We are given a directed graph. We need compute whether the graph has negative cycle or not. A negative cycle is one in which the overall sum of the cycle comes negative.
Negative weights are found in various applications of graphs. For example, instead of paying cost for a path, we may get some advantage if we follow the path.
Input : 4 4 0 1 1 1 2 -1 2 3 -1 3 0 -1 Output : Yes The graph contains a negative cycle.
We have discussed Bellman Ford Algorithm based solution for this problem.
In this post, Floyd Warshall Algorithm based solution is discussed that works for both connected and disconnected graphs.
Distance of any node from itself is always zero. But in some cases, as in this example, when we traverse further from 4 to 1, the distance comes out to be -2, i.e. distance of 1 from 1 will become -2. This is our catch, we just have to check the nodes distance from itself and if it comes out to be negative, we will detect the required negative cycle.
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- Floyd Warshall Algorithm | DP-16
- Comparison of Dijkstra’s and Floyd–Warshall algorithms
- Detect a negative cycle in a Graph | (Bellman Ford)
- How does Floyd's slow and fast pointers approach work?
- Degree of a Cycle Graph
- Coloring a Cycle Graph
- Hamiltonian Cycle | Backtracking-6
- Detect cycle in an undirected graph
- Detect cycle in an undirected graph using BFS
- Detect Cycle in a Directed Graph using BFS
- Detect Cycle in a Directed Graph
- Check if a graphs has a cycle of odd length
- Detect Cycle in a directed graph using colors
- Check if there is a cycle with odd weight sum in an undirected graph
- Karp's minimum mean (or average) weight cycle algorithm