Floyd-Warshall is an algorithm to find the shortest paths between all pairs of nodes in a graph. You can implement it in TypeScript using dynamic programming and an adjacency matrix.

The Floyd-Warshall algorithm is a dynamic programming approach for finding the shortest paths between all pairs of nodes in a weighted graph. Unlike Dijkstra’s algorithm, which finds the shortest paths from a single source, Floyd-Warshall solves the all-pairs shortest path problem in O(n³) time complexity, where n is the number of vertices. This makes it ideal for dense graphs. The algorithm works by initializing a distance matrix, where each entry dist[i][j] holds the current known shortest distance from node i to node j. The matrix is then updated iteratively by considering each node as an intermediate node in potential new paths. If a shorter path is found through an intermediate node, the matrix is updated to reflect this new shortest distance. In TypeScript, you can implement Floyd-Warshall using a 2D array to represent the distance matrix and a triple-nested loop to iteratively update the distances. Floyd-Warshall is especially useful in applications like network routing, where you need to calculate shortest paths for all pairs of routers, or in urban planning systems, where you want to determine the shortest travel routes between all points in a city.