code: def astar_path(
      G, source, target, heuristic=None, weight="weight", *, cutoff=None
  ):
      """Returns a list of nodes in a shortest path between source and target
      using the A* ("A-star") algorithm.
  
      There may be more than one shortest path.  This returns only one.
  
      Parameters
      ----------
      G : NetworkX graph
  
      source : node
         Starting node for path
  
      target : node
         Ending node for path
  
      heuristic : function
         A function to evaluate the estimate of the distance
         from the a node to the target.  The function takes
         two nodes arguments and must return a number.
         If the heuristic is inadmissible (if it might
         overestimate the cost of reaching the goal from a node),
         the result may not be a shortest path.
         The algorithm does not support updating heuristic
         values for the same node due to caching the first
         heuristic calculation per node.
  
      weight : string or function
         If this is a string, then edge weights will be accessed via the
         edge attribute with this key (that is, the weight of the edge
         joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
         such edge attribute exists, the weight of the edge is assumed to
         be one.
         If this is a function, the weight of an edge is the value
         returned by the function. The function must accept exactly three
         positional arguments: the two endpoints of an edge and the
         dictionary of edge attributes for that edge. The function must
         return a number or None to indicate a hidden edge.
  
      cutoff : float, optional
         If this is provided, the search will be bounded to this value. I.e. if
         the evaluation function surpasses this value for a node n, the node will not
         be expanded further and will be ignored. More formally, let h'(n) be the
         heuristic function, and g(n) be the cost of reaching n from the source node. Then,
         if g(n) + h'(n) > cutoff, the node will not be explored further.
         Note that if the heuristic is inadmissible, it is possible that paths
         are ignored even though they satisfy the cutoff.
  
      Raises
      ------
      NetworkXNoPath
          If no path exists between source and target.
  
      Examples
      --------
      >>> G = nx.path_graph(5)
      >>> print(nx.astar_path(G, 0, 4))
      [0, 1, 2, 3, 4]
      >>> G = nx.grid_graph(dim=[3, 3])  # nodes are two-tuples (x,y)
      >>> nx.set_edge_attributes(G, {e: e[1][0] * 2 for e in G.edges()}, "cost")
      >>> def dist(a, b):
      ...     (x1, y1) = a
      ...     (x2, y2) = b
      ...     return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5
      >>> print(nx.astar_path(G, (0, 0), (2, 2), heuristic=dist, weight="cost"))
      [(0, 0), (0, 1), (0, 2), (1, 2), (2, 2)]
  
      Notes
      -----
      Edge weight attributes must be numerical.
      Distances are calculated as sums of weighted edges traversed.
  
      The weight function can be used to hide edges by returning None.
      So ``weight = lambda u, v, d: 1 if d['color']=="red" else None``
      will find the shortest red path.
  
      See Also
      --------
      shortest_path, dijkstra_path
  
      """
      if source not in G or target not in G:
          msg = f"Either source {source} or target {target} is not in G"
          raise nx.NodeNotFound(msg)
  
      if heuristic is None:
          # The default heuristic is h=0 - same as Dijkstra's algorithm
          def heuristic(u, v):
              return 0
  
      push = heappush
      pop = heappop
      weight = _weight_function(G, weight)
  
      G_succ = (
          G._adj
      )  # For speed-up (and works for both directed and undirected graphs)
  
      # The queue stores priority, node, cost to reach, and parent.
      # Uses Python heapq to keep in priority order.
      # Add a counter to the queue to prevent the underlying heap from
      # attempting to compare the nodes themselves. The hash breaks ties in the
      # priority and is guaranteed unique for all nodes in the graph.
      c = count()
      queue = [(0, next(c), source, 0, None)]
  
      # Maps enqueued nodes to distance of discovered paths and the
      # computed heuristics to target. We avoid computing the heuristics
      # more than once and inserting the node into the queue too many times.
      enqueued = {}
      # Maps explored nodes to parent closest to the source.
      explored = {}
  
      while queue:
          # Pop the smallest item from queue.
          _, __, curnode, dist, parent = pop(queue)
  
          if curnode == target:
              path = [curnode]
              node = parent
              while node is not None:
                  path.append(node)
                  node = explored[node]
              path.reverse()
              return path
  
          if curnode in explored:
              # Do not override the parent of starting node
              if explored[curnode] is None:
                  continue
  
              # Skip bad paths that were enqueued before finding a better one
              qcost, h = enqueued[curnode]
              if qcost < dist:
                  continue
  
          explored[curnode] = parent
  
          for neighbor, w in G_succ[curnode].items():
              cost = weight(curnode, neighbor, w)
              if cost is None:
                  continue
              ncost = dist + cost
              if neighbor in enqueued:
                  qcost, h = enqueued[neighbor]
                  # if qcost <= ncost, a less costly path from the
                  # neighbor to the source was already determined.
                  # Therefore, we won't attempt to push this neighbor
                  # to the queue
                  if qcost <= ncost:
                      continue
              else:
                  h = heuristic(neighbor, target)
  
              if cutoff and ncost + h > cutoff:
                  continue
  
              enqueued[neighbor] = ncost, h
              push(
                  queue, (ncost + h, next(c), neighbor, ncost, curnode)
              )
  
      raise nx.NetworkXNoPath(
          f"Node {target} not reachable from {source}"
      )
  
imports: from heapq import heappop, heappush
  from itertools import count
  import networkx
  from networkx.algorithms.shortest_paths.weighted import _weight_function
label_desc: Use image node_id 1 for calling a global function with example usage: astar_path(G, source, target, heuristic, weight) and returns: int, path