VhAdZddlmZddlmZmZddlmZddlZ ddl m Z gdZ dZ e jd d(d Ze jd d(d Ze jd d)d Ze jd d)dZe jd d*dZe jd d)dZe jd d)dZe jd d*dZd+dZ d+dZe jd d)dZe jd d)dZe jd d)dZe jd d)dZe jd  d,dZ d-dZ d.dZe jd d(dZ e jd d(dZ!e jd d(dZ"e jd d(dZ#e jd d)d Z$e jd d(d!Z%e jd d(d"Z&e jd d(d#Z'e jd d/d$Z(e jd d(d%Z)e jd d(d&Z*e jd d(d'Z+y)0z/ Shortest path algorithms for weighted graphs. )deque)heappopheappush)countN)_build_paths_from_predecessors) dijkstra_pathdijkstra_path_lengthbidirectional_dijkstrasingle_source_dijkstrasingle_source_dijkstra_path"single_source_dijkstra_path_lengthmulti_source_dijkstramulti_source_dijkstra_path!multi_source_dijkstra_path_lengthall_pairs_dijkstraall_pairs_dijkstra_pathall_pairs_dijkstra_path_length!dijkstra_predecessor_and_distancebellman_ford_pathbellman_ford_path_lengthsingle_source_bellman_fordsingle_source_bellman_ford_path&single_source_bellman_ford_path_lengthall_pairs_bellman_ford_path"all_pairs_bellman_ford_path_length%bellman_ford_predecessor_and_distancenegative_edge_cyclefind_negative_cyclegoldberg_radzikjohnsoncRtrS|jrfdSfdS)a_Returns a function that returns the weight of an edge. The returned function is specifically suitable for input to functions :func:`_dijkstra` and :func:`_bellman_ford_relaxation`. Parameters ---------- G : NetworkX graph. weight : string or function If it is callable, `weight` itself is returned. If it is a string, it is assumed to be the name of the edge attribute that represents the weight of an edge. In that case, a function is returned that gets the edge weight according to the specified edge attribute. Returns ------- function This function returns a callable that accepts exactly three inputs: a node, an node adjacent to the first one, and the edge attribute dictionary for the eedge joining those nodes. That function returns a number representing the weight of an edge. If `G` is a multigraph, and `weight` is not callable, the minimum edge weight over all parallel edges is returned. If any edge does not have an attribute with key `weight`, it is assumed to have weight one. cHtfd|jDS)Nc3BK|]}|jdyw)Nget).0attrweights [/home/dcms/DCMS/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/weighted.py z5_weight_function....Ms"N4488FA#6"Ns)minvalues)uvdr)s r*z"_weight_function..Mss"N188:"NNc(|jdS)Nr$r%)r.r/datar)s r*r1z"_weight_function..Nsdhhvq1r2)callable is_multigraph)Gr)s `r*_weight_functionr8)s*<  NN 11r2r)) edge_attrsc*t||||\}}|S)a} Returns the shortest weighted path from source to target in G. Uses Dijkstra's Method to compute the shortest weighted path between two nodes in a graph. Parameters ---------- G : NetworkX graph source : node Starting node target : node Ending 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. Returns ------- path : list List of nodes in a shortest path. Raises ------ NodeNotFound If `source` is not in `G`. NetworkXNoPath If no path exists between source and target. Examples -------- >>> G = nx.path_graph(5) >>> print(nx.dijkstra_path(G, 0, 4)) [0, 1, 2, 3, 4] Find edges of shortest path in Multigraph >>> G = nx.MultiDiGraph() >>> G.add_weighted_edges_from([(1, 2, 0.75), (1, 2, 0.5), (2, 3, 0.5), (1, 3, 1.5)]) >>> nodes = nx.dijkstra_path(G, 1, 3) >>> edges = nx.utils.pairwise(nodes) >>> list( ... (u, v, min(G[u][v], key=lambda k: G[u][v][k].get("weight", 1))) ... for u, v in edges ... ) [(1, 2, 1), (2, 3, 0)] 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. The weight function can be used to include node weights. >>> def func(u, v, d): ... node_u_wt = G.nodes[u].get("node_weight", 1) ... node_v_wt = G.nodes[v].get("node_weight", 1) ... edge_wt = d.get("weight", 1) ... return node_u_wt / 2 + node_v_wt / 2 + edge_wt In this example we take the average of start and end node weights of an edge and add it to the weight of the edge. The function :func:`single_source_dijkstra` computes both path and length-of-path if you need both, use that. See Also -------- bidirectional_dijkstra bellman_ford_path single_source_dijkstra targetr)r r7sourcer<r)lengthpaths r*rrQst,AvfVTNVT Kr2c||vrtjd|d||k(ryt||}t||||} ||S#t$r!}tj d|d||d}~wwxYw)aXReturns the shortest weighted path length in G from source to target. Uses Dijkstra's Method to compute the shortest weighted path length between two nodes in a graph. Parameters ---------- G : NetworkX graph source : node label starting node for path target : node label ending node for path 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. Returns ------- length : number Shortest path length. Raises ------ NodeNotFound If `source` is not in `G`. NetworkXNoPath If no path exists between source and target. Examples -------- >>> G = nx.path_graph(5) >>> nx.dijkstra_path_length(G, 0, 4) 4 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. The function :func:`single_source_dijkstra` computes both path and length-of-path if you need both, use that. See Also -------- bidirectional_dijkstra bellman_ford_path_length single_source_dijkstra Node  not found in graphrr< not reachable from N)nx NodeNotFoundr8 _dijkstraKeyErrorNetworkXNoPathr7r?r<r)r@errs r*r r sHQoofX-@ABB  a (F q&& 8FWf~ W%x/CF8 LMSVVWsA A/A**A/c"t||h||S)a0Find shortest weighted paths in G from a source node. Compute shortest path between source and all other reachable nodes for a weighted graph. Parameters ---------- G : NetworkX graph source : node Starting node for path. cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- paths : dictionary Dictionary of shortest path lengths keyed by target. Raises ------ NodeNotFound If `source` is not in `G`. Examples -------- >>> G = nx.path_graph(5) >>> path = nx.single_source_dijkstra_path(G, 0) >>> path[4] [0, 1, 2, 3, 4] 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 -------- single_source_dijkstra, single_source_bellman_ford cutoffr))rr7r?rPr)s r*r r s| &a&& PPr2c"t||h||S)aFind shortest weighted path lengths in G from a source node. Compute the shortest path length between source and all other reachable nodes for a weighted graph. Parameters ---------- G : NetworkX graph source : node label Starting node for path cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- length : dict Dict keyed by node to shortest path length from source. Raises ------ NodeNotFound If `source` is not in `G`. Examples -------- >>> G = nx.path_graph(5) >>> length = nx.single_source_dijkstra_path_length(G, 0) >>> length[4] 4 >>> for node in [0, 1, 2, 3, 4]: ... print(f"{node}: {length[node]}") 0: 0 1: 1 2: 2 3: 3 4: 4 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 -------- single_source_dijkstra, single_source_bellman_ford_path_length rO)rrQs r*r r @sJ -QPV WWr2c$t||h|||S)a Find shortest weighted paths and lengths from a source node. Compute the shortest path length between source and all other reachable nodes for a weighted graph. Uses Dijkstra's algorithm to compute shortest paths and lengths between a source and all other reachable nodes in a weighted graph. Parameters ---------- G : NetworkX graph source : node label Starting node for path target : node label, optional Ending node for path cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- distance, path : pair of dictionaries, or numeric and list. If target is None, paths and lengths to all nodes are computed. The return value is a tuple of two dictionaries keyed by target nodes. The first dictionary stores distance to each target node. The second stores the path to each target node. If target is not None, returns a tuple (distance, path), where distance is the distance from source to target and path is a list representing the path from source to target. Raises ------ NodeNotFound If `source` is not in `G`. Examples -------- >>> G = nx.path_graph(5) >>> length, path = nx.single_source_dijkstra(G, 0) >>> length[4] 4 >>> for node in [0, 1, 2, 3, 4]: ... print(f"{node}: {length[node]}") 0: 0 1: 1 2: 2 3: 3 4: 4 >>> path[4] [0, 1, 2, 3, 4] >>> length, path = nx.single_source_dijkstra(G, 0, 1) >>> length 1 >>> path [0, 1] 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. Based on the Python cookbook recipe (119466) at https://code.activestate.com/recipes/119466/ This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems). See Also -------- single_source_dijkstra_path single_source_dijkstra_path_length single_source_bellman_ford )rPr<r)r)r7r?r<rPr)s r*r r sB ! F8F6& r2c*t||||\}}|S)aFind shortest weighted paths in G from a given set of source nodes. Compute shortest path between any of the source nodes and all other reachable nodes for a weighted graph. Parameters ---------- G : NetworkX graph sources : non-empty set of nodes Starting nodes for paths. If this is just a set containing a single node, then all paths computed by this function will start from that node. If there are two or more nodes in the set, the computed paths may begin from any one of the start nodes. cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- paths : dictionary Dictionary of shortest paths keyed by target. Examples -------- >>> G = nx.path_graph(5) >>> path = nx.multi_source_dijkstra_path(G, {0, 4}) >>> path[1] [0, 1] >>> path[3] [4, 3] 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. Raises ------ ValueError If `sources` is empty. NodeNotFound If any of `sources` is not in `G`. See Also -------- multi_source_dijkstra, multi_source_bellman_ford rOrT)r7sourcesrPr)r@rAs r*rrsL)GF6RLFD Kr2c|s td|D]}||vstjd|dt||}t ||||S)aFind shortest weighted path lengths in G from a given set of source nodes. Compute the shortest path length between any of the source nodes and all other reachable nodes for a weighted graph. Parameters ---------- G : NetworkX graph sources : non-empty set of nodes Starting nodes for paths. If this is just a set containing a single node, then all paths computed by this function will start from that node. If there are two or more nodes in the set, the computed paths may begin from any one of the start nodes. cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- length : dict Dict keyed by node to shortest path length to nearest source. Examples -------- >>> G = nx.path_graph(5) >>> length = nx.multi_source_dijkstra_path_length(G, {0, 4}) >>> for node in [0, 1, 2, 3, 4]: ... print(f"{node}: {length[node]}") 0: 0 1: 1 2: 2 3: 1 4: 0 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. Raises ------ ValueError If `sources` is empty. NodeNotFound If any of `sources` is not in `G`. See Also -------- multi_source_dijkstra sources must not be emptyrCrD)rP) ValueErrorrGrHr8_dijkstra_multisource)r7rVrPr)ss r*rr8sdR 455 B A://E!,?"@A ABa (F GVF CCr2cT|s td|D]}||vstjd|d||vrd|gfSt||}|Dcic]}||g}}t ||||||}|||fS ||||fScc}w#t $r} tj d|d| d} ~ wwxYw) a Find shortest weighted paths and lengths from a given set of source nodes. Uses Dijkstra's algorithm to compute the shortest paths and lengths between one of the source nodes and the given `target`, or all other reachable nodes if not specified, for a weighted graph. Parameters ---------- G : NetworkX graph sources : non-empty set of nodes Starting nodes for paths. If this is just a set containing a single node, then all paths computed by this function will start from that node. If there are two or more nodes in the set, the computed paths may begin from any one of the start nodes. target : node label, optional Ending node for path cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- distance, path : pair of dictionaries, or numeric and list If target is None, returns a tuple of two dictionaries keyed by node. The first dictionary stores distance from one of the source nodes. The second stores the path from one of the sources to that node. If target is not None, returns a tuple of (distance, path) where distance is the distance from source to target and path is a list representing the path from source to target. Examples -------- >>> G = nx.path_graph(5) >>> length, path = nx.multi_source_dijkstra(G, {0, 4}) >>> for node in [0, 1, 2, 3, 4]: ... print(f"{node}: {length[node]}") 0: 0 1: 1 2: 2 3: 1 4: 0 >>> path[1] [0, 1] >>> path[3] [4, 3] >>> length, path = nx.multi_source_dijkstra(G, {0, 4}, 1) >>> length 1 >>> path [0, 1] 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. Based on the Python cookbook recipe (119466) at https://code.activestate.com/recipes/119466/ This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems). Raises ------ ValueError If `sources` is empty. NodeNotFound If any of `sources` is not in `G`. See Also -------- multi_source_dijkstra_path multi_source_dijkstra_path_length rXrCrDr)pathsrPr<Nz No path to .)rYrGrHr8rZrJrK) r7rVr<rPr)r[r?r]distrMs r*rrsH 455 B A://E!,?"@A ABF8} a (F,3 4&VfX  4E 4  7F%v D~e}BV eFm,, 5 B+fXQ 78cABs A:0 A?? B'B""B'c (t||g|||||S)aUses Dijkstra's algorithm to find shortest weighted paths from a single source. This is a convenience function for :func:`_dijkstra_multisource` with all the arguments the same, except the keyword argument `sources` set to ``[source]``. )predr]rPr<)rZ)r7r?r)rar]rPr<s r*rIrIs" ! F8V$eF6 r2ct|j}i}i} t} g} |D]} d| | <t| dt| | f!| rt | \} }}||vr| ||<||k(r |S||j D]\}}||||}||||z}|||kDr#||vr4||}||kr t dd|@||k(sF||j|[|| vs|| |kr5|| |<t| |t| |f| |||gz||<||g||<|| |k(s|||j|| r|S)a{Uses Dijkstra's algorithm to find shortest weighted paths Parameters ---------- G : NetworkX graph sources : non-empty iterable of nodes Starting nodes for paths. If this is just an iterable containing a single node, then all paths computed by this function will start from that node. If there are two or more nodes in this iterable, the computed paths may begin from any one of the start nodes. weight: function Function with (u, v, data) input that returns that edge's weight or None to indicate a hidden edge pred: dict of lists, optional(default=None) dict to store a list of predecessors keyed by that node If None, predecessors are not stored. paths: dict, optional (default=None) dict to store the path list from source to each node, keyed by node. If None, paths are not stored. target : node label, optional Ending node for path. Search is halted when target is found. cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. Returns ------- distance : dictionary A mapping from node to shortest distance to that node from one of the source nodes. Raises ------ NodeNotFound If any of `sources` is not in `G`. Notes ----- The optional predecessor and path dictionaries can be accessed by the caller through the original pred and paths objects passed as arguments. No need to explicitly return pred or paths. rzContradictory paths found:znegative weights?)_adjrrnextritemsrYappend)r7rVr)rar]rPr<G_succr_seencfringer?r0_r/r.ecostvu_distu_dists r*rZrZsjVVF D D A F/V !T!Wf-./ FO Aq 9 Q ; 8 K71IOO% &DAq!Q?D|1gnG!V#DyaV#$%ACVWW%'V*;GNN1%$'DG"3!Q'47A!67$$Qx1#~E!H# cDGDG##GNN1%/ & D Kr2c||vrtjd|dt||}|gi}|t|||||fS)aCompute weighted shortest path length and predecessors. Uses Dijkstra's Method to obtain the shortest weighted paths and return dictionaries of predecessors for each node and distance for each node from the `source`. Parameters ---------- G : NetworkX graph source : node label Starting node for path cutoff : integer or float, optional Length (sum of edge weights) at which the search is stopped. If cutoff is provided, only return paths with summed weight <= cutoff. 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. Returns ------- pred, distance : dictionaries Returns two dictionaries representing a list of predecessors of a node and the distance to each node. Raises ------ NodeNotFound If `source` is not in `G`. Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. The list of predecessors contains more than one element only when there are more than one shortest paths to the key node. Examples -------- >>> G = nx.path_graph(5, create_using=nx.DiGraph()) >>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0) >>> sorted(pred.items()) [(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])] >>> sorted(dist.items()) [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)] >>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0, 1) >>> sorted(pred.items()) [(0, []), (1, [0])] >>> sorted(dist.items()) [(0, 0), (1, 1)] rC is not found in the graph)rarP)rGrHr8rI)r7r?rPr)ras r*rrusRDQoofX-GHII a (F B