Dijkstra's Shortest Path
受眾: Software Engineer類別: Computer Science
簡介
Visualizes Dijkstra's algorithm on a weighted directed graph with 6 nodes. The animation shows the priority queue (min-heap), greedy node exploration, distance table updates at each step, and the final shortest path tree highlighted in gold.
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Dijkstra's Shortest Path
Description
Visualizes Dijkstra's algorithm on a weighted directed graph with 6 nodes. The animation shows the priority queue (min-heap), greedy node exploration, distance table updates at each step, and the final shortest path tree highlighted in gold.
Phases
| # | Phase Name | Duration | Description |
|---|---|---|---|
| 1 | Intro | 3s | Title and graph displayed with edge weights |
| 2 | Initialization | 4s | Source node highlighted, distance table initialized (0 for source, ∞ for rest) |
| 3 | Priority Queue | 3s | Priority queue shown with initial entry |
| 4 | Exploration Loop | 24s | Iteratively: dequeue minimum, relax edges, update distances and PQ |
| 5 | Final Path | 6s | Shortest path from source to all nodes highlighted in gold |
| 6 | Outro | 4s | Summary of distances shown |
Layout
+--------------------------------------------------+
| Title: Dijkstra's Shortest Path |
+--------------------------------------------------+
| |
| Graph (center-left): |
| A |
| / \ |
| B C |
| / \ / \ |
| D E F |
| |
| Distance Table (right): |
| Node | Dist | Prev |
| A | 0 | - |
| B | ∞ | - |
| ... |
| |
| Priority Queue (bottom-right): |
| [(0,A), ...] |
+--------------------------------------------------+
Area Descriptions
- Center-left: Graph visualization with weighted directed edges
- Right panel: Distance table updating at each step
- Bottom panel: Priority queue contents
Assets & Dependencies
- Fonts: LaTeX / sans-serif
- Manim version: ManimCE 0.19.1
Notes
- Visited nodes turn green
- Current node being processed turns yellow
- Relaxed edges turn cyan
- Final shortest path edges turn gold with increased stroke width