All Points Shortest Path
The Floyd-Warshall algorithm is a dynamic programming technique used in competitive programming to find the shortest paths between all pairs of vertices in a weighted, directed graph. Unlike Dijkstra’s and Bellman-Ford’s algorithms, which focus on single-source shortest paths, Floyd-Warshall efficiently computes the shortest paths for every vertex pair simultaneously. Due to its \(O(V^3)\) time complexity, it’s best suited for graphs with a relatively small number of vertices, typically when $ V ≤ 400 $ in most competitive scenarios.