How can I implement the Floyd-Warshall algorithm in Python?

How can I implement the Floyd-Warshall algorithm in Python?

To implement the Floyd-Warshall algorithm in Python, you can start by creating a 2D array to represent the graph's adjacency matrix.

Can you show me a sample code for that?

Sure! Here's a simple implementation:

def floyd_warshall(graph):
    num_vertices = len(graph)
    dist = [[float('inf')] * num_vertices for _ in range(num_vertices)]

    for i in range(num_vertices):
        for j in range(num_vertices):
            dist[i][j] = graph[i][j]

    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

This function takes a graph represented as an adjacency matrix and returns the shortest paths.

What does the adjacency matrix look like?

The adjacency matrix is a 2D list where the element at row i and column j represents the weight of the edge from vertex i to vertex j. If there's no edge, you can use float('inf'). For example:

graph = [
    [0, 3, float('inf'), 7],
    [8, 0, 2, float('inf')],
    [5, float('inf'), 0, 1],
    [2, float('inf'), float('inf'), 0]
]