Bellman-Ford Algorithm
The Bellman-Ford algorithm is a graph algorithm used to find the shortest paths from a single source vertex to all other vertices in a weighted graph. It can handle graphs with negative edge weights, unlike Dijkstra's algorithm, and detects negative weight cycles that would make shortest paths undefined. The algorithm works by relaxing all edges repeatedly, typically for V-1 iterations where V is the number of vertices.
Developers should learn the Bellman-Ford algorithm when working on problems involving shortest paths in graphs with negative weights, such as in network routing protocols, financial arbitrage detection, or game development with cost-based movement. It is essential for scenarios where Dijkstra's algorithm fails due to negative edges, and its ability to detect negative cycles makes it valuable for cycle detection in weighted directed graphs.