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annotate planemo/lib/python3.7/site-packages/networkx/generators/trees.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1 # -*- encoding: utf-8 -*-
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2 # Copyright (C) 2015-2019 by
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3 # Jeffrey Finkelstein <jeffrey.finkelstein@gmail.com>
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4 # NetworkX developers
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5 # All rights reserved.
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6 # BSD license.
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7 #
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8 # Authors: Jeffrey Finkelstein <jeffrey.finkelstein@gmail.com>
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9 """Functions for generating trees."""
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10 from collections import defaultdict
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11
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12 import networkx as nx
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13 from networkx.utils import generate_unique_node
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14 from networkx.utils import py_random_state
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15
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16 __all__ = ['prefix_tree', 'random_tree']
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17
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18 #: The nil node, the only leaf node in a prefix tree.
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19 #:
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20 #: Each predecessor of the nil node corresponds to the end of a path
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21 #: used to generate the prefix tree.
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22 NIL = 'NIL'
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23
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24
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25 def prefix_tree(paths):
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26 """Creates a directed prefix tree from the given list of iterables.
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27
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28 Parameters
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29 ----------
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30 paths: iterable of lists
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31 An iterable over "paths", which are themselves lists of
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32 nodes. Common prefixes among these paths are converted into
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33 common initial segments in the generated tree.
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34
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35 Most commonly, this may be an iterable over lists of integers,
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36 or an iterable over Python strings.
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37
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38 Returns
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39 -------
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40 T: DiGraph
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41 A directed graph representing an arborescence consisting of the
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42 prefix tree generated by `paths`. Nodes are directed "downward",
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43 from parent to child. A special "synthetic" root node is added
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44 to be the parent of the first node in each path. A special
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45 "synthetic" leaf node, the "nil" node, is added to be the child
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46 of all nodes representing the last element in a path. (The
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47 addition of this nil node technically makes this not an
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48 arborescence but a directed acyclic graph; removing the nil node
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49 makes it an arborescence.)
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50
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51 Each node has an attribute 'source' whose value is the original
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52 element of the path to which this node corresponds. The 'source'
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53 of the root node is None, and the 'source' of the nil node is
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54 :data:`.NIL`.
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55
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56 The root node is the only node of in-degree zero in the graph,
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57 and the nil node is the only node of out-degree zero. For
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58 convenience, the nil node can be accessed via the :data:`.NIL`
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59 attribute; for example::
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60
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61 >>> from networkx.generators.trees import NIL
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62 >>> paths = ['ab', 'abs', 'ad']
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63 >>> T, root = nx.prefix_tree(paths)
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64 >>> T.predecessors(NIL) # doctest: +SKIP
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65
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66 root : string
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67 The randomly generated uuid of the root node.
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68
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69 Notes
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70 -----
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71 The prefix tree is also known as a *trie*.
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72
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73 Examples
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74 --------
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75 Create a prefix tree from a list of strings with some common
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76 prefixes::
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77
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78 >>> strings = ['ab', 'abs', 'ad']
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79 >>> T, root = nx.prefix_tree(strings)
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80
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81 Continuing the above example, to recover the original paths that
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82 generated the prefix tree, traverse up the tree from the
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83 :data:`.NIL` node to the root::
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84
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85 >>> from networkx.generators.trees import NIL
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86 >>>
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87 >>> strings = ['ab', 'abs', 'ad']
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88 >>> T, root = nx.prefix_tree(strings)
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89 >>> recovered = []
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90 >>> for v in T.predecessors(NIL):
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91 ... s = ''
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92 ... while v != root:
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93 ... # Prepend the character `v` to the accumulator `s`.
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94 ... s = str(T.nodes[v]['source']) + s
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95 ... # Each non-nil, non-root node has exactly one parent.
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96 ... v = next(T.predecessors(v))
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97 ... recovered.append(s)
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98 >>> sorted(recovered)
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99 ['ab', 'abs', 'ad']
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100
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101 """
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102 def _helper(paths, root, B):
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103 """Recursively create a trie from the given list of paths.
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104
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105 `paths` is a list of paths, each of which is itself a list of
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106 nodes, relative to the given `root` (but not including it). This
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107 list of paths will be interpreted as a tree-like structure, in
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108 which two paths that share a prefix represent two branches of
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109 the tree with the same initial segment.
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110
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111 `root` is the parent of the node at index 0 in each path.
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112
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113 `B` is the "accumulator", the :class:`networkx.DiGraph`
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114 representing the branching to which the new nodes and edges will
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115 be added.
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116
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117 """
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118 # Create a mapping from each head node to the list of tail paths
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119 # remaining beneath that node.
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120 children = defaultdict(list)
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121 for path in paths:
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122 # If the path is the empty list, that represents the empty
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123 # string, so we add an edge to the NIL node.
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124 if not path:
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125 B.add_edge(root, NIL)
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126 continue
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127 # TODO In Python 3, this should be `child, *rest = path`.
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128 child, rest = path[0], path[1:]
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129 # `child` may exist as the head of more than one path in `paths`.
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130 children[child].append(rest)
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131 # Add a node for each child found above and add edges from the
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132 # root to each child. In this loop, `head` is the child and
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133 # `tails` is the list of remaining paths under that child.
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134 for head, tails in children.items():
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135 # We need to relabel each child with a unique name. To do
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136 # this we simply change each key in the dictionary to be a
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137 # (key, uuid) pair.
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138 new_head = generate_unique_node()
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139 # Ensure the new child knows the name of the old child so
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140 # that the user can recover the mapping to the original
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141 # nodes.
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142 B.add_node(new_head, source=head)
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143 B.add_edge(root, new_head)
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144 _helper(tails, new_head, B)
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145
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146 # Initialize the prefix tree with a root node and a nil node.
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147 T = nx.DiGraph()
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148 root = generate_unique_node()
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149 T.add_node(root, source=None)
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150 T.add_node(NIL, source=NIL)
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151 # Populate the tree.
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152 _helper(paths, root, T)
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153 return T, root
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154
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155
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156 # From the Wikipedia article on Prüfer sequences:
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157 #
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158 # > Generating uniformly distributed random Prüfer sequences and
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159 # > converting them into the corresponding trees is a straightforward
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160 # > method of generating uniformly distributed random labelled trees.
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161 #
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162 @py_random_state(1)
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163 def random_tree(n, seed=None):
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164 """Returns a uniformly random tree on `n` nodes.
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165
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166 Parameters
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167 ----------
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168 n : int
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169 A positive integer representing the number of nodes in the tree.
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170 seed : integer, random_state, or None (default)
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171 Indicator of random number generation state.
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172 See :ref:`Randomness<randomness>`.
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173
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174 Returns
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175 -------
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176 NetworkX graph
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177 A tree, given as an undirected graph, whose nodes are numbers in
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178 the set {0, …, *n* - 1}.
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179
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180 Raises
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181 ------
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182 NetworkXPointlessConcept
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183 If `n` is zero (because the null graph is not a tree).
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184
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185 Notes
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186 -----
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187 The current implementation of this function generates a uniformly
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188 random Prüfer sequence then converts that to a tree via the
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189 :func:`~networkx.from_prufer_sequence` function. Since there is a
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190 bijection between Prüfer sequences of length *n* - 2 and trees on
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191 *n* nodes, the tree is chosen uniformly at random from the set of
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192 all trees on *n* nodes.
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193
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194 """
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195 if n == 0:
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196 raise nx.NetworkXPointlessConcept('the null graph is not a tree')
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197 # Cannot create a Prüfer sequence unless `n` is at least two.
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198 if n == 1:
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199 return nx.empty_graph(1)
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200 sequence = [seed.choice(range(n)) for i in range(n - 2)]
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201 return nx.from_prufer_sequence(sequence)