Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/generators/trees.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Functions for generating trees.""" |
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2 from collections import defaultdict |
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3 |
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4 import networkx as nx |
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5 from networkx.utils import generate_unique_node |
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6 from networkx.utils import py_random_state |
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7 |
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8 __all__ = ["prefix_tree", "random_tree"] |
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9 |
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10 #: The nil node, the only leaf node in a prefix tree. |
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11 #: |
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12 #: Each predecessor of the nil node corresponds to the end of a path |
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13 #: used to generate the prefix tree. |
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14 NIL = "NIL" |
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15 |
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16 |
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17 def prefix_tree(paths): |
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18 """Creates a directed prefix tree from the given list of iterables. |
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19 |
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20 Parameters |
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21 ---------- |
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22 paths: iterable of lists |
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23 An iterable over "paths", which are themselves lists of |
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24 nodes. Common prefixes among these paths are converted into |
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25 common initial segments in the generated tree. |
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26 |
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27 Most commonly, this may be an iterable over lists of integers, |
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28 or an iterable over Python strings. |
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29 |
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30 Returns |
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31 ------- |
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32 T: DiGraph |
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33 A directed graph representing an arborescence consisting of the |
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34 prefix tree generated by `paths`. Nodes are directed "downward", |
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35 from parent to child. A special "synthetic" root node is added |
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36 to be the parent of the first node in each path. A special |
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37 "synthetic" leaf node, the "nil" node, is added to be the child |
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38 of all nodes representing the last element in a path. (The |
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39 addition of this nil node technically makes this not an |
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40 arborescence but a directed acyclic graph; removing the nil node |
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41 makes it an arborescence.) |
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42 |
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43 Each node has an attribute 'source' whose value is the original |
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44 element of the path to which this node corresponds. The 'source' |
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45 of the root node is None, and the 'source' of the nil node is |
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46 :data:`.NIL`. |
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47 |
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48 The root node is the only node of in-degree zero in the graph, |
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49 and the nil node is the only node of out-degree zero. For |
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50 convenience, the nil node can be accessed via the :data:`.NIL` |
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51 attribute; for example:: |
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52 |
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53 >>> from networkx.generators.trees import NIL |
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54 >>> paths = ["ab", "abs", "ad"] |
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55 >>> T, root = nx.prefix_tree(paths) |
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56 >>> T.predecessors(NIL) |
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57 <dict_keyiterator object at 0x...> |
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58 |
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59 root : string |
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60 The randomly generated uuid of the root node. |
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61 |
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62 Notes |
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63 ----- |
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64 The prefix tree is also known as a *trie*. |
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65 |
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66 Examples |
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67 -------- |
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68 Create a prefix tree from a list of strings with some common |
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69 prefixes:: |
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70 |
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71 >>> strings = ["ab", "abs", "ad"] |
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72 >>> T, root = nx.prefix_tree(strings) |
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73 |
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74 Continuing the above example, to recover the original paths that |
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75 generated the prefix tree, traverse up the tree from the |
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76 :data:`.NIL` node to the root:: |
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77 |
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78 >>> from networkx.generators.trees import NIL |
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79 >>> |
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80 >>> strings = ["ab", "abs", "ad"] |
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81 >>> T, root = nx.prefix_tree(strings) |
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82 >>> recovered = [] |
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83 >>> for v in T.predecessors(NIL): |
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84 ... s = "" |
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85 ... while v != root: |
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86 ... # Prepend the character `v` to the accumulator `s`. |
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87 ... s = str(T.nodes[v]["source"]) + s |
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88 ... # Each non-nil, non-root node has exactly one parent. |
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89 ... v = next(T.predecessors(v)) |
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90 ... recovered.append(s) |
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91 >>> sorted(recovered) |
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92 ['ab', 'abs', 'ad'] |
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93 |
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94 """ |
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95 |
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96 def _helper(paths, root, B): |
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97 """Recursively create a trie from the given list of paths. |
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98 |
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99 `paths` is a list of paths, each of which is itself a list of |
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100 nodes, relative to the given `root` (but not including it). This |
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101 list of paths will be interpreted as a tree-like structure, in |
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102 which two paths that share a prefix represent two branches of |
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103 the tree with the same initial segment. |
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104 |
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105 `root` is the parent of the node at index 0 in each path. |
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106 |
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107 `B` is the "accumulator", the :class:`networkx.DiGraph` |
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108 representing the branching to which the new nodes and edges will |
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109 be added. |
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110 |
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111 """ |
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112 # Create a mapping from each head node to the list of tail paths |
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113 # remaining beneath that node. |
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114 children = defaultdict(list) |
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115 for path in paths: |
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116 # If the path is the empty list, that represents the empty |
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117 # string, so we add an edge to the NIL node. |
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118 if not path: |
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119 B.add_edge(root, NIL) |
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120 continue |
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121 child, *rest = path |
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122 # `child` may exist as the head of more than one path in `paths`. |
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123 children[child].append(rest) |
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124 # Add a node for each child found above and add edges from the |
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125 # root to each child. In this loop, `head` is the child and |
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126 # `tails` is the list of remaining paths under that child. |
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127 for head, tails in children.items(): |
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128 # We need to relabel each child with a unique name. To do |
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129 # this we simply change each key in the dictionary to be a |
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130 # (key, uuid) pair. |
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131 new_head = generate_unique_node() |
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132 # Ensure the new child knows the name of the old child so |
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133 # that the user can recover the mapping to the original |
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134 # nodes. |
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135 B.add_node(new_head, source=head) |
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136 B.add_edge(root, new_head) |
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137 _helper(tails, new_head, B) |
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138 |
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139 # Initialize the prefix tree with a root node and a nil node. |
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140 T = nx.DiGraph() |
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141 root = generate_unique_node() |
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142 T.add_node(root, source=None) |
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143 T.add_node(NIL, source=NIL) |
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144 # Populate the tree. |
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145 _helper(paths, root, T) |
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146 return T, root |
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147 |
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148 |
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149 # From the Wikipedia article on Prüfer sequences: |
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150 # |
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151 # > Generating uniformly distributed random Prüfer sequences and |
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152 # > converting them into the corresponding trees is a straightforward |
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153 # > method of generating uniformly distributed random labelled trees. |
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154 # |
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155 @py_random_state(1) |
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156 def random_tree(n, seed=None): |
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157 """Returns a uniformly random tree on `n` nodes. |
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158 |
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159 Parameters |
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160 ---------- |
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161 n : int |
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162 A positive integer representing the number of nodes in the tree. |
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163 seed : integer, random_state, or None (default) |
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164 Indicator of random number generation state. |
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165 See :ref:`Randomness<randomness>`. |
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166 |
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167 Returns |
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168 ------- |
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169 NetworkX graph |
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170 A tree, given as an undirected graph, whose nodes are numbers in |
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171 the set {0, …, *n* - 1}. |
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172 |
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173 Raises |
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174 ------ |
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175 NetworkXPointlessConcept |
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176 If `n` is zero (because the null graph is not a tree). |
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177 |
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178 Notes |
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179 ----- |
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180 The current implementation of this function generates a uniformly |
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181 random Prüfer sequence then converts that to a tree via the |
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182 :func:`~networkx.from_prufer_sequence` function. Since there is a |
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183 bijection between Prüfer sequences of length *n* - 2 and trees on |
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184 *n* nodes, the tree is chosen uniformly at random from the set of |
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185 all trees on *n* nodes. |
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186 |
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187 """ |
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188 if n == 0: |
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189 raise nx.NetworkXPointlessConcept("the null graph is not a tree") |
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190 # Cannot create a Prüfer sequence unless `n` is at least two. |
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191 if n == 1: |
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192 return nx.empty_graph(1) |
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193 sequence = [seed.choice(range(n)) for i in range(n - 2)] |
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194 return nx.from_prufer_sequence(sequence) |