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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.

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.

AlgorithmDifficultyTime ComplexitySpace Complexity
Binary SearchBeginnerO(log n)O(1)
Bubble SortBeginnerO(n²)O(1)
Cocktail Shaker SortBeginnerO(n²)O(1)
Insertion SortBeginnerO(n²)O(1)
Linear SearchBeginnerO(n)O(1)
Selection SortBeginnerO(n²)O(1)
Breadth-First SearchIntermediateO(V + E)O(V)
Depth-First SearchIntermediateO(V + E)O(V)
Heap SortIntermediateO(n log n)O(1)
Merge SortIntermediateO(n log n)O(n)
QuickSortIntermediateO(n log n)O(log n)
Dijkstra’s Shortest PathAdvancedO((V + E) log V)O(V)

Core building blocks of neural networks, from single neurons to gradient-based optimization. These visualizations help build intuition for how deep learning models learn.

AlgorithmDifficultyTime ComplexitySpace Complexity
Single Neuron / PerceptronBeginnerO(n)O(1)
BackpropagationIntermediateO(Σ n_l × n_{l+1})O(Σ n_l × n_{l+1})
Convolution (2D)IntermediateO(H × W × K² × C)O(H × W + K²)
Feedforward Neural NetworkIntermediateO(Σ n_l × n_{l-1})O(Σ n_l)
Gradient DescentIntermediateO(T × d)O(d)

Components of modern generative AI architectures, focusing on the transformer pipeline from raw text to contextualized representations.

AlgorithmDifficultyTime ComplexitySpace Complexity
BPE TokenizationBeginnerO(n × m)O(n)
Self-Attention (Scaled Dot-Product)IntermediateO(n² × d)O(n² + n × d)
Token EmbeddingsIntermediateO(n × d)O(V × d)
Multi-Head AttentionAdvancedO(h × n² × d_k)O(h × n² + n × d)
Transformer BlockAdvancedO(n² × d + n × d × d_ff)O(n² + n × d_ff)

Fundamental quantum computing concepts, from single-qubit states on the Bloch sphere to multi-qubit algorithms like Grover’s search and quantum teleportation.

AlgorithmDifficultyTime ComplexitySpace Complexity
Qubit States & Bloch SphereBeginnerN/A (state representation)O(1) per qubit
Quantum Gates & CircuitsIntermediateO(2^n * g)O(2^n)
Superposition & MeasurementIntermediateO(2^n)O(2^n)
Grover’s Search AlgorithmAdvancedO(√N)O(N) where N = 2^n
Quantum TeleportationAdvancedO(1) gatesO(1) — 3 qubits