Bellman Ford algorithm works by overestimating the length of the path from the starting vertex to all other vertices. Then it iteratively relaxes those estimates by finding new paths that are shorter than the previously overestimated paths.

Why does Bellman-Ford Run V times?

In Bellman-Ford algorithm, to find out the shortest path, we need to relax all the edges of the graph. This process is repeated at most (V-1) times, where V is the number of vertices in the graph.

Why does Bellman-Ford work with negative weights?

A negative weight cycle is a cycle with weights that sum to a negative number. The Bellman-Ford algorithm propagates correct distance estimates to all nodes in a graph in V-1 steps, unless there is a negative weight cycle. If there is a negative weight cycle, you can go on relaxing its nodes indefinitely.