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```// Initialize an empty queue and dictionary
queue = empty
visited = {P: 0}

// Add P to the queue with distance 0
queue.push((P, 0))

// While the queue is not empty
while queue is not empty:
// Remove the junction with smallest distance from P
current, distance = queue.pop()

// Mark current as visited
visited[current] = distance

// If G has been visited, reconstruct the shortest path and return it
if current == G:
path = [G]
while path[-1] != P:
for neighbor in neighbors[path[-1]]:
if neighbor in visited and visited[neighbor] == visited[path[-1]] - 1:
path.append(neighbor)
break
path.reverse()
return path

// Find the unvisited neighbors of current and sort them in alphabetical order
unvisited_neighbors = sorted([neighbor for neighbor in neighbors[current] if neighbor not in visited])

// For each unvisited neighbor of current
for neighbor in unvisited_neighbors:
// Calculate the distance from P to neighbor through current
new_distance = distance + pathway_length(current, neighbor)

// Update the dictionary if the new distance is shorter
if neighbor not in visited or new_distance < visited[neighbor]:
visited[neighbor] = new_distance

// Add neighbor to the queue with the new distance
queue.push((neighbor, new_distance))
```