CodingPanCake

Mastering Matrix Decompositions and SVD: LU, QR, Eigendecomposition, and Singular Value Decomposition

Algorithms & Applied Linear Algebra At the heart of machine learning, image processing, quantum computing, and high-performance numerical computing lies Matrix Factorization (Decomposition) . Decomposing a complex matrix into simp…

Heavy-Light Decomposition Under the Hood: Algorithmic Mechanics, Mathematical Proofs, and Production C++ Implementation

Advanced Tree Data Structures In software engineering and competitive programming, range queries on 1D arrays are effortlessly handled by Segment Trees or Fenwick Trees (BIT) in $O(\log N)$ time. However, when values are distributed…