Algorithm Design and Complexity Analysis

This repository contains formal solutions and rigorous complexity analysis for algorithmic problems sourced primarily from LeetCode.

The objective is to provide a comprehensive engineering approach to these challenges, prioritizing theoretical correctness, asymptotic behavior, and formal optimization techniques over simple implementation.

Repository Structure

Each entry corresponds to a specific LeetCode problem and is organized to include:

1. Source Code: Optimized implementation (C++, Java, or Python).
2. Documentation: A technical report covering:
   • Problem constraints and edge case analysis.
   • Algorithmic paradigm selection (e.g., Dynamic Programming, Graph Theory, Sliding Window).
   • Formal time and space complexity derivation using Big O notation.
   • Mathematical proof of correctness (where applicable).

Methodology

The analysis follows standard academic rigor:

• Correctness: Verification via loop invariants or inductive reasoning.
• Asymptotic Analysis: Evaluation of Worst-Case, Average-Case, and Best-Case scenarios relative to input size constraints.
• Recurrence Relations: Derivation and solving of recurrences for recursive solutions.

Attribution and Tools

The algorithmic logic, mathematical proofs, and source code implementations are original work.

Generative AI tools were utilized strictly for:

• LaTeX and Markdown formatting.
• Syntactical structuring of the documentation.