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# astar_path

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.

  See also

  `shortest_path`, `dijkstra_path`

  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.

  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)]