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.
Each entry corresponds to a specific LeetCode problem and is organized to include:
- Source Code: Optimized implementation (C++, Java, or Python).
- 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).
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.
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.