Astar

function A*(start, goal)
// The set of nodes already evaluated
closedSet := {}

// The set of currently discovered nodes that are not evaluated yet.
// Initially, only the start node is known.
openSet := {start}

// For each node, which node it can most efficiently be reached from.
// If a node can be reached from many nodes, cameFrom will eventually contain the
// most efficient previous step.
cameFrom := the empty map

// For each node, the cost of getting from the start node to that node.
gScore := map with default value of Infinity

// The cost of going from start to start is zero.
gScore[start] := 0

// For each node, the total cost of getting from the start node to the goal
// by passing by that node. That value is partly known, partly heuristic.
fScore := map with default value of Infinity

// For the first node, that value is completely heuristic.
fScore[start] := heuristic_cost_estimate(start, goal)

while openSet is not empty
current := the node in openSet having the lowest fScore[] value
if current = goal
return reconstruct_path(cameFrom, current)

openSet.Remove(current)
closedSet.Add(current)

for each neighbor of current
if neighbor in closedSet
continue // Ignore the neighbor which is already evaluated.

if neighbor not in openSet // Discover a new node
openSet.Add(neighbor)

// The distance from start to a neighbor
tentative_gScore := gScore[current] + dist_between(current, neighbor)
if tentative_gScore >= gScore[neighbor]
continue // This is not a better path.

// This path is the best until now. Record it!
cameFrom[neighbor] := current
gScore[neighbor] := tentative_gScore
fScore[neighbor] := gScore[neighbor] + heuristic_cost_estimate(neighbor, goal)

return failure

function reconstruct_path(cameFrom, current)
total_path := [current]
while current in cameFrom.Keys:
current := cameFrom[current]
total_path.append(current)
return total_path