Dijkstra Algorithm

Dijkstra behaves like water flowing downhill: it always expands first into the cheapest terrain, filling low-cost regions before even touching costly ones. The path you see forms as if water found the easiest valleys through the map, avoiding steep ‘mountain’ costs and hugging the darkest blue zones where movement is cheapest.

Even though the animation feels like it instantly “just finds the best path,” what’s actually happening is that Dijkstra expands outward through the grid, always choosing the cheapest neighboring cell next. It behaves like water flowing downhill — filling the lowest-cost areas first and only climbing into higher-cost regions when absolutely necessary. The final path you see is the cheapest corridor through the terrain.

This visualization shows how Dijkstra’s algorithm tries many possible routes and always follows the cheapest-cost direction first. It briefly displays the current best path as it explores, then finally reveals the optimal path that avoids expensive (green) areas and travels mostly through low-cost blue regions.

If we strip away graph-theory glamor, Dijkstra is basically: Greedy crawl outward from the start node, always expanding cheapest known path first.