (Maximum Subarray Sum)
- Maximum Subarray Product
- Container With Most Water
- Two Sum Problem
- Three Sum Problem
- Four Sum Problem
- K Sum Problem (Generalization)
- Trapping Rain Water
- Product of Array Except Self
- Next Greater Element
- Previous Smaller Element
- Stock Buy and Sell Problems (Variations)
- Rotate Array (Optimized Approaches)
- Spiral Matrix Traversal
- Diagonal Traversal of Matrix
- Transpose of a Matrix
- Matrix Multiplication
- Searching in a Sorted Matrix
- Finding the Median of Two Sorted Arrays
- Merge Intervals
- Meeting Rooms I & II
- Group Anagrams
- Longest Consecutive Sequence
- Subarray Sum Equals K
- Minimum Size Subarray Sum
- Practice Problems: Array Manipulation
- Practice Problems: Array Search and Sorting
III. Advanced Concepts and Applications (30 Chapters)
- Advanced Array Manipulation Techniques
- Sparse Matrices and Their Representation
- Dynamic Programming with Arrays
- Greedy Algorithms with Arrays
- Divide and Conquer with Arrays
- Backtracking with Arrays
- Graph Traversal with Adjacency Matrix (using Arrays)
- Segment Trees (Introduction)
- Binary Indexed Trees (Fenwick Trees)
- Range Queries on Arrays
- 2D Prefix Sum
- Matrix Chain Multiplication
- Longest Increasing Subsequence
- Longest Common Subsequence (using 2D arrays)
- Palindromic Substrings
- Submatrix Sum Queries
- Maximum Area Histogram
- Largest Rectangle in Histogram
- Sliding Window Maximum
- K Closest Points to Origin
- Top K Frequent Elements
- Array Problems and Bit Manipulation
- Array Problems and Number Theory
- Array Problems and Geometry
- Case Study: Solving Real-World Problems with Arrays
- Competitive Programming Strategies for Array Problems
- Optimizing Array Code for Speed and Memory
- Testing and Debugging Strategies for Array Implementations
- Array Problem Solving Techniques: Pattern Recognition
- Array Problem Solving Techniques: Problem Decomposition
IV. Expert Level and Competitive Programming Challenges (20 Chapters)
- Advanced Array Problem Sets (Codeforces, LeetCode, etc.)
- Hard Level Array Problems and Solutions
- Contests and Challenges: Array Focus
- Analyzing Time and Space Complexity of Advanced Array Algorithms
- Advanced Optimization Techniques for Array Problems
- Parallel Processing with Arrays
- Distributed Arrays
- Implementing Arrays in Different Programming Paradigms
- Array Libraries and Frameworks
- Performance Tuning of Array Implementations
- Advanced Debugging and Profiling of Array Code
- Code Review and Best Practices for Array Implementations
- Array and System Design
- Array and Embedded Systems
- Array and Operating Systems
- Research Topics in Arrays
- The Future of Arrays
- Arrays and Machine Learning (NumPy Arrays)
- Arrays and Artificial Intelligence
- Mastering Arrays for Competitive Programming Success