### Floyd Warshall Algorithm to find shortest path weighted directed Graph.

- Its an algorithm that finds the shortest path between every pair of vertices of graph
- Supports negative edges-weights but not negative-weight cycles
- Runs in O(n^3) times
- Increases numbers of hops allowed by 1 with each iteration.
- Its a dynamic programming algorithm
- Application of Floyd Warshall Algorithm
- Clean’s algorithm
- Transitive closure
- Widest path in the graph

##### Algorithm:

- Need two matrix of same size of graph (Distance matrix and path matrix)
- Initially – We put all distances in distance matrix if there is any distance in graph
- And use infinity in distance matrix if there is no path
- It iterate for all vertices one by one
- if
`d[i] [j] > d[i][k] + d[k][j]`

then update distance matrix and path matrix. - Here eveytime we’re checking do we have a shortest path from i to j by take k as intermediate vertex

- if

Latest Source Code:

Github: FloydWarshallShortestPath.java

**Output:**

From To Distance 0 0 0 0 1 3 0 2 1 0 3 -1 1 0 -3 1 1 0 1 2 -2 1 3 -4 2 0 -1 2 1 2 2 2 0 2 3 -2 3 0 1 3 1 4 3 2 2 3 3 0