Floyd Warshall Algorithm
The Floyd Warshall algorithm is a dynamic programming algorithm used to find the shortest paths between all pairs of vertices in a weighted graph, which can have positive or negative edge weights (but no negative cycles). It works by iteratively improving path estimates through intermediate vertices, making it efficient for dense graphs where other algorithms like Dijkstra's would be less optimal. The algorithm is widely applied in network routing, traffic optimization, and solving all-pairs shortest path problems in computer science and operations research.
Developers should learn the Floyd Warshall algorithm when they need to compute shortest paths between all pairs of nodes in a graph, such as in network analysis, GPS routing systems, or social network distance calculations. It is particularly useful for dense graphs with up to a few hundred vertices due to its O(V^3) time complexity, and it handles negative weights (unlike Dijkstra's algorithm), making it suitable for applications like currency arbitrage detection or certain optimization problems.