nx_functions

# Curled from networkX documentation

def astar_path(G, source, target, heuristic=None, weight="weight"):
    """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.

    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.

    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)]


    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)

    # 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[curnode].items():
            ncost = dist + weight(curnode, neighbor, w)
            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)
            enqueued[neighbor] = ncost, h
            push(queue, (ncost + h, next(c), neighbor, ncost, curnode))

    raise nx.NetworkXNoPath(f"Node {target} not reachable from {source}")

def astar_path_length(G, source, target, heuristic=None, weight="weight"):
    """Returns the length of the shortest path between source and target using
    the A* ("A-star") algorithm.

    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.

    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.
    Raises
    ------
    NetworkXNoPath
        If no path exists between source and target.

    See Also
    --------
    astar_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)

    weight = _weight_function(G, weight)
    path = astar_path(G, source, target, heuristic, weight)
    return sum(weight(u, v, G[u][v]) for u, v in zip(path[:-1], path[1:]))