What is the Floyd-Warshall algorithm used for?

The Floyd-Warshall algorithm is used to find the shortest paths between all pairs of vertices in a weighted, directed graph. It can handle both positive and negative edge weights, but not negative cycles.

How is the Floyd-Warshall algorithm related to dynamic programming?

The Floyd-Warshall algorithm is a classic example of dynamic programming. It builds up a solution by iteratively considering all possible intermediate vertices for each pair of start and end nodes. The solution for a larger set of intermediate vertices is built upon the solutions for smaller sets.

Data Structures & Algorithms

Floyd-Warshall Algorithm

Excel in your coding interviews by understanding the Floyd-Warshall algorithm. Our guide covers the all-pairs shortest path problem, its dynamic programming approach, and offers AI-powered practice.

Floyd-Warshall Algorithm Implementation

Here is a Python implementation of the Floyd-Warshall algorithm. It uses a matrix to store the shortest distances between every pair of vertices.


def floyd_warshall(graph):
    num_vertices = len(graph)
    dist = list(map(lambda i: list(map(lambda j: j, i)), graph))

    for k in range(num_vertices):
        for i in range(num_vertices):
            for j in range(num_vertices):
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])

    return dist

AI Coach Tip: The Floyd-Warshall algorithm has a time complexity of O(V^3), making it suitable for smaller graphs. Its simplicity and ability to find all-pairs shortest paths make it a valuable tool. Remember the three nested loops structure: the outer loop iterates through intermediate vertices, and the inner loops iterate through all pairs of source and destination vertices.