In this article, I will explain What is Bellman-Ford Algorithm and How Does it Work.

Bellman-Ford algorithm is a dynamic programming algorithm used to find the shortest path between a source vertex and all other vertices in a weighted graph, even when the graph contains negative weight edges. The algorithm works by initially setting the distance to the source vertex as zero and the distance to all other vertices as infinity.

Then, the algorithm relaxes all edges in the graph repeatedly, where relaxing an edge means updating the distance of the adjacent vertex if it can be improved by going through the selected edge. The algorithm repeats this process for a number of iterations equal to the number of vertices in the graph.

After these iterations, the algorithm checks for negative-weight cycles in the graph by performing an additional iteration of relaxing all edges. If the distance of any vertex can be further reduced in this iteration, it means that the graph contains a negative-weight cycle, and the algorithm terminates with a negative-weight cycle detected.

The time complexity of Bellman-Ford algorithm is O(VE), where V is the number of vertices and E is the number of edges in the graph. The algorithm is slower than Dijkstra’s algorithm, but it can handle negative-weight edges and negative-weight cycles, which makes it useful in certain applications where these conditions are present.

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