Algorithmic Design Patterns & Computational Logic

A structured repository consolidating algorithmic design patterns, computational problem-solving frameworks, and performance optimization techniques.

---

📘 Abstract

This repository serves as a systematic archive of algorithmic patterns, emphasizing scalability, memory optimization, and reusable logic. Unlike standard solution dumps, this project focuses on the framework-oriented approach to reasoning—identifying recurring computational structures and transforming intuition into deterministic, production-ready code.

The objective is to bridge the gap between theoretical computer science concepts and practical software engineering constraints.

---

⚙️ Engineering Methodology

Every solution in this repository adheres to a strict engineering standard, analyzed through the following lens:

• Pattern Recognition: Detecting recurring computational motifs (e.g., Sliding Window, Monotonic Stacks, Fast & Slow Pointers).
• Abstraction Design: Generalizing solutions into reusable functional modules rather than ad-hoc scripts.
• Asymptotic Profiling: Rigorous evaluation of $T(n)$ (Time) and $S(n)$ (Space) complexity.
• Memory Management: Prioritizing in-place operations to minimize auxiliary space overhead.

---

📂 Repository Taxonomy

The directory structure is organized by algorithmic domain, with each domain further stratified by difficulty tier (Easy, Medium, Hard) to track progressive complexity.

leetcode-patterns/
│
├── Arrays/                 # Sliding Window, Two Pointers, Prefix Sums
│   ├── Easy/
│   ├── Medium/
│   └── Hard/
│
├── Backtracking/           # Permutations, Combinations, N-Queens
│   ├── [Tiered Subfolders]
│
├── Binary_Search/          # Search Space Reduction, Rotated Arrays
│   ├── [Tiered Subfolders]
│
├── Bit_Manipulation/       # XOR Logic, Masking, Bitwise Operations
│   ├── [Tiered Subfolders]
│
├── Dynamic_Programming/    # Memoization, Tabulation, Knapsack Patterns
│   ├── [Tiered Subfolders]
│
├── Graphs/                 # BFS, DFS, Union-Find, Topological Sort
│   ├── [Tiered Subfolders]
│
├── LinkedList/             # Pointer Manipulation, Cycle Detection, Merging
│   ├── [Tiered Subfolders]
│
├── Math/                   # Number Theory, Geometry, Combinatorics
│   ├── [Tiered Subfolders]
│
├── Recursion/              # Base Cases, Recursive Trees
│   ├── [Tiered Subfolders]
│
├── Stack_Queue/            # Monotonic Stacks, Priority Queues, Buffer Management
│   ├── [Tiered Subfolders]
│
├── Strings/                # Parsing, Tries, String Matching Algorithms
│   ├── [Tiered Subfolders]
│
└── Trees/                  # Binary Search Trees, Traversals, Serialization
    ├── Easy/
    ├── Medium/
    └── Hard/

---

🧮 Complexity Analysis Standards

All implementations include explicit analytical documentation within the source code comments:

Metric	Notation	Definition
Time Complexity	$O(f(n))$	Upper bound on execution time relative to input size $n$.
Space Complexity	$O(g(n))$	Auxiliary memory required (excluding output storage).

Example Annotation:

/**
 * Approach: Floyd's Tortoise and Hare
 * Time Complexity: O(n) - Linear traversal.
 * Space Complexity: O(1) - Constant space, no external hash set used.
 */

---

⚡ Selected Optimizations (Case Studies)

Highlights of algorithmic refactoring and efficiency improvements.

1. Graph Traversal & State Management

• Problem: Number of Islands (Grid DFS/BFS)
• Optimization: Refactored from an external visited Set ($O(m \times n)$ space) to in-place modification of the grid, reducing auxiliary space complexity to $O(1)$ (excluding stack frames).

2. Dynamic Programming

• Problem: Climbing Stairs / House Robber
• Optimization: Optimized from a standard integer array (dp[]) to two variables, reducing Space Complexity from $O(n)$ to $O(1)$.

---

📊 Performance Metrics

Live data synchronized via LeetCode API.

📎 Version Control Protocol

Commit messages follow the Conventional Commits specification to ensure a clean history:

• feat: New pattern or problem inclusion.
• perf: Code refactoring for improved time/space complexity.
• docs: Updates to analysis, comments, or documentation.
• fix: Correction of edge cases or boundary logic.

---

🧾 License

This repository is released under the MIT License.