Bellman-Ford Algorithm

Single-source shortest paths with negative edge weights

Click "Next Step" to begin the Bellman-Ford algorithm

Unvisited

Relaxing

Updated

Finalized

Negative Edge

Iteration

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Edge Being Relaxed

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Distances

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Algorithm

Bellman-Ford(G, s):
  for each v in V: d[v] = ∞, π[v] = NIL
  d[s] = 0
  for i = 1 to |V|-1:          ← outer loop
    for each edge (u,v) in E:   ← relax all edges
      if d[v] > d[u] + w(u,v):
        d[v] = d[u] + w(u,v)
        π[v] = u
  // Negative cycle check
  for each edge (u,v) in E:
    if d[v] > d[u] + w(u,v):
      return "Negative cycle!"