o 3ήcQ7@sfdZddlmZddlZgdZdddZddd Zdd d Zdd d Z dddZ ddZ ddZ dS)zBBasic algorithms for breadth-first searching the nodes of a graph.)dequeN) bfs_edgesbfs_treebfs_predecessorsbfs_successorsdescendants_at_distance bfs_layersc #str|fdd}|h}|durt|}t||||fg}|rb|d\}}} z$t| } | |vrO|| fV|| |dkrO|| |d|| fWn ty]|Ynw|s%dSdS)aIterate 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. 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 sort_neighbors : function A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. Yields ------ edge Edges in the breadth-first search starting from `source`. Examples -------- >>> G = nx.path_graph(3) >>> print(list(nx.bfs_edges(G, 0))) [(0, 1), (1, 2)] >>> print(list(nx.bfs_edges(G, source=0, depth_limit=1))) [(0, 1)] 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 cst|S)N)iter)node _neighborssort_neighborsY/tmp/pip-target-vg8gfxp4/lib/python/networkx/algorithms/traversal/breadth_first_search.pyHsz#generic_bfs_edges..Nr)callablelenrnextaddappend StopIterationpopleft) Gsource neighbors depth_limitr visitedqueueparent depth_nowchildrenchildrr rgeneric_bfs_edgess,6     r#Fccs6|r |r |j}n|j}t|||||EdHdS)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 A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. 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` N) is_directed predecessorsrr#)rrreverserr successorsrrrr[s  JrcCs2t}||t|||||d}|||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 A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. Returns ------- T: NetworkX DiGraph An oriented tree Examples -------- >>> G = nx.path_graph(3) >>> print(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]) >>> print(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_genrrrrs5  rccs*t||||dD] \}}||fVq dS)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 A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. 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) >>> print(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)]) >>> print(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]) >>> print(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]) >>> print(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 strrrrs : rccsZ|}g}t||||dD]\}}||kr||q ||fV|g}|}q ||fVdS)aReturns 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 A function that takes the list of neighbors of given node as input, and returns an *iterator* over these neighbors but with custom ordering. 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) >>> print(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)]) >>> print(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]) >>> print(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]) >>> print(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 r.N)rr)rrrr rr!pcrrrr.s:  rccs||vr|g}t|}t|}|D]}||vr!td|dq|rJ|Vt}|D]}||D]}||vrB||||q2q,|}|s$dSdS)apReturns 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 list 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)listsetr( NetworkXErrorrr)rsources current_layerrr next_layerr r"rrrrvs*    rcCsR||vr td|dt||}t|D]\}}||kr%t|SqtS)aReturns all nodes at a fixed `distance` from `source` in `G`. Parameters ---------- G : NetworkX graph A graph source : node in `G` distance : the distance of the wanted nodes from `source` Returns ------- set() The descendants of `source` in `G` at the given `distance` from `source` Examples -------- >>> 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() r3r4)r(r7r enumerater6)rrdistance bfs_generatorilayerrrrrs  r)NNN)FNN)NN) __doc__ collectionsrnetworkxr(__all__r#rrrrrrrrrrs  K Q B @H 3