Bellman-Ford Algorithm Tutorial with Python Implementation

The Bellman-Ford algorithm is a versatile algorithm used for finding the shortest paths from a source vertex to all other vertices in a weighted graph, even in the presence of negative-weight edges. This algorithm can be applied to both directed and undirected graphs.

Overview:

The basic idea behind the Bellman-Ford algorithm is to relax edges iteratively, updating the shortest distance estimates for each vertex until convergence. The algorithm’s main strength lies in its ability to handle graphs with negative weight edges, making it suitable for a wider range of scenarios compared to Dijkstra’s algorithm.

Steps of the Bellman-Ford Algorithm:

1. Initialization:

Start by initializing the distance to the source vertex as 0 and the distances to all other vertices as positive infinity. Create an array to store the predecessor of each vertex.

distance = [float("inf")]*num_vertices
predecessor = [None]*num_vertices
distance[source] = 0

2. Relax Edges:

Iterate over all edges in the graph and relax them. Relaxing an edge means checking if there’s a shorter path to the destination vertex through the current edge.