Why Does the Reduction of Distance in the N’th Relaxation Indicates the Existence of a Negative Cycle?
As previously discussed, achieving the single source shortest paths to all other nodes takes N-1 relaxations. If the N’th relaxation further reduces the shortest distance for any node, it implies that a certain edge with negative weight has been traversed once more. It is important to note that during the N-1 relaxations, we presumed that each vertex is traversed only once. However, the reduction of distance during the N’th relaxation indicates revisiting a vertex.
Bellman–Ford Algorithm
Imagine you have a map with different cities connected by roads, each road having a certain distance. The Bellman–Ford algorithm is like a guide that helps you find the shortest path from one city to all other cities, even if some roads have negative lengths. It’s like a GPS for computers, useful for figuring out the quickest way to get from one point to another in a network. In this article, we’ll take a closer look at how this algorithm works and why it’s so handy in solving everyday problems.
Table of Content
- Bellman-Ford Algorithm
- The idea behind Bellman Ford Algorithm
- Principle of Relaxation of Edges for Bellman-Ford
- Why Relaxing Edges N-1 times, gives us Single Source Shortest Path?
- Why Does the Reduction of Distance in the N’th Relaxation Indicates the Existence of a Negative Cycle?
- Working of Bellman-Ford Algorithm to Detect the Negative cycle in the graph
- Algorithm to Find Negative Cycle in a Directed Weighted Graph Using Bellman-Ford
- Handling Disconnected Graphs in the Algorithm
- Complexity Analysis of Bellman-Ford Algorithm
- Bellman Ford’s Algorithm Applications
- Drawback of Bellman Ford’s Algorithm
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