emahtab / floyd-warshall-algorithm

Floyd Warshall Algorithm

Floyd Warshall algorithm is used to find the shortest ath from any vertex to any other vertex in a weighted graph.

Algorithm:

1. Create a 2D array matrix of n * n , where n is the number of vertices in the weighted graph
2. Initialize the 2D array matrix[i][i] = 0 and all other cells as matrix[i][j] = Integer.MAX_VALUE (some higher value)
3. Loop over the 2D array n times, k = 0 to less than n, and update the matrix[i][j] as below

for(int k = 0; k < N; k++)
  for(int i = 0; i < N; i++)
    for(int j = 0; j < N; j++)
      matrix[i][j] = Math.min(matrix[i][j], matrix[i][k] + matrix[k][j]);

4. At the end we will have the shorted path from any vertex i to any vertex j in the matrix.

References :

https://www.youtube.com/watch?v=oNI0rf2P9gE

Problems :

1. https://leetcode.com/problems/network-delay-time
2. https://leetcode.com/problems/course-schedule-iv