Shortest Path
Dijkstra: Greedy, faster, doesn't handle negative weights.
Bellman-Ford: Slower, handles negative weights, detects negative cycles.
d(s,v) = \min_u\{d(s,u) + w(u,v) : (u,v) \in E\}
Dijkstra greedily selects the closest unvisited node, always finding optimal paths.
Dijkstra powers GPS navigation, network routing, and game pathfinding algorithms.
How does your phone's maps app find the fastest route to your destination?
d(s,v) = \min_u\{d(s,u) + w(u,v) : (u,v) \in E\}
Use this formula to calculate the relationship between different variables in this concept.
Finding the shortest route with minimum travel time in a road network.