Big-O Complexity
対象: High Schoolカテゴリ: Computer Science
説明
Plots growth curves for the six major Big-O complexity classes on a shared set of axes. A ValueTracker animates n growing, showing how quickly each curve diverges. A reference table maps each complexity to example algorithms.
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Big-O Complexity
Description
Plots growth curves for the six major Big-O complexity classes on a shared set of axes. A ValueTracker animates n growing, showing how quickly each curve diverges. A reference table maps each complexity to example algorithms.
Phases
| # | Phase Name | Duration | Description |
|---|---|---|---|
| 1 | Title Card | 3s | Title fades in |
| 2 | Axes Setup | 3s | Labeled axes appear |
| 3 | Draw Curves | 14s | Each curve drawn sequentially with label, distinct color |
| 4 | ValueTracker | 8s | Vertical line sweeps right; dots on each curve highlight |
| 5 | Algorithm Table | 8s | Table: complexity → example algorithms |
| 6 | Outro | 3s | Fade out |
Layout
+------------------------------------------------------+
| Big-O Complexity |
+------------------------------------------------------+
| |
| y = runtime ^ |
| | O(2^n) ↗ |
| | O(n²) ↗ |
| | O(n log n) ↗ |
| | O(n) / |
| | O(log n)~ |
| |___O(1)______________ |
| +-----------------------> n |
| |
| Complexity | Example Algorithm |
| O(1) | Array index lookup |
| O(log n) | Binary Search |
| O(n) | Linear Search |
| O(n log n) | Merge Sort |
| O(n²) | Bubble Sort |
| O(2^n) | Brute-force Subsets |
+------------------------------------------------------+
Area Descriptions
- Top: Title
- Main area: Manim Axes with 6 colored curves
- Bottom: Algorithm reference table
Assets & Dependencies
- Fonts: LaTeX / sans-serif
- Manim version: ManimCE 0.19.1
Notes
- x range 0–8, y range 0–12 (clipped) to keep curves visible
- Colors: O(1)=white, O(log n)=cyan, O(n)=neon green, O(n log n)=yellow, O(n²)=orange, O(2^n)=red
- ValueTracker vertical dashed line sweeps from x=1 to x=6
- Table appears on right side after curves are drawn