👉 The Floyd-Warshall algorithm is an efficient method for finding shortest paths in a weighted, directed graph with positive or negative edge weights (but no negative cycles). It operates by iteratively updating a distance matrix to reflect the shortest path distances between all pairs of vertices. Initially, the distance matrix is populated with direct edge weights or infinity for non-existent edges, and then through a series of updates based on the current and potential intermediate vertices, it gradually computes the shortest paths. This dynamic programming approach ensures that by the end of the algorithm, the matrix contains the shortest path distances between every pair of vertices, making it a powerful tool for solving all-pairs shortest path problems.
