Dijkstra's Algorithm Explained in 60 Seconds #Shorts

3D graph with weighted edges. The frontier expands, edges relax, and the shortest path lights up green.

Subject: Algorithms

--- Transcript ---
1. Initialize all distances to infinity, then set the starting node A to distance 0. This forms our initial frontier.
2. Set A as the start point with distance 0. All other nodes have infinite distance until we discover shorter paths.
3. Visit node A (the closest unvisited node). Mark it as visited - we
4. Relax edges from A: update distances to neighbors B (4) and E (2) if we found shorter paths.
5. Visit E next (distance 2 - the smallest among unvisited). The greedy choice always picks the closest frontier node.
6. From E, relax edges to F (2+3=5) and H (2+1=3). Add these to our expanding frontier.
7. Visit H (distance 3). Continue the pattern: visit closest unvisited node, then relax its edges.
8. From H, we can reach C with distance 3+5=8. Also check if we can improve paths to B and F.
9. Visit B, then F, expanding our search. Each step, we relax edges and potentially find better paths.
10. The algorithm continues: visit C, then G, always choosing the unvisited node with minimum distance.
11. Finally reach D. The algorithm guarantees this is the shortest possible path from A to any node.
12. The shortest path from A to D is highlighted: A→E→H→F→G→D with total distance 8.

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