Suppose Open and Closed are hash tables of states.

Search(s)
   d[s] = 0
   pred[s] = null
   PQ = {s}
   Open = {s}
   Closed = {}
   while PQ ≠ {} do
      u = Remove[PQ]
      Remove(Open,u)
      if success
         then return u
      else
         for each v ∈ Expand(u) do
             if there is an x such that x = v and x ∈ Open  // Scenario 1
                if d[v] < d[x]
                   then d[x] = d[v]
                        pred[x] = pred[v]
                        Promote(PQ,x)
             else if there is an x such that x = v and x ∈ Closed  // Scenario 2
                if d[v] < d[x]
                   then d[x] = d[v]
                        pred[x] = pred[v]
                        Add(PQ,x)
                        Add(Open,x)
                        Remove(Closed,x)
             else
                Add(PQ,v)
                Add(Open,v)
         Add(Closed,u)
   return null