Vh"dZddlmZmZddlmZddlZddlm Z ddgZ ejdd ddd d Z ejdd  ddd d Z y)zBShortest paths and path lengths using the A* ("A star") algorithm.)heappopheappush)countN)_weight_function astar_pathastar_path_lengthweight heuristic) edge_attrspreserve_node_attrscutoffc ||vrtjd|d||vrtjd|d|d}t||}|j}t }dt ||ddfg}i} i} |rt |\} } } }}| |k(r2| g}|}||j|| |}||j|S| | vr| | T| | \}}||krb|| | <|| jD]a\}}|| ||}|||z}|| vr| |\}}||kr *|||}|r ||z|kDr>||f| |<t|||zt |||| fc|rtjd|d|) a 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 zSource is not in GzTarget Ncy)Nr)uvs X/home/dcms/DCMS/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/astar.pyr zastar_path..heuristicfsrzNode z not reachable from ) nx NodeNotFoundr_adjrnextrappendreverseitemsrNetworkXNoPath)Gsourcetargetr r rG_succcqueueenqueuedexplored___curnodedistparentpathnodeqcosthneighborwcostncosts rrr sdQoox|<== Qoox|<== a (F VVF Aa&!T * +E HH '.u~$2wf f 9DD" D!~" LLNK h  ( (HE1t|"!'?002 LKHa'8Q/D|4KE8##H-q E>h/%!)f,!&HX  UUQYQ5'J K) L3 ^  eF8+?xH IIrc |vs|vrd|d|d}tj|tt||||}t fdt |dd|ddDS) aWReturns 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. 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 -------- astar_path zEither source z or target rr c3DK|]\}}||||yw)Nr).0rrrr s r z$astar_path_length..s&JAvaAaDG$Js N)rrrrsumzip)rr r!r r rmsgr,s` ` rrrszvQ&/vhk&Fooc"" a (F aF6 JD JT#2YQR1IJ JJr)Nr )__doc__heapqrr itertoolsrnetworkxr+networkx.algorithms.shortest_paths.weightedr__all__ _dispatchablerrrrrrDsH#H , -X;G^JT^JH^JBX;G.6@KBF@KH@Kr