Algorithm Reference
Eigenvue includes 27 algorithms across four categories: Classical Algorithms, Deep Learning, Generative AI, and Quantum Computing. Each algorithm provides step-by-step visual explanations, interactive playback controls, and shareable deep links. Click any algorithm name below to view its detailed documentation, including input options, step format, and educational content.
Classical Algorithms
Section titled “Classical Algorithms”Foundational algorithms for searching, sorting, and graph traversal. These form the basis of computer science education and are essential building blocks for more advanced topics.
| Algorithm | Difficulty | Time Complexity | Space Complexity |
|---|---|---|---|
| Binary Search | Beginner | O(log n) | O(1) |
| Bubble Sort | Beginner | O(n²) | O(1) |
| Cocktail Shaker Sort | Beginner | O(n²) | O(1) |
| Insertion Sort | Beginner | O(n²) | O(1) |
| Linear Search | Beginner | O(n) | O(1) |
| Selection Sort | Beginner | O(n²) | O(1) |
| Breadth-First Search | Intermediate | O(V + E) | O(V) |
| Depth-First Search | Intermediate | O(V + E) | O(V) |
| Heap Sort | Intermediate | O(n log n) | O(1) |
| Merge Sort | Intermediate | O(n log n) | O(n) |
| QuickSort | Intermediate | O(n log n) | O(log n) |
| Dijkstra’s Shortest Path | Advanced | O((V + E) log V) | O(V) |
Deep Learning
Section titled “Deep Learning”Core building blocks of neural networks, from single neurons to gradient-based optimization. These visualizations help build intuition for how deep learning models learn.
| Algorithm | Difficulty | Time Complexity | Space Complexity |
|---|---|---|---|
| Single Neuron / Perceptron | Beginner | O(n) | O(1) |
| Backpropagation | Intermediate | O(Σ n_l × n_{l+1}) | O(Σ n_l × n_{l+1}) |
| Convolution (2D) | Intermediate | O(H × W × K² × C) | O(H × W + K²) |
| Feedforward Neural Network | Intermediate | O(Σ n_l × n_{l-1}) | O(Σ n_l) |
| Gradient Descent | Intermediate | O(T × d) | O(d) |
Generative AI
Section titled “Generative AI”Components of modern generative AI architectures, focusing on the transformer pipeline from raw text to contextualized representations.
| Algorithm | Difficulty | Time Complexity | Space Complexity |
|---|---|---|---|
| BPE Tokenization | Beginner | O(n × m) | O(n) |
| Self-Attention (Scaled Dot-Product) | Intermediate | O(n² × d) | O(n² + n × d) |
| Token Embeddings | Intermediate | O(n × d) | O(V × d) |
| Multi-Head Attention | Advanced | O(h × n² × d_k) | O(h × n² + n × d) |
| Transformer Block | Advanced | O(n² × d + n × d × d_ff) | O(n² + n × d_ff) |
Quantum Computing
Section titled “Quantum Computing”Fundamental quantum computing concepts, from single-qubit states on the Bloch sphere to multi-qubit algorithms like Grover’s search and quantum teleportation.
| Algorithm | Difficulty | Time Complexity | Space Complexity |
|---|---|---|---|
| Qubit States & Bloch Sphere | Beginner | N/A (state representation) | O(1) per qubit |
| Quantum Gates & Circuits | Intermediate | O(2^n * g) | O(2^n) |
| Superposition & Measurement | Intermediate | O(2^n) | O(2^n) |
| Grover’s Search Algorithm | Advanced | O(√N) | O(N) where N = 2^n |
| Quantum Teleportation | Advanced | O(1) gates | O(1) — 3 qubits |