Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/simple_paths.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 from heapq import heappush, heappop |
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2 from itertools import count |
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3 |
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4 import networkx as nx |
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5 from networkx.utils import not_implemented_for |
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6 from networkx.utils import pairwise |
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7 from networkx.utils import empty_generator |
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8 from networkx.algorithms.shortest_paths.weighted import _weight_function |
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9 |
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10 __all__ = [ |
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11 "all_simple_paths", |
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12 "is_simple_path", |
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13 "shortest_simple_paths", |
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14 "all_simple_edge_paths", |
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15 ] |
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16 |
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17 |
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18 def is_simple_path(G, nodes): |
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19 """Returns True if and only if `nodes` form a simple path in `G`. |
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20 |
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21 A *simple path* in a graph is a nonempty sequence of nodes in which |
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22 no node appears more than once in the sequence, and each adjacent |
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23 pair of nodes in the sequence is adjacent in the graph. |
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24 |
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25 Parameters |
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26 ---------- |
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27 nodes : list |
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28 A list of one or more nodes in the graph `G`. |
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29 |
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30 Returns |
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31 ------- |
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32 bool |
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33 Whether the given list of nodes represents a simple path in `G`. |
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34 |
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35 Notes |
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36 ----- |
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37 An empty list of nodes is not a path but a list of one node is a |
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38 path. Here's an explanation why. |
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39 |
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40 This function operates on *node paths*. One could also consider |
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41 *edge paths*. There is a bijection between node paths and edge |
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42 paths. |
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43 |
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44 The *length of a path* is the number of edges in the path, so a list |
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45 of nodes of length *n* corresponds to a path of length *n* - 1. |
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46 Thus the smallest edge path would be a list of zero edges, the empty |
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47 path. This corresponds to a list of one node. |
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48 |
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49 To convert between a node path and an edge path, you can use code |
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50 like the following:: |
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51 |
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52 >>> from networkx.utils import pairwise |
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53 >>> nodes = [0, 1, 2, 3] |
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54 >>> edges = list(pairwise(nodes)) |
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55 >>> edges |
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56 [(0, 1), (1, 2), (2, 3)] |
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57 >>> nodes = [edges[0][0]] + [v for u, v in edges] |
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58 >>> nodes |
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59 [0, 1, 2, 3] |
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60 |
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61 Examples |
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62 -------- |
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63 >>> G = nx.cycle_graph(4) |
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64 >>> nx.is_simple_path(G, [2, 3, 0]) |
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65 True |
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66 >>> nx.is_simple_path(G, [0, 2]) |
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67 False |
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68 |
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69 """ |
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70 # The empty list is not a valid path. Could also return |
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71 # NetworkXPointlessConcept here. |
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72 if len(nodes) == 0: |
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73 return False |
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74 # If the list is a single node, just check that the node is actually |
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75 # in the graph. |
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76 if len(nodes) == 1: |
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77 return nodes[0] in G |
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78 # Test that no node appears more than once, and that each |
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79 # adjacent pair of nodes is adjacent. |
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80 return len(set(nodes)) == len(nodes) and all(v in G[u] for u, v in pairwise(nodes)) |
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81 |
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82 |
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83 def all_simple_paths(G, source, target, cutoff=None): |
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84 """Generate all simple paths in the graph G from source to target. |
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85 |
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86 A simple path is a path with no repeated nodes. |
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87 |
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88 Parameters |
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89 ---------- |
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90 G : NetworkX graph |
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91 |
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92 source : node |
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93 Starting node for path |
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94 |
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95 target : nodes |
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96 Single node or iterable of nodes at which to end path |
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97 |
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98 cutoff : integer, optional |
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99 Depth to stop the search. Only paths of length <= cutoff are returned. |
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100 |
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101 Returns |
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102 ------- |
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103 path_generator: generator |
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104 A generator that produces lists of simple paths. If there are no paths |
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105 between the source and target within the given cutoff the generator |
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106 produces no output. |
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107 |
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108 Examples |
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109 -------- |
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110 This iterator generates lists of nodes:: |
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111 |
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112 >>> G = nx.complete_graph(4) |
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113 >>> for path in nx.all_simple_paths(G, source=0, target=3): |
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114 ... print(path) |
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115 ... |
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116 [0, 1, 2, 3] |
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117 [0, 1, 3] |
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118 [0, 2, 1, 3] |
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119 [0, 2, 3] |
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120 [0, 3] |
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121 |
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122 You can generate only those paths that are shorter than a certain |
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123 length by using the `cutoff` keyword argument:: |
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124 |
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125 >>> paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2) |
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126 >>> print(list(paths)) |
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127 [[0, 1, 3], [0, 2, 3], [0, 3]] |
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128 |
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129 To get each path as the corresponding list of edges, you can use the |
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130 :func:`networkx.utils.pairwise` helper function:: |
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131 |
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132 >>> paths = nx.all_simple_paths(G, source=0, target=3) |
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133 >>> for path in map(nx.utils.pairwise, paths): |
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134 ... print(list(path)) |
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135 [(0, 1), (1, 2), (2, 3)] |
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136 [(0, 1), (1, 3)] |
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137 [(0, 2), (2, 1), (1, 3)] |
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138 [(0, 2), (2, 3)] |
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139 [(0, 3)] |
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140 |
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141 Pass an iterable of nodes as target to generate all paths ending in any of several nodes:: |
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142 |
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143 >>> G = nx.complete_graph(4) |
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144 >>> for path in nx.all_simple_paths(G, source=0, target=[3, 2]): |
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145 ... print(path) |
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146 ... |
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147 [0, 1, 2] |
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148 [0, 1, 2, 3] |
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149 [0, 1, 3] |
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150 [0, 1, 3, 2] |
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151 [0, 2] |
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152 [0, 2, 1, 3] |
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153 [0, 2, 3] |
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154 [0, 3] |
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155 [0, 3, 1, 2] |
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156 [0, 3, 2] |
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157 |
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158 Iterate over each path from the root nodes to the leaf nodes in a |
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159 directed acyclic graph using a functional programming approach:: |
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160 |
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161 >>> from itertools import chain |
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162 >>> from itertools import product |
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163 >>> from itertools import starmap |
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164 >>> from functools import partial |
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165 >>> |
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166 >>> chaini = chain.from_iterable |
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167 >>> |
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168 >>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)]) |
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169 >>> roots = (v for v, d in G.in_degree() if d == 0) |
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170 >>> leaves = (v for v, d in G.out_degree() if d == 0) |
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171 >>> all_paths = partial(nx.all_simple_paths, G) |
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172 >>> list(chaini(starmap(all_paths, product(roots, leaves)))) |
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173 [[0, 1, 2], [0, 3, 2]] |
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174 |
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175 The same list computed using an iterative approach:: |
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176 |
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177 >>> G = nx.DiGraph([(0, 1), (1, 2), (0, 3), (3, 2)]) |
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178 >>> roots = (v for v, d in G.in_degree() if d == 0) |
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179 >>> leaves = (v for v, d in G.out_degree() if d == 0) |
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180 >>> all_paths = [] |
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181 >>> for root in roots: |
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182 ... for leaf in leaves: |
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183 ... paths = nx.all_simple_paths(G, root, leaf) |
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184 ... all_paths.extend(paths) |
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185 >>> all_paths |
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186 [[0, 1, 2], [0, 3, 2]] |
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187 |
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188 Iterate over each path from the root nodes to the leaf nodes in a |
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189 directed acyclic graph passing all leaves together to avoid unnecessary |
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190 compute:: |
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191 |
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192 >>> G = nx.DiGraph([(0, 1), (2, 1), (1, 3), (1, 4)]) |
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193 >>> roots = (v for v, d in G.in_degree() if d == 0) |
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194 >>> leaves = [v for v, d in G.out_degree() if d == 0] |
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195 >>> all_paths = [] |
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196 >>> for root in roots: |
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197 ... paths = nx.all_simple_paths(G, root, leaves) |
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198 ... all_paths.extend(paths) |
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199 >>> all_paths |
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200 [[0, 1, 3], [0, 1, 4], [2, 1, 3], [2, 1, 4]] |
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201 |
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202 Notes |
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203 ----- |
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204 This algorithm uses a modified depth-first search to generate the |
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205 paths [1]_. A single path can be found in $O(V+E)$ time but the |
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206 number of simple paths in a graph can be very large, e.g. $O(n!)$ in |
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207 the complete graph of order $n$. |
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208 |
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209 References |
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210 ---------- |
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211 .. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms", |
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212 Addison Wesley Professional, 3rd ed., 2001. |
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213 |
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214 See Also |
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215 -------- |
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216 all_shortest_paths, shortest_path |
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217 |
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218 """ |
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219 if source not in G: |
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220 raise nx.NodeNotFound(f"source node {source} not in graph") |
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221 if target in G: |
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222 targets = {target} |
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223 else: |
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224 try: |
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225 targets = set(target) |
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226 except TypeError as e: |
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227 raise nx.NodeNotFound(f"target node {target} not in graph") from e |
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228 if source in targets: |
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229 return empty_generator() |
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230 if cutoff is None: |
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231 cutoff = len(G) - 1 |
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232 if cutoff < 1: |
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233 return empty_generator() |
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234 if G.is_multigraph(): |
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235 return _all_simple_paths_multigraph(G, source, targets, cutoff) |
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236 else: |
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237 return _all_simple_paths_graph(G, source, targets, cutoff) |
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238 |
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239 |
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240 def _all_simple_paths_graph(G, source, targets, cutoff): |
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241 visited = dict.fromkeys([source]) |
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242 stack = [iter(G[source])] |
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243 while stack: |
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244 children = stack[-1] |
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245 child = next(children, None) |
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246 if child is None: |
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247 stack.pop() |
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248 visited.popitem() |
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249 elif len(visited) < cutoff: |
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250 if child in visited: |
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251 continue |
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252 if child in targets: |
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253 yield list(visited) + [child] |
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254 visited[child] = None |
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255 if targets - set(visited.keys()): # expand stack until find all targets |
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256 stack.append(iter(G[child])) |
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257 else: |
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258 visited.popitem() # maybe other ways to child |
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259 else: # len(visited) == cutoff: |
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260 for target in (targets & (set(children) | {child})) - set(visited.keys()): |
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261 yield list(visited) + [target] |
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262 stack.pop() |
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263 visited.popitem() |
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264 |
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265 |
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266 def _all_simple_paths_multigraph(G, source, targets, cutoff): |
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267 visited = dict.fromkeys([source]) |
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268 stack = [(v for u, v in G.edges(source))] |
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269 while stack: |
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270 children = stack[-1] |
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271 child = next(children, None) |
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272 if child is None: |
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273 stack.pop() |
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274 visited.popitem() |
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275 elif len(visited) < cutoff: |
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276 if child in visited: |
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277 continue |
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278 if child in targets: |
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279 yield list(visited) + [child] |
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280 visited[child] = None |
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281 if targets - set(visited.keys()): |
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282 stack.append((v for u, v in G.edges(child))) |
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283 else: |
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284 visited.popitem() |
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285 else: # len(visited) == cutoff: |
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286 for target in targets - set(visited.keys()): |
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287 count = ([child] + list(children)).count(target) |
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288 for i in range(count): |
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289 yield list(visited) + [target] |
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290 stack.pop() |
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291 visited.popitem() |
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292 |
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293 |
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294 def all_simple_edge_paths(G, source, target, cutoff=None): |
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295 """Generate lists of edges for all simple paths in G from source to target. |
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296 |
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297 A simple path is a path with no repeated nodes. |
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298 |
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299 Parameters |
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300 ---------- |
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301 G : NetworkX graph |
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302 |
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303 source : node |
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304 Starting node for path |
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305 |
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306 target : nodes |
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307 Single node or iterable of nodes at which to end path |
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308 |
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309 cutoff : integer, optional |
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310 Depth to stop the search. Only paths of length <= cutoff are returned. |
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311 |
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312 Returns |
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313 ------- |
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314 path_generator: generator |
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315 A generator that produces lists of simple paths. If there are no paths |
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316 between the source and target within the given cutoff the generator |
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317 produces no output. |
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318 For multigraphs, the list of edges have elements of the form `(u,v,k)`. |
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319 Where `k` corresponds to the edge key. |
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320 |
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321 Examples |
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322 -------- |
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323 |
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324 Print the simple path edges of a Graph:: |
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325 |
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326 >>> g = nx.Graph([(1, 2), (2, 4), (1, 3), (3, 4)]) |
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327 >>> for path in sorted(nx.all_simple_edge_paths(g, 1, 4)): |
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328 ... print(path) |
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329 [(1, 2), (2, 4)] |
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330 [(1, 3), (3, 4)] |
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331 |
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332 Print the simple path edges of a MultiGraph. Returned edges come with |
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333 their associated keys:: |
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334 |
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335 >>> mg = nx.MultiGraph() |
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336 >>> mg.add_edge(1, 2, key="k0") |
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337 'k0' |
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338 >>> mg.add_edge(1, 2, key="k1") |
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339 'k1' |
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340 >>> mg.add_edge(2, 3, key="k0") |
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341 'k0' |
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342 >>> for path in sorted(nx.all_simple_edge_paths(mg, 1, 3)): |
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343 ... print(path) |
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344 [(1, 2, 'k0'), (2, 3, 'k0')] |
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345 [(1, 2, 'k1'), (2, 3, 'k0')] |
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346 |
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347 |
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348 Notes |
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349 ----- |
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350 This algorithm uses a modified depth-first search to generate the |
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351 paths [1]_. A single path can be found in $O(V+E)$ time but the |
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352 number of simple paths in a graph can be very large, e.g. $O(n!)$ in |
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353 the complete graph of order $n$. |
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354 |
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355 References |
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356 ---------- |
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357 .. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms", |
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358 Addison Wesley Professional, 3rd ed., 2001. |
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359 |
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360 See Also |
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361 -------- |
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362 all_shortest_paths, shortest_path, all_simple_paths |
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363 |
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364 """ |
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365 if source not in G: |
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366 raise nx.NodeNotFound("source node %s not in graph" % source) |
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367 if target in G: |
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368 targets = {target} |
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369 else: |
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370 try: |
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371 targets = set(target) |
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372 except TypeError: |
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373 raise nx.NodeNotFound("target node %s not in graph" % target) |
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374 if source in targets: |
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375 return [] |
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376 if cutoff is None: |
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377 cutoff = len(G) - 1 |
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378 if cutoff < 1: |
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379 return [] |
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380 if G.is_multigraph(): |
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381 for simp_path in _all_simple_edge_paths_multigraph(G, source, targets, cutoff): |
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382 yield simp_path |
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383 else: |
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384 for simp_path in _all_simple_paths_graph(G, source, targets, cutoff): |
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385 yield list(zip(simp_path[:-1], simp_path[1:])) |
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386 |
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387 |
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388 def _all_simple_edge_paths_multigraph(G, source, targets, cutoff): |
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389 if not cutoff or cutoff < 1: |
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390 return [] |
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391 visited = [source] |
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392 stack = [iter(G.edges(source, keys=True))] |
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393 |
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394 while stack: |
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395 children = stack[-1] |
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396 child = next(children, None) |
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397 if child is None: |
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398 stack.pop() |
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399 visited.pop() |
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400 elif len(visited) < cutoff: |
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401 if child[1] in targets: |
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402 yield visited[1:] + [child] |
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403 elif child[1] not in [v[0] for v in visited[1:]]: |
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404 visited.append(child) |
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405 stack.append(iter(G.edges(child[1], keys=True))) |
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406 else: # len(visited) == cutoff: |
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407 for (u, v, k) in [child] + list(children): |
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408 if v in targets: |
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409 yield visited[1:] + [(u, v, k)] |
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410 stack.pop() |
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411 visited.pop() |
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412 |
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413 |
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414 @not_implemented_for("multigraph") |
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415 def shortest_simple_paths(G, source, target, weight=None): |
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416 """Generate all simple paths in the graph G from source to target, |
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417 starting from shortest ones. |
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418 |
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419 A simple path is a path with no repeated nodes. |
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420 |
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421 If a weighted shortest path search is to be used, no negative weights |
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422 are allowed. |
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423 |
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424 Parameters |
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425 ---------- |
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426 G : NetworkX graph |
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427 |
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428 source : node |
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429 Starting node for path |
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430 |
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431 target : node |
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432 Ending node for path |
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433 |
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434 weight : string or function |
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435 If it is a string, it is the name of the edge attribute to be |
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436 used as a weight. |
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437 |
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438 If it is a function, the weight of an edge is the value returned |
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439 by the function. The function must accept exactly three positional |
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440 arguments: the two endpoints of an edge and the dictionary of edge |
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441 attributes for that edge. The function must return a number. |
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442 |
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443 If None all edges are considered to have unit weight. Default |
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444 value None. |
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445 |
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446 Returns |
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447 ------- |
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448 path_generator: generator |
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449 A generator that produces lists of simple paths, in order from |
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450 shortest to longest. |
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451 |
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452 Raises |
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453 ------ |
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454 NetworkXNoPath |
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455 If no path exists between source and target. |
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456 |
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457 NetworkXError |
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458 If source or target nodes are not in the input graph. |
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459 |
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460 NetworkXNotImplemented |
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461 If the input graph is a Multi[Di]Graph. |
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462 |
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463 Examples |
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464 -------- |
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465 |
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466 >>> G = nx.cycle_graph(7) |
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467 >>> paths = list(nx.shortest_simple_paths(G, 0, 3)) |
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468 >>> print(paths) |
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469 [[0, 1, 2, 3], [0, 6, 5, 4, 3]] |
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470 |
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471 You can use this function to efficiently compute the k shortest/best |
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472 paths between two nodes. |
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473 |
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474 >>> from itertools import islice |
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475 >>> def k_shortest_paths(G, source, target, k, weight=None): |
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476 ... return list( |
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477 ... islice(nx.shortest_simple_paths(G, source, target, weight=weight), k) |
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478 ... ) |
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479 >>> for path in k_shortest_paths(G, 0, 3, 2): |
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480 ... print(path) |
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481 [0, 1, 2, 3] |
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482 [0, 6, 5, 4, 3] |
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483 |
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484 Notes |
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485 ----- |
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486 This procedure is based on algorithm by Jin Y. Yen [1]_. Finding |
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487 the first $K$ paths requires $O(KN^3)$ operations. |
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488 |
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489 See Also |
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490 -------- |
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491 all_shortest_paths |
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492 shortest_path |
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493 all_simple_paths |
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494 |
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495 References |
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496 ---------- |
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497 .. [1] Jin Y. Yen, "Finding the K Shortest Loopless Paths in a |
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498 Network", Management Science, Vol. 17, No. 11, Theory Series |
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499 (Jul., 1971), pp. 712-716. |
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500 |
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501 """ |
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502 if source not in G: |
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503 raise nx.NodeNotFound(f"source node {source} not in graph") |
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504 |
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505 if target not in G: |
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506 raise nx.NodeNotFound(f"target node {target} not in graph") |
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507 |
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508 if weight is None: |
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509 length_func = len |
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510 shortest_path_func = _bidirectional_shortest_path |
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511 else: |
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512 wt = _weight_function(G, weight) |
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513 |
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514 def length_func(path): |
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515 return sum( |
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516 wt(u, v, G.get_edge_data(u, v)) for (u, v) in zip(path, path[1:]) |
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517 ) |
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518 |
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519 shortest_path_func = _bidirectional_dijkstra |
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520 |
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521 listA = list() |
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522 listB = PathBuffer() |
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523 prev_path = None |
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524 while True: |
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525 if not prev_path: |
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526 length, path = shortest_path_func(G, source, target, weight=weight) |
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527 listB.push(length, path) |
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528 else: |
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529 ignore_nodes = set() |
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530 ignore_edges = set() |
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531 for i in range(1, len(prev_path)): |
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532 root = prev_path[:i] |
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533 root_length = length_func(root) |
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534 for path in listA: |
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535 if path[:i] == root: |
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536 ignore_edges.add((path[i - 1], path[i])) |
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537 try: |
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538 length, spur = shortest_path_func( |
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539 G, |
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540 root[-1], |
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541 target, |
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542 ignore_nodes=ignore_nodes, |
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543 ignore_edges=ignore_edges, |
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544 weight=weight, |
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545 ) |
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546 path = root[:-1] + spur |
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547 listB.push(root_length + length, path) |
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548 except nx.NetworkXNoPath: |
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549 pass |
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550 ignore_nodes.add(root[-1]) |
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551 |
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552 if listB: |
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553 path = listB.pop() |
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554 yield path |
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555 listA.append(path) |
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556 prev_path = path |
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557 else: |
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558 break |
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559 |
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560 |
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561 class PathBuffer: |
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562 def __init__(self): |
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563 self.paths = set() |
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564 self.sortedpaths = list() |
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565 self.counter = count() |
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566 |
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567 def __len__(self): |
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568 return len(self.sortedpaths) |
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569 |
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570 def push(self, cost, path): |
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571 hashable_path = tuple(path) |
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572 if hashable_path not in self.paths: |
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573 heappush(self.sortedpaths, (cost, next(self.counter), path)) |
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574 self.paths.add(hashable_path) |
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575 |
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576 def pop(self): |
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577 (cost, num, path) = heappop(self.sortedpaths) |
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578 hashable_path = tuple(path) |
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579 self.paths.remove(hashable_path) |
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580 return path |
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581 |
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582 |
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583 def _bidirectional_shortest_path( |
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584 G, source, target, ignore_nodes=None, ignore_edges=None, weight=None |
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585 ): |
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586 """Returns the shortest path between source and target ignoring |
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587 nodes and edges in the containers ignore_nodes and ignore_edges. |
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588 |
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589 This is a custom modification of the standard bidirectional shortest |
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590 path implementation at networkx.algorithms.unweighted |
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591 |
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592 Parameters |
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593 ---------- |
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594 G : NetworkX graph |
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595 |
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596 source : node |
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597 starting node for path |
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598 |
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599 target : node |
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600 ending node for path |
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601 |
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602 ignore_nodes : container of nodes |
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603 nodes to ignore, optional |
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604 |
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605 ignore_edges : container of edges |
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606 edges to ignore, optional |
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607 |
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608 weight : None |
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609 This function accepts a weight argument for convenience of |
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610 shortest_simple_paths function. It will be ignored. |
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611 |
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612 Returns |
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613 ------- |
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614 path: list |
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615 List of nodes in a path from source to target. |
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616 |
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617 Raises |
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618 ------ |
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619 NetworkXNoPath |
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620 If no path exists between source and target. |
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621 |
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622 See Also |
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623 -------- |
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624 shortest_path |
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625 |
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626 """ |
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627 # call helper to do the real work |
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628 results = _bidirectional_pred_succ(G, source, target, ignore_nodes, ignore_edges) |
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629 pred, succ, w = results |
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630 |
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631 # build path from pred+w+succ |
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632 path = [] |
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633 # from w to target |
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634 while w is not None: |
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635 path.append(w) |
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636 w = succ[w] |
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637 # from source to w |
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638 w = pred[path[0]] |
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639 while w is not None: |
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640 path.insert(0, w) |
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641 w = pred[w] |
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642 |
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643 return len(path), path |
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644 |
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645 |
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646 def _bidirectional_pred_succ(G, source, target, ignore_nodes=None, ignore_edges=None): |
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647 """Bidirectional shortest path helper. |
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648 Returns (pred,succ,w) where |
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649 pred is a dictionary of predecessors from w to the source, and |
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650 succ is a dictionary of successors from w to the target. |
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651 """ |
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652 # does BFS from both source and target and meets in the middle |
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653 if ignore_nodes and (source in ignore_nodes or target in ignore_nodes): |
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654 raise nx.NetworkXNoPath(f"No path between {source} and {target}.") |
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655 if target == source: |
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656 return ({target: None}, {source: None}, source) |
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657 |
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658 # handle either directed or undirected |
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659 if G.is_directed(): |
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660 Gpred = G.predecessors |
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661 Gsucc = G.successors |
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662 else: |
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663 Gpred = G.neighbors |
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664 Gsucc = G.neighbors |
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665 |
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666 # support optional nodes filter |
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667 if ignore_nodes: |
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668 |
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669 def filter_iter(nodes): |
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670 def iterate(v): |
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671 for w in nodes(v): |
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672 if w not in ignore_nodes: |
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673 yield w |
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674 |
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675 return iterate |
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676 |
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677 Gpred = filter_iter(Gpred) |
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678 Gsucc = filter_iter(Gsucc) |
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679 |
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680 # support optional edges filter |
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681 if ignore_edges: |
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682 if G.is_directed(): |
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683 |
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684 def filter_pred_iter(pred_iter): |
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685 def iterate(v): |
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686 for w in pred_iter(v): |
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687 if (w, v) not in ignore_edges: |
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|
688 yield w |
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|
689 |
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|
690 return iterate |
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|
691 |
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|
692 def filter_succ_iter(succ_iter): |
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693 def iterate(v): |
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694 for w in succ_iter(v): |
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695 if (v, w) not in ignore_edges: |
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|
696 yield w |
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|
697 |
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|
698 return iterate |
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|
699 |
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|
700 Gpred = filter_pred_iter(Gpred) |
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701 Gsucc = filter_succ_iter(Gsucc) |
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702 |
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|
703 else: |
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|
704 |
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|
705 def filter_iter(nodes): |
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|
706 def iterate(v): |
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|
707 for w in nodes(v): |
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708 if (v, w) not in ignore_edges and (w, v) not in ignore_edges: |
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|
709 yield w |
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|
710 |
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|
711 return iterate |
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|
712 |
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|
713 Gpred = filter_iter(Gpred) |
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|
714 Gsucc = filter_iter(Gsucc) |
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|
715 |
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|
716 # predecesssor and successors in search |
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|
717 pred = {source: None} |
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718 succ = {target: None} |
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|
719 |
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|
720 # initialize fringes, start with forward |
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|
721 forward_fringe = [source] |
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722 reverse_fringe = [target] |
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|
723 |
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724 while forward_fringe and reverse_fringe: |
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725 if len(forward_fringe) <= len(reverse_fringe): |
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|
726 this_level = forward_fringe |
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727 forward_fringe = [] |
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|
728 for v in this_level: |
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|
729 for w in Gsucc(v): |
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|
730 if w not in pred: |
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parents:
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|
731 forward_fringe.append(w) |
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|
732 pred[w] = v |
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|
733 if w in succ: |
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|
734 # found path |
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|
735 return pred, succ, w |
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|
736 else: |
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737 this_level = reverse_fringe |
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738 reverse_fringe = [] |
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|
739 for v in this_level: |
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740 for w in Gpred(v): |
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741 if w not in succ: |
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742 succ[w] = v |
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|
743 reverse_fringe.append(w) |
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parents:
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744 if w in pred: |
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|
745 # found path |
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parents:
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|
746 return pred, succ, w |
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|
747 |
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|
748 raise nx.NetworkXNoPath(f"No path between {source} and {target}.") |
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|
749 |
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parents:
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|
750 |
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parents:
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|
751 def _bidirectional_dijkstra( |
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parents:
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|
752 G, source, target, weight="weight", ignore_nodes=None, ignore_edges=None |
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parents:
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|
753 ): |
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parents:
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changeset
|
754 """Dijkstra's algorithm for shortest paths using bidirectional search. |
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parents:
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|
755 |
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parents:
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|
756 This function returns the shortest path between source and target |
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parents:
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|
757 ignoring nodes and edges in the containers ignore_nodes and |
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parents:
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|
758 ignore_edges. |
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parents:
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|
759 |
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parents:
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|
760 This is a custom modification of the standard Dijkstra bidirectional |
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parents:
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|
761 shortest path implementation at networkx.algorithms.weighted |
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parents:
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|
762 |
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parents:
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|
763 Parameters |
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|
764 ---------- |
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parents:
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|
765 G : NetworkX graph |
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|
766 |
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parents:
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|
767 source : node |
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parents:
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|
768 Starting node. |
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|
769 |
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parents:
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|
770 target : node |
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parents:
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|
771 Ending node. |
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|
772 |
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parents:
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|
773 weight: string, function, optional (default='weight') |
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|
774 Edge data key or weight function corresponding to the edge weight |
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parents:
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|
775 |
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|
776 ignore_nodes : container of nodes |
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parents:
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|
777 nodes to ignore, optional |
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|
778 |
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parents:
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|
779 ignore_edges : container of edges |
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parents:
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|
780 edges to ignore, optional |
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|
781 |
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parents:
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|
782 Returns |
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parents:
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|
783 ------- |
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parents:
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|
784 length : number |
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parents:
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785 Shortest path length. |
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parents:
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|
786 |
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parents:
diff
changeset
|
787 Returns a tuple of two dictionaries keyed by node. |
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|
788 The first dictionary stores distance from the source. |
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parents:
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789 The second stores the path from the source to that node. |
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parents:
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|
790 |
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parents:
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|
791 Raises |
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parents:
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changeset
|
792 ------ |
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parents:
diff
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|
793 NetworkXNoPath |
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parents:
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|
794 If no path exists between source and target. |
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parents:
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|
795 |
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parents:
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|
796 Notes |
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parents:
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|
797 ----- |
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parents:
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|
798 Edge weight attributes must be numerical. |
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parents:
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|
799 Distances are calculated as sums of weighted edges traversed. |
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parents:
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|
800 |
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parents:
diff
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|
801 In practice bidirectional Dijkstra is much more than twice as fast as |
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shellac
parents:
diff
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|
802 ordinary Dijkstra. |
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parents:
diff
changeset
|
803 |
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parents:
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|
804 Ordinary Dijkstra expands nodes in a sphere-like manner from the |
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parents:
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|
805 source. The radius of this sphere will eventually be the length |
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shellac
parents:
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|
806 of the shortest path. Bidirectional Dijkstra will expand nodes |
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parents:
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|
807 from both the source and the target, making two spheres of half |
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parents:
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|
808 this radius. Volume of the first sphere is pi*r*r while the |
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shellac
parents:
diff
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|
809 others are 2*pi*r/2*r/2, making up half the volume. |
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|
810 |
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parents:
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|
811 This algorithm is not guaranteed to work if edge weights |
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parents:
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|
812 are negative or are floating point numbers |
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shellac
parents:
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|
813 (overflows and roundoff errors can cause problems). |
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parents:
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|
814 |
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parents:
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|
815 See Also |
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shellac
parents:
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|
816 -------- |
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shellac
parents:
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|
817 shortest_path |
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parents:
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|
818 shortest_path_length |
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parents:
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|
819 """ |
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parents:
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|
820 if ignore_nodes and (source in ignore_nodes or target in ignore_nodes): |
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parents:
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|
821 raise nx.NetworkXNoPath(f"No path between {source} and {target}.") |
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parents:
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|
822 if source == target: |
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parents:
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|
823 return (0, [source]) |
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parents:
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|
824 |
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|
825 # handle either directed or undirected |
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parents:
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826 if G.is_directed(): |
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parents:
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|
827 Gpred = G.predecessors |
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828 Gsucc = G.successors |
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829 else: |
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parents:
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830 Gpred = G.neighbors |
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parents:
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|
831 Gsucc = G.neighbors |
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parents:
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|
832 |
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parents:
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833 # support optional nodes filter |
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parents:
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834 if ignore_nodes: |
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parents:
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|
835 |
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parents:
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|
836 def filter_iter(nodes): |
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parents:
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837 def iterate(v): |
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838 for w in nodes(v): |
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839 if w not in ignore_nodes: |
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parents:
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840 yield w |
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parents:
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|
841 |
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parents:
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842 return iterate |
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parents:
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|
843 |
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parents:
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844 Gpred = filter_iter(Gpred) |
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parents:
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845 Gsucc = filter_iter(Gsucc) |
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parents:
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846 |
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parents:
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847 # support optional edges filter |
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848 if ignore_edges: |
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parents:
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849 if G.is_directed(): |
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parents:
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850 |
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parents:
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851 def filter_pred_iter(pred_iter): |
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852 def iterate(v): |
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853 for w in pred_iter(v): |
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854 if (w, v) not in ignore_edges: |
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855 yield w |
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parents:
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|
856 |
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parents:
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857 return iterate |
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858 |
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859 def filter_succ_iter(succ_iter): |
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860 def iterate(v): |
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861 for w in succ_iter(v): |
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862 if (v, w) not in ignore_edges: |
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parents:
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863 yield w |
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parents:
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|
864 |
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parents:
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|
865 return iterate |
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parents:
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|
866 |
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parents:
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|
867 Gpred = filter_pred_iter(Gpred) |
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parents:
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868 Gsucc = filter_succ_iter(Gsucc) |
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|
869 |
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870 else: |
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parents:
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|
871 |
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parents:
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872 def filter_iter(nodes): |
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873 def iterate(v): |
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874 for w in nodes(v): |
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parents:
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875 if (v, w) not in ignore_edges and (w, v) not in ignore_edges: |
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shellac
parents:
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|
876 yield w |
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parents:
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|
877 |
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parents:
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|
878 return iterate |
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parents:
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|
879 |
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parents:
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|
880 Gpred = filter_iter(Gpred) |
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parents:
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|
881 Gsucc = filter_iter(Gsucc) |
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parents:
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|
882 |
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parents:
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|
883 push = heappush |
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884 pop = heappop |
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parents:
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|
885 # Init: Forward Backward |
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parents:
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|
886 dists = [{}, {}] # dictionary of final distances |
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parents:
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887 paths = [{source: [source]}, {target: [target]}] # dictionary of paths |
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parents:
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|
888 fringe = [[], []] # heap of (distance, node) tuples for |
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889 # extracting next node to expand |
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parents:
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890 seen = [{source: 0}, {target: 0}] # dictionary of distances to |
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891 # nodes seen |
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parents:
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892 c = count() |
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parents:
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893 # initialize fringe heap |
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parents:
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|
894 push(fringe[0], (0, next(c), source)) |
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parents:
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|
895 push(fringe[1], (0, next(c), target)) |
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896 # neighs for extracting correct neighbor information |
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897 neighs = [Gsucc, Gpred] |
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898 # variables to hold shortest discovered path |
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parents:
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899 # finaldist = 1e30000 |
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parents:
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900 finalpath = [] |
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901 dir = 1 |
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902 while fringe[0] and fringe[1]: |
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parents:
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|
903 # choose direction |
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parents:
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|
904 # dir == 0 is forward direction and dir == 1 is back |
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parents:
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905 dir = 1 - dir |
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906 # extract closest to expand |
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parents:
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907 (dist, _, v) = pop(fringe[dir]) |
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908 if v in dists[dir]: |
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parents:
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909 # Shortest path to v has already been found |
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910 continue |
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911 # update distance |
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912 dists[dir][v] = dist # equal to seen[dir][v] |
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parents:
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913 if v in dists[1 - dir]: |
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parents:
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914 # if we have scanned v in both directions we are done |
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915 # we have now discovered the shortest path |
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parents:
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|
916 return (finaldist, finalpath) |
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parents:
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|
917 |
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shellac
parents:
diff
changeset
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918 wt = _weight_function(G, weight) |
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919 for w in neighs[dir](v): |
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920 if dir == 0: # forward |
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921 minweight = wt(v, w, G.get_edge_data(v, w)) |
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922 vwLength = dists[dir][v] + minweight |
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923 else: # back, must remember to change v,w->w,v |
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924 minweight = wt(w, v, G.get_edge_data(w, v)) |
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925 vwLength = dists[dir][v] + minweight |
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926 |
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927 if w in dists[dir]: |
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928 if vwLength < dists[dir][w]: |
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929 raise ValueError("Contradictory paths found: negative weights?") |
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930 elif w not in seen[dir] or vwLength < seen[dir][w]: |
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931 # relaxing |
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932 seen[dir][w] = vwLength |
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933 push(fringe[dir], (vwLength, next(c), w)) |
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934 paths[dir][w] = paths[dir][v] + [w] |
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935 if w in seen[0] and w in seen[1]: |
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936 # see if this path is better than than the already |
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937 # discovered shortest path |
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938 totaldist = seen[0][w] + seen[1][w] |
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939 if finalpath == [] or finaldist > totaldist: |
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940 finaldist = totaldist |
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941 revpath = paths[1][w][:] |
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942 revpath.reverse() |
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943 finalpath = paths[0][w] + revpath[1:] |
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944 raise nx.NetworkXNoPath(f"No path between {source} and {target}.") |