How does the Bellman-Ford algorithm work?

How does the Bellman-Ford algorithm work?

The Bellman-Ford algorithm finds the shortest paths from a single source vertex to all other vertices in a graph.

Can you explain how to implement it in Python?

Sure! You can implement it using a loop to relax the edges repeatedly. Would you like to see a code example?

Yes, please show me the code!

Here's a simple implementation:

class Graph:
    def __init__(self, vertices):
        self.V = vertices  # No. of vertices
        self.graph = []  # default dictionary

    def add_edge(self, u, v, w):
        self.graph.append((u, v, w))

    def bellman_ford(self, src):
        dist = [float("inf")] * self.V
        dist[src] = 0

        for _ in range(self.V - 1):
            for u, v, w in self.graph:
                if dist[u] != float("inf") and dist[u] + w < dist[v]:
                    dist[v] = dist[u] + w

        return dist

This code defines a graph and implements the Bellman-Ford algorithm.

What are the time and space complexities of this algorithm?

The time complexity is O(V * E) where V is the number of vertices and E is the number of edges. The space complexity is O(V) for storing the distance array.