VhGldZddlmZddlZgdZej ddZej ddZej ddd Z ej dd Z ej dd Z ej d Z d Z dZdZdZej dZej dZy)zBBasic algorithms for breadth-first searching the nodes of a graph.)dequeN) bfs_edgesbfs_treebfs_predecessorsbfs_successorsdescendants_at_distance bfs_layersbfs_labeled_edgesgeneric_bfs_edgesc#ZK| |j}| t|}|h}t|}d}|||fg}|ro||kri|}g}|D]Q\} } | D]7} | |vs|j| |j| || f| | f9t||k(sQy|dz }|r||krgyyyyw)aA Iterate over edges in a breadth-first search. The breadth-first search begins at `source` and enqueues the neighbors of newly visited nodes specified by the `neighbors` function. Parameters ---------- G : NetworkX graph source : node Starting node for the breadth-first search; this function iterates over only those edges in the component reachable from this node. neighbors : function A function that takes a newly visited node of the graph as input and returns an *iterator* (not just a list) of nodes that are neighbors of that node with custom ordering. If not specified, this is just the ``G.neighbors`` method, but in general it can be any function that returns an iterator over some or all of the neighbors of a given node, in any order. depth_limit : int, optional(default=len(G)) Specify the maximum search depth. Yields ------ edge Edges in the breadth-first search starting from `source`. Examples -------- >>> G = nx.path_graph(7) >>> list(nx.generic_bfs_edges(G, source=0)) [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6)] >>> list(nx.generic_bfs_edges(G, source=2)) [(2, 1), (2, 3), (1, 0), (3, 4), (4, 5), (5, 6)] >>> list(nx.generic_bfs_edges(G, source=2, depth_limit=2)) [(2, 1), (2, 3), (1, 0), (3, 4)] The `neighbors` param can be used to specify the visitation order of each node's neighbors generically. In the following example, we modify the default neighbor to return *odd* nodes first: >>> def odd_first(n): ... return sorted(G.neighbors(n), key=lambda x: x % 2, reverse=True) >>> G = nx.star_graph(5) >>> list(nx.generic_bfs_edges(G, source=0)) # Default neighbor ordering [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)] >>> list(nx.generic_bfs_edges(G, source=0, neighbors=odd_first)) [(0, 1), (0, 3), (0, 5), (0, 2), (0, 4)] Notes ----- This implementation is from `PADS`_, which was in the public domain when it was first accessed in July, 2004. The modifications to allow depth limits are based on the Wikipedia article "`Depth-limited-search`_". .. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search Nr) neighborslenaddappend) Gsourcer depth_limitseenndepthnext_parents_childrenthis_parents_childrenparentchildrenchilds b/home/dcms/DCMS/lib/python3.12/site-packages/networkx/algorithms/traversal/breadth_first_search.pyr r sDKK !f 8D AA E$i&789 EK$7 5 " 5  FH! ($HHUO)00%59I1JK %-'  ( 4yA~    EK$7 $7 sAB+AB+B+'B+c#K|r|jr |jn |jt||fd|Ed{yt|||Ed{y77w)a Iterate over edges in a breadth-first-search starting at source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search; this function iterates over only those edges in the component reachable from this node. reverse : bool, optional If True traverse a directed graph in the reverse direction depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function (default=None) A function that takes an iterator over nodes as the input, and returns an iterable of the same nodes with a custom ordering. For example, `sorted` will sort the nodes in increasing order. Yields ------ edge: 2-tuple of nodes Yields edges resulting from the breadth-first search. Examples -------- To get the edges in a breadth-first search:: >>> G = nx.path_graph(3) >>> list(nx.bfs_edges(G, 0)) [(0, 1), (1, 2)] >>> list(nx.bfs_edges(G, source=0, depth_limit=1)) [(0, 1)] To get the nodes in a breadth-first search order:: >>> G = nx.path_graph(3) >>> root = 2 >>> edges = nx.bfs_edges(G, root) >>> nodes = [root] + [v for u, v in edges] >>> nodes [2, 1, 0] Notes ----- The naming of this function is very similar to :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs`. The difference is that ``edge_bfs`` yields edges even if they extend back to an already explored node while this generator yields the edges of the tree that results from a breadth-first-search (BFS) so no edges are reported if they extend to already explored nodes. That means ``edge_bfs`` reports all edges while ``bfs_edges`` only reports those traversed by a node-based BFS. Yet another description is that ``bfs_edges`` reports the edges traversed during BFS while ``edge_bfs`` reports all edges in the order they are explored. Based on the breadth-first search implementation in PADS [1]_ by D. Eppstein, July 2004; with modifications to allow depth limits as described in [2]_. References ---------- .. [1] http://www.ics.uci.edu/~eppstein/PADS/BFS.py. .. [2] https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- bfs_tree :func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges` :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs` Nc2t|S)N)iter)nodesort_neighbors successorss rzbfs_edges..sD 48H)I$J) is_directed predecessorsrr )rrreverserr"r#s `@rrrlskX1==?^^ [[ !$ vJK   %Q KHHH   Is$AA(A$A(A&A(&A(T) returns_graphctj}|j|t|||||}|j ||S)aReturns an oriented tree constructed from of a breadth-first-search starting at source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search reverse : bool, optional If True traverse a directed graph in the reverse direction depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function (default=None) A function that takes an iterator over nodes as the input, and returns an iterable of the same nodes with a custom ordering. For example, `sorted` will sort the nodes in increasing order. Returns ------- T: NetworkX DiGraph An oriented tree Examples -------- >>> G = nx.path_graph(3) >>> list(nx.bfs_tree(G, 1).edges()) [(1, 0), (1, 2)] >>> H = nx.Graph() >>> nx.add_path(H, [0, 1, 2, 3, 4, 5, 6]) >>> nx.add_path(H, [2, 7, 8, 9, 10]) >>> sorted(list(nx.bfs_tree(H, source=3, depth_limit=3).edges())) [(1, 0), (2, 1), (2, 7), (3, 2), (3, 4), (4, 5), (5, 6), (7, 8)] Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. The modifications to allow depth limits based on the Wikipedia article "`Depth-limited-search`_". .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- dfs_tree bfs_edges edge_bfs )r(rr")nxDiGraphadd_noderadd_edges_from)rrr(rr"T edges_gens rrrsJn AJJv % IY Hr%c#FKt||||D] \}}||f yw)aReturns an iterator of predecessors in breadth-first-search from source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function (default=None) A function that takes an iterator over nodes as the input, and returns an iterable of the same nodes with a custom ordering. For example, `sorted` will sort the nodes in increasing order. Returns ------- pred: iterator (node, predecessor) iterator where `predecessor` is the predecessor of `node` in a breadth first search starting from `source`. Examples -------- >>> G = nx.path_graph(3) >>> dict(nx.bfs_predecessors(G, 0)) {1: 0, 2: 1} >>> H = nx.Graph() >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) >>> dict(nx.bfs_predecessors(H, 0)) {1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2} >>> M = nx.Graph() >>> nx.add_path(M, [0, 1, 2, 3, 4, 5, 6]) >>> nx.add_path(M, [2, 7, 8, 9, 10]) >>> sorted(nx.bfs_predecessors(M, source=1, depth_limit=3)) [(0, 1), (2, 1), (3, 2), (4, 3), (7, 2), (8, 7)] >>> N = nx.DiGraph() >>> nx.add_path(N, [0, 1, 2, 3, 4, 7]) >>> nx.add_path(N, [3, 5, 6, 7]) >>> sorted(nx.bfs_predecessors(N, source=2)) [(3, 2), (4, 3), (5, 3), (6, 5), (7, 4)] Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004. The modifications to allow depth limits based on the Wikipedia article "`Depth-limited-search`_". .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- bfs_tree bfs_edges edge_bfs rr"N)r)rrrr"sts rrr s5x 6{>1!f s!c#K|}g}t||||D]'\}}||k(r|j|||f|g}|})||fyw)a Returns an iterator of successors in breadth-first-search from source. Parameters ---------- G : NetworkX graph source : node Specify starting node for breadth-first search depth_limit : int, optional(default=len(G)) Specify the maximum search depth sort_neighbors : function (default=None) A function that takes an iterator over nodes as the input, and returns an iterable of the same nodes with a custom ordering. For example, `sorted` will sort the nodes in increasing order. Returns ------- succ: iterator (node, successors) iterator where `successors` is the non-empty list of successors of `node` in a breadth first search from `source`. To appear in the iterator, `node` must have successors. Examples -------- >>> G = nx.path_graph(3) >>> dict(nx.bfs_successors(G, 0)) {0: [1], 1: [2]} >>> H = nx.Graph() >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) >>> dict(nx.bfs_successors(H, 0)) {0: [1, 2], 1: [3, 4], 2: [5, 6]} >>> G = nx.Graph() >>> nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) >>> nx.add_path(G, [2, 7, 8, 9, 10]) >>> dict(nx.bfs_successors(G, source=1, depth_limit=3)) {1: [0, 2], 2: [3, 7], 3: [4], 7: [8]} >>> G = nx.DiGraph() >>> nx.add_path(G, [0, 1, 2, 3, 4, 5]) >>> dict(nx.bfs_successors(G, source=3)) {3: [4], 4: [5]} Notes ----- Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py by D. Eppstein, July 2004.The modifications to allow depth limits based on the Wikipedia article "`Depth-limited-search`_". .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search See Also -------- bfs_tree bfs_edges edge_bfs r2N)rr)rrrr"rrpcs rrrKspxFH 6{>1 ; OOA  x  3 8 sAAc#K||vr|g}t|}t|}|D]}||vstjd|d|rD|g}|D]3}||D])}||vs|j ||j |+5|}|rCyyw)aReturns an iterator of all the layers in breadth-first search traversal. Parameters ---------- G : NetworkX graph A graph over which to find the layers using breadth-first search. sources : node in `G` or iterable of nodes in `G` Specify starting nodes for single source or multiple sources breadth-first search. Yields ------ layer : list of nodes Yields list of nodes at the same distance from `sources`. Examples -------- >>> G = nx.path_graph(5) >>> dict(enumerate(nx.bfs_layers(G, [0, 4]))) {0: [0, 4], 1: [1, 3], 2: [2]} >>> H = nx.Graph() >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) >>> dict(enumerate(nx.bfs_layers(H, [1]))) {0: [1], 1: [0, 3, 4], 2: [2], 3: [5, 6]} >>> dict(enumerate(nx.bfs_layers(H, [1, 6]))) {0: [1, 6], 1: [0, 3, 4, 2], 2: [5]} The node  is not in the graph.N)setlistr+ NetworkXErrorrr)rsourcesvisited current_layerr next_layerr!rs rr r s<!|)'lGMMN ?""Yvh6K#LM MN  ! -D4 -'KK&%%e, - - #  s'B 3B *B  B r(treeforwardlevelc#(K||vr|g}|j}|j}t}|r |jn |j}t j |d}t|j}|j}|j} |r~| \} } || D]`} | |vr | dzx|| <} || | f| | tf'|| } | | k(r| |vs6| | tfB| | kr | | tfS|sV| | tfb|| |r}yyw)alIterate over edges in a breadth-first search (BFS) labeled by type. We generate triple of the form (*u*, *v*, *d*), where (*u*, *v*) is the edge being explored in the breadth-first search and *d* is one of the strings 'tree', 'forward', 'level', or 'reverse'. A 'tree' edge is one in which *v* is first discovered and placed into the layer below *u*. A 'forward' edge is one in which *u* is on the layer above *v* and *v* has already been discovered. A 'level' edge is one in which both *u* and *v* occur on the same layer. A 'reverse' edge is one in which *u* is on a layer below *v*. We emit each edge exactly once. In an undirected graph, 'reverse' edges do not occur, because each is discovered either as a 'tree' or 'forward' edge. Parameters ---------- G : NetworkX graph A graph over which to find the layers using breadth-first search. sources : node in `G` or list of nodes in `G` Starting nodes for single source or multiple sources breadth-first search Yields ------ edges: generator A generator of triples (*u*, *v*, *d*) where (*u*, *v*) is the edge being explored and *d* is described above. Examples -------- >>> G = nx.cycle_graph(4, create_using=nx.DiGraph) >>> list(nx.bfs_labeled_edges(G, 0)) [(0, 1, 'tree'), (1, 2, 'tree'), (2, 3, 'tree'), (3, 0, 'reverse')] >>> G = nx.complete_graph(3) >>> list(nx.bfs_labeled_edges(G, 0)) [(0, 1, 'tree'), (0, 2, 'tree'), (1, 2, 'level')] >>> list(nx.bfs_labeled_edges(G, [0, 1])) [(0, 1, 'level'), (0, 2, 'tree'), (1, 2, 'forward')] rr N)_adjr&r;discardrdictfromkeysritemsrpopleft TREE_EDGE LEVEL_EDGE FORWARD_EDGE REVERSE_EDGE)rr>rdirectedr?visitrqueuepushpopuduvdvs rr r sR!|)I}}HeG'GOOW[[E MM'1 %E %++- E <>> G = nx.path_graph(5) >>> nx.descendants_at_distance(G, 2, 2) {0, 4} >>> H = nx.DiGraph() >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) >>> nx.descendants_at_distance(H, 0, 2) {3, 4, 5, 6} >>> nx.descendants_at_distance(H, 5, 0) {5} >>> nx.descendants_at_distance(H, 5, 1) set() r9r:)r+r=r enumerater;)rrdistance bfs_generatorilayers rrrsh<Q6(2GHIIMM!V,Mm,5 =u:  5Lr%)NN)FNN)__doc__ collectionsrnetworkxr+__all__ _dispatchabler rrrrr rOrLrNrMr rr%rresH UUpUIUIp%@ &@ F>>BFFR1#1#h    GGT$$r%