Asymptotic Time & Space Complexities
| Algorithm |
Best |
Average |
Worst |
Space |
Stability |
Paradigm |
| Quick Sort |
O(N log N) |
O(N log N) |
O(N²) |
O(log N) |
No |
Divide & Conquer (Dual-Pivot) |
| Merge Sort |
O(N log N) |
O(N log N) |
O(N log N) |
O(N) |
Yes |
Divide & Conquer (Out-of-Place) |
| Heap Sort |
O(N log N) |
O(N log N) |
O(N log N) |
O(1) |
No |
Binary Max-Heap Sift-Down |
| Radix Sort |
O(N · k) |
O(N · k) |
O(N · k) |
O(N + k) |
Yes |
Non-Comparative LSD Bucket |
| Shell Sort |
O(N log N) |
O(N^1.3) |
O(N²) |
O(1) |
No |
Diminishing Gap Insertion |
| Tim Sort |
O(N) |
O(N log N) |
O(N log N) |
O(N) |
Yes |
Adaptive Natural Run Merge |
| Insertion Sort |
O(N) |
O(N²) |
O(N²) |
O(1) |
Yes |
Incremental Insertion |
| Cocktail Shaker |
O(N) |
O(N²) |
O(N²) |
O(1) |
Yes |
Bidirectional Bubble Pass |
| Selection Sort |
O(N²) |
O(N²) |
O(N²) |
O(1) |
No |
Linear Extrema Selection |
| Bogo Sort |
O(N) |
O((N+1)!) |
O(∞) |
O(1) |
No |
Stochastic Permutation (Chaos) |
Dimensional Projections & Geometries (20 Modes)
2D Planar
Vertical Bars, Cartesian Scatter, Symmetric Pyramid, Waveform Oscilloscope, Disparity Heatmap, Proximity Graph.
Polar & Curvilinear
360° Radial Dial, Galaxy Spiral, Sunflower Phyllotaxis, Butterfly Curve, Supernova Starburst, Concentric Radar Rings.
3D Volumetric
Isometric Pillars, DNA Helix 3D, Geodesic Sphere Globe 3D, Donut Torus 3D, Holographic Cylinder 3D, Infinite Warp Tunnel 3D, Heightfield Mesh 3D, Lissajous Knot 3D.