A comprehensive collection of algorithmic and mathematical problem solutions, combining classical data structure challenges with advanced algebraic, geometric, and computational mathematics problems.
A curated collection of algorithmic and mathematical solutions, covering discrete data structures, graph algorithms, and advanced algebraic methods.
The repository is divided into two major parts:
| Module | Description |
|---|---|
Algebraic Algorithms |
A collection of mathematical and algebraic algorithmic problems, focusing on fields, matrices, circuits, and advanced approximations. Each task is standalone and deeply documented. |
Algorithms for Discrete Data Structures |
Solutions to algorithmic problems on discrete data structures, organized by difficulty level. Includes topics from stacks and queues to automata, compression, and graph theory. |
Each submodule includes self-contained problems, each with:
- README.md describing the problem
- Source code (
.cpp,.hor.py) implementing the algorithm
Algorithms-and-Math/
│
├── Algebraic/
│ ├── Task_0/ ... Task_10/
│ └── README.md
│
├── On-Discrete-DS/
│ ├── 1-Easy/
│ │ └── Name0/ ... NameN/
│ ├── 2-Moderate/
│ │ └── Name0/ ... NameN/
│ ├── 3-Challenging/
│ │ └── Name0/ ... NameN/
│ ├── 4-Hard/
│ │ └── Name0/ ... NameN/
│ │
│ └── README.md
│
└── README.md
Located in Algebraic/
Focuses on the intersection of mathematics and computer science, emphasizing algebraic design, probabilistic reasoning, and geometric computation.
Representative areas:
- Linear and symbolic algebra
- Boolean and arithmetic circuit design
- Modular arithmetic and finite fields
- Graph spectral theory and combinatorial design
- Lattice reduction and integer relation problems
- Quaternion-based geometric transformations
| Task | Topic |
|---|---|
| Task_1 | Parallel prefix disjunction circuit with logarithmic depth and optimal gate complexity |
| Task_3 | Polynomial factorization over finite fields |
| Task_5 | Bose–Shrikhande code construction |
| Task_7 | Minimum density cut via spectral approximation |
| Task_9 | Integer relation detection using LLL reduction |
| Task_10 | Composite 3D rotation using quaternions |
Located in On-Discrete-DS/
- Data Structures: stacks, queues, trees, and hash sets, etc.
- String Algorithms: prefix/Z-functions, automata, substring statistics, etc.
- Dynamic Programming & Greedy: state optimization and sequence merging, etc.
- Graph Algorithms: max flow, traversal, reachability, and spectral properties, etc.
- Text Processing: pattern matching, compression, and frequency analysis, etc.
- Advanced Topics: suffix automata, Burrows–Wheeler transform, fuzzy matching, etc.
| Category | Description |
|---|---|
| Easy | Introductory algorithmic challenges (queues, stacks, simple greedy) |
| Moderate | Intermediate topics (graph traversal, knapsack, string analysis) |
| Challenging | Multi-step reasoning, range queries, and hybrid methods |
| Hard | Expert-level algorithms (compression, suffix structures, advanced pattern matching) |
- Languages: Primarily C++ (
C++17/C++20), with some Python and C tasks - Structure: Each task folder is fully self-contained
- Documentation: Every task has an individual
README.md - Complexity Notes: Time and space complexity are often provided per task
- Build: Standard C++ toolchain (
g++,clang++,cmake, etc.) can be used to compile solutions
This repository is intended for:
- Learning and reference - explore algorithms across math and CS
- Competitive programming preparation - categorized by difficulty
- Algorithm design study - investigate diverse solution strategies
- Research and teaching - provide reproducible algorithmic examples
All code and documentation in this repository is licensed under the Apache License 2.0.
Author: Mikhael A. (mixaisealx)
Repository: Algorithms-and-Math