How can I implement the Bellman-Ford algorithm in Python?

How can I implement the Bellman-Ford algorithm in Python?

The Bellman-Ford algorithm is used to find the shortest paths from a single source vertex to all other vertices in a weighted graph. Would you like a step-by-step implementation?

Yes, please provide the code and explain each part.

Sure! Here's a basic implementation:

class Graph:
    def __init__(self, vertices):
        self.V = vertices  # Number of vertices
        self.graph = []  # List to store graph edges

    def add_edge(self, u, v, w):
        self.graph.append((u, v, w))  # Add edge with weight

    def bellman_ford(self, src):
        dist = [float('inf')] * self.V  # Initialize distances
        dist[src] = 0  # Distance to source is 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  # Update distance

        # Check for negative-weight cycles
        for u, v, w in self.graph:
            if dist[u] != float('inf') and dist[u] + w < dist[v]:
                print("Graph contains negative weight cycle")
                return

        return dist

This code defines a Graph class, adds edges, and implements the Bellman-Ford algorithm.

Can you explain how the distance updates work in this algorithm?

Absolutely! The algorithm relaxes all edges repeatedly. For each edge (u, v) with weight w, it checks if the current known distance to u plus w is less than the known distance to v. If it is, it updates the distance to v. This process is repeated for V-1 times, where V is the number of vertices, ensuring that the shortest paths are found.