Dijkstra Algorithm Questions
The main difference between the Dijkstra Algorithm and the Bellman-Ford Algorithm lies in their approach to finding the shortest path in a graph.
1. Dijkstra Algorithm:
- It is a greedy algorithm that works on graphs with non-negative edge weights.
- It starts from a source node and explores the neighboring nodes, updating the distances to reach each node.
- It maintains a priority queue to select the node with the minimum distance at each step.
- Dijkstra's algorithm guarantees finding the shortest path when all edge weights are non-negative.
2. Bellman-Ford Algorithm:
- It is a dynamic programming algorithm that can handle graphs with negative edge weights.
- It iteratively relaxes all the edges in the graph for V-1 times, where V is the number of vertices.
- It updates the distances to reach each node by considering all possible paths.
- Bellman-Ford algorithm can detect negative cycles in the graph, which makes it useful in scenarios where negative edge weights are present.
In summary, Dijkstra's algorithm is more efficient for graphs with non-negative edge weights, while Bellman-Ford algorithm is more versatile and can handle graphs with negative edge weights and detect negative cycles.