ó ,µ[c@sydZddlmZddlZddlmZddlmZddgZdZ d „Z ed ƒdd „ƒZ dS( sFunctions for generating trees.iÿÿÿÿ(t defaultdictN(tgenerate_unique_node(tpy_random_statet prefix_treet random_treetNILcsd‡fd†‰tjƒ}tƒ}|j|ddƒ|jtdtƒˆ|||ƒ||fS(sì Creates a directed prefix tree from the given list of iterables. Parameters ---------- paths: iterable of lists An iterable over "paths", which are themselves lists of nodes. Common prefixes among these paths are converted into common initial segments in the generated tree. Most commonly, this may be an iterable over lists of integers, or an iterable over Python strings. Returns ------- DiGraph A directed graph representing an arborescence consisting of the prefix tree generated by `paths`. Nodes are directed "downward", from parent to child. A special "synthetic" root node is added to be the parent of the first node in each path. A special "synthetic" leaf node, the "nil" node, is added to be the child of all nodes representing the last element in a path. (The addition of this nil node technically makes this not an arborescence but a directed acyclic graph; removing the nil node makes it an arborescence.) Each node has an attribute 'source' whose value is the original element of the path to which this node corresponds. The 'source' of the root node is None, and the 'source' of the nil node is :data:`.NIL`. The root node is the only node of in-degree zero in the graph, and the nil node is the only node of out-degree zero. For convenience, the nil node can be accessed via the :data:`.NIL` attribute; for example:: >>> from networkx.generators.trees import NIL >>> paths = ['ab', 'abs', 'ad'] >>> T = nx.prefix_tree(paths) >>> T.predecessors(NIL) # doctest: +SKIP Notes ----- The prefix tree is also known as a *trie*. Examples -------- Create a prefix tree from a list of strings with some common prefixes:: >>> strings = ['ab', 'abs', 'ad'] >>> T, root = nx.prefix_tree(strings) Continuing the above example, to recover the original paths that generated the prefix tree, traverse up the tree from the :data:`.NIL` node to the root:: >>> from networkx.generators.trees import NIL >>> >>> strings = ['ab', 'abs', 'ad'] >>> T, root = nx.prefix_tree(strings) >>> recovered = [] >>> for v in T.predecessors(NIL): ... s = '' ... while v != root: ... # Prepend the character `v` to the accumulator `s`. ... s = str(T.node[v]['source']) + s ... # Each non-nil, non-root node has exactly one parent. ... v = next(T.predecessors(v)) ... recovered.append(s) >>> sorted(recovered) ['ab', 'abs', 'ad'] c s¼ttƒ}xP|D]H}|s5|j|tƒqn|d|d}}||j|ƒqWxV|jƒD]H\}}tƒ} |j| d|ƒ|j|| ƒˆ|| |ƒqlWdS(smRecursively create a trie from the given list of paths. `paths` is a list of paths, each of which is itself a list of nodes, relative to the given `root` (but not including it). This list of paths will be interpreted as a tree-like structure, in which two paths that share a prefix represent two branches of the tree with the same initial segment. `root` is the parent of the node at index 0 in each path. `B` is the "accumulator", the :class:`networkx.DiGraph` representing the branching to which the new nodes and edges will be added. iitsourceN(Rtlisttadd_edgeRtappendtitemsRtadd_node( tpathstroottBtchildrentpathtchildtresttheadttailstnew_head(t_helper(s8lib/python2.7/site-packages/networkx/generators/trees.pyRcs   RN(tnxtDiGraphRR tNoneR(R tTR ((Rs8lib/python2.7/site-packages/networkx/generators/trees.pyRsJ-  icCsv|dkrtjdƒ‚n|dkr7tjdƒSgt|dƒD]}|jt|ƒƒ^qH}tj|ƒS(sÑReturns a uniformly random tree on `n` nodes. Parameters ---------- n : int A positive integer representing the number of nodes in the tree. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- NetworkX graph A tree, given as an undirected graph, whose nodes are numbers in the set {0, …, *n* - 1}. Raises ------ NetworkXPointlessConcept If `n` is zero (because the null graph is not a tree). Notes ----- The current implementation of this function generates a uniformly random Prüfer sequence then converts that to a tree via the :func:`~networkx.from_prufer_sequence` function. Since there is a bijection between Prüfer sequences of length *n* - 2 and trees on *n* nodes, the tree is chosen uniformly at random from the set of all trees on *n* nodes. isthe null graph is not a treeii(RtNetworkXPointlessConceptt empty_graphtrangetchoicetfrom_prufer_sequence(tntseedtitsequence((s8lib/python2.7/site-packages/networkx/generators/trees.pyRŸs !   2( t__doc__t collectionsRtnetworkxRtnetworkx.utilsRRt__all__RRRR(((s8lib/python2.7/site-packages/networkx/generators/trees.pyt s   †