Floyd-Warshall Algorithm

All-pairs shortest paths via dynamic programming on intermediate vertices

Click "Next Step" to begin Floyd-Warshall

Pivot: —

Graph

Distance Matrix D

Pivot vertex/row/col

Checking D[i][k]+D[k][j]

Updated cell

Algorithm

Floyd-Warshall(W):
  D = W  // copy weight matrix
  for k = 1 to n:             ← pivot vertex
    for i = 1 to n:
      for j = 1 to n:
        D[i][j] = min(D[i][j],
                      D[i][k] + D[k][j])
  return D