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Bellman-Ford - Technical Overview

1. Algorithm Description: The Bellman-Ford algorithm calculates the shortest path from a single source vertex to all other vertices in a graph, handling negative weight edges.

2. Steps of the Bellman-Ford Algorithm:

• Initialize distances from the source to all vertices as infinite and to the source itself as 0.
• Relax all edges |V| - 1 times.
• If the distance to a vertex can be shortened by a path, update the distance.
• Check for negative-weight cycles by verifying if any edge can be relaxed further.

3. Time Complexity: O(V * E) where V is the number of vertices and E is the number of edges.

4. Space Complexity: O(V) due to the storage of distances and predecessors.

5. Usage: Bellman-Ford is useful for graphs with negative weights and can detect negative weight cycles.