Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/shortest_paths/unweighted.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 """ |
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2 Shortest path algorithms for unweighted graphs. |
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3 """ |
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4 import networkx as nx |
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5 |
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6 __all__ = [ |
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7 "bidirectional_shortest_path", |
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8 "single_source_shortest_path", |
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9 "single_source_shortest_path_length", |
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10 "single_target_shortest_path", |
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11 "single_target_shortest_path_length", |
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12 "all_pairs_shortest_path", |
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13 "all_pairs_shortest_path_length", |
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14 "predecessor", |
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15 ] |
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16 |
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17 |
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18 def single_source_shortest_path_length(G, source, cutoff=None): |
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19 """Compute the shortest path lengths from source to all reachable nodes. |
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20 |
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21 Parameters |
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22 ---------- |
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23 G : NetworkX graph |
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24 |
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25 source : node |
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26 Starting node for path |
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27 |
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28 cutoff : integer, optional |
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29 Depth to stop the search. Only paths of length <= cutoff are returned. |
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30 |
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31 Returns |
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32 ------- |
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33 lengths : dict |
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34 Dict keyed by node to shortest path length to source. |
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35 |
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36 Examples |
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37 -------- |
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38 >>> G = nx.path_graph(5) |
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39 >>> length = nx.single_source_shortest_path_length(G, 0) |
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40 >>> length[4] |
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41 4 |
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42 >>> for node in length: |
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43 ... print(f"{node}: {length[node]}") |
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44 0: 0 |
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45 1: 1 |
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46 2: 2 |
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47 3: 3 |
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48 4: 4 |
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49 |
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50 See Also |
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51 -------- |
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52 shortest_path_length |
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53 """ |
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54 if source not in G: |
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55 raise nx.NodeNotFound(f"Source {source} is not in G") |
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56 if cutoff is None: |
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57 cutoff = float("inf") |
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58 nextlevel = {source: 1} |
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59 return dict(_single_shortest_path_length(G.adj, nextlevel, cutoff)) |
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60 |
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61 |
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62 def _single_shortest_path_length(adj, firstlevel, cutoff): |
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63 """Yields (node, level) in a breadth first search |
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64 |
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65 Shortest Path Length helper function |
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66 Parameters |
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67 ---------- |
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68 adj : dict |
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69 Adjacency dict or view |
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70 firstlevel : dict |
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71 starting nodes, e.g. {source: 1} or {target: 1} |
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72 cutoff : int or float |
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73 level at which we stop the process |
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74 """ |
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75 seen = {} # level (number of hops) when seen in BFS |
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76 level = 0 # the current level |
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77 nextlevel = set(firstlevel) # set of nodes to check at next level |
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78 n = len(adj) |
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79 while nextlevel and cutoff >= level: |
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80 thislevel = nextlevel # advance to next level |
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81 nextlevel = set() # and start a new set (fringe) |
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82 found = [] |
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83 for v in thislevel: |
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84 if v not in seen: |
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85 seen[v] = level # set the level of vertex v |
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86 found.append(v) |
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87 yield (v, level) |
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88 if len(seen) == n: |
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89 return |
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90 for v in found: |
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91 nextlevel.update(adj[v]) |
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92 level += 1 |
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93 del seen |
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94 |
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95 |
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96 def single_target_shortest_path_length(G, target, cutoff=None): |
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97 """Compute the shortest path lengths to target from all reachable nodes. |
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98 |
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99 Parameters |
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100 ---------- |
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101 G : NetworkX graph |
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102 |
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103 target : node |
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104 Target node for path |
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105 |
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106 cutoff : integer, optional |
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107 Depth to stop the search. Only paths of length <= cutoff are returned. |
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108 |
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109 Returns |
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110 ------- |
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111 lengths : iterator |
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112 (source, shortest path length) iterator |
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113 |
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114 Examples |
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115 -------- |
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116 >>> G = nx.path_graph(5, create_using=nx.DiGraph()) |
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117 >>> length = dict(nx.single_target_shortest_path_length(G, 4)) |
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118 >>> length[0] |
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119 4 |
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120 >>> for node in range(5): |
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121 ... print(f"{node}: {length[node]}") |
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122 0: 4 |
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123 1: 3 |
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124 2: 2 |
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125 3: 1 |
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126 4: 0 |
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127 |
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128 See Also |
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129 -------- |
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130 single_source_shortest_path_length, shortest_path_length |
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131 """ |
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132 if target not in G: |
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133 raise nx.NodeNotFound(f"Target {target} is not in G") |
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134 |
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135 if cutoff is None: |
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136 cutoff = float("inf") |
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137 # handle either directed or undirected |
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138 adj = G.pred if G.is_directed() else G.adj |
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139 nextlevel = {target: 1} |
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140 return _single_shortest_path_length(adj, nextlevel, cutoff) |
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141 |
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142 |
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143 def all_pairs_shortest_path_length(G, cutoff=None): |
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144 """Computes the shortest path lengths between all nodes in `G`. |
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145 |
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146 Parameters |
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147 ---------- |
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148 G : NetworkX graph |
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149 |
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150 cutoff : integer, optional |
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151 Depth at which to stop the search. Only paths of length at most |
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152 `cutoff` are returned. |
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153 |
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154 Returns |
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155 ------- |
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156 lengths : iterator |
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157 (source, dictionary) iterator with dictionary keyed by target and |
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158 shortest path length as the key value. |
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159 |
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160 Notes |
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161 ----- |
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162 The iterator returned only has reachable node pairs. |
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163 |
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164 Examples |
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165 -------- |
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166 >>> G = nx.path_graph(5) |
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167 >>> length = dict(nx.all_pairs_shortest_path_length(G)) |
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168 >>> for node in [0, 1, 2, 3, 4]: |
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169 ... print(f"1 - {node}: {length[1][node]}") |
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170 1 - 0: 1 |
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171 1 - 1: 0 |
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172 1 - 2: 1 |
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173 1 - 3: 2 |
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174 1 - 4: 3 |
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175 >>> length[3][2] |
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176 1 |
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177 >>> length[2][2] |
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178 0 |
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179 |
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180 """ |
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181 length = single_source_shortest_path_length |
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182 # TODO This can be trivially parallelized. |
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183 for n in G: |
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184 yield (n, length(G, n, cutoff=cutoff)) |
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185 |
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186 |
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187 def bidirectional_shortest_path(G, source, target): |
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188 """Returns a list of nodes in a shortest path between source and target. |
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189 |
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190 Parameters |
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191 ---------- |
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192 G : NetworkX graph |
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193 |
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194 source : node label |
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195 starting node for path |
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196 |
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197 target : node label |
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198 ending node for path |
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199 |
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200 Returns |
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201 ------- |
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202 path: list |
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203 List of nodes in a path from source to target. |
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204 |
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205 Raises |
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206 ------ |
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207 NetworkXNoPath |
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208 If no path exists between source and target. |
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209 |
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210 See Also |
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211 -------- |
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212 shortest_path |
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213 |
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214 Notes |
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215 ----- |
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216 This algorithm is used by shortest_path(G, source, target). |
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217 """ |
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218 |
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219 if source not in G or target not in G: |
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220 msg = f"Either source {source} or target {target} is not in G" |
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221 raise nx.NodeNotFound(msg) |
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222 |
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223 # call helper to do the real work |
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224 results = _bidirectional_pred_succ(G, source, target) |
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225 pred, succ, w = results |
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226 |
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227 # build path from pred+w+succ |
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228 path = [] |
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229 # from source to w |
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230 while w is not None: |
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231 path.append(w) |
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232 w = pred[w] |
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233 path.reverse() |
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234 # from w to target |
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235 w = succ[path[-1]] |
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236 while w is not None: |
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237 path.append(w) |
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238 w = succ[w] |
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239 |
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240 return path |
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241 |
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242 |
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243 def _bidirectional_pred_succ(G, source, target): |
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244 """Bidirectional shortest path helper. |
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245 |
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246 Returns (pred, succ, w) where |
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247 pred is a dictionary of predecessors from w to the source, and |
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248 succ is a dictionary of successors from w to the target. |
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249 """ |
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250 # does BFS from both source and target and meets in the middle |
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251 if target == source: |
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252 return ({target: None}, {source: None}, source) |
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253 |
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254 # handle either directed or undirected |
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255 if G.is_directed(): |
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256 Gpred = G.pred |
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257 Gsucc = G.succ |
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258 else: |
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259 Gpred = G.adj |
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260 Gsucc = G.adj |
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261 |
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262 # predecesssor and successors in search |
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263 pred = {source: None} |
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264 succ = {target: None} |
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265 |
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266 # initialize fringes, start with forward |
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267 forward_fringe = [source] |
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268 reverse_fringe = [target] |
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269 |
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270 while forward_fringe and reverse_fringe: |
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271 if len(forward_fringe) <= len(reverse_fringe): |
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272 this_level = forward_fringe |
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273 forward_fringe = [] |
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274 for v in this_level: |
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275 for w in Gsucc[v]: |
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276 if w not in pred: |
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277 forward_fringe.append(w) |
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278 pred[w] = v |
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279 if w in succ: # path found |
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280 return pred, succ, w |
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281 else: |
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282 this_level = reverse_fringe |
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283 reverse_fringe = [] |
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284 for v in this_level: |
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285 for w in Gpred[v]: |
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286 if w not in succ: |
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287 succ[w] = v |
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288 reverse_fringe.append(w) |
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289 if w in pred: # found path |
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290 return pred, succ, w |
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291 |
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292 raise nx.NetworkXNoPath(f"No path between {source} and {target}.") |
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293 |
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294 |
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295 def single_source_shortest_path(G, source, cutoff=None): |
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296 """Compute shortest path between source |
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297 and all other nodes reachable from source. |
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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 label |
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304 Starting node for path |
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305 |
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306 cutoff : integer, optional |
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307 Depth to stop the search. Only paths of length <= cutoff are returned. |
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308 |
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309 Returns |
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310 ------- |
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311 lengths : dictionary |
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312 Dictionary, keyed by target, of shortest paths. |
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313 |
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314 Examples |
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315 -------- |
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316 >>> G = nx.path_graph(5) |
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317 >>> path = nx.single_source_shortest_path(G, 0) |
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318 >>> path[4] |
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319 [0, 1, 2, 3, 4] |
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320 |
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321 Notes |
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322 ----- |
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323 The shortest path is not necessarily unique. So there can be multiple |
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324 paths between the source and each target node, all of which have the |
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325 same 'shortest' length. For each target node, this function returns |
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326 only one of those paths. |
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327 |
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328 See Also |
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329 -------- |
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330 shortest_path |
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331 """ |
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332 if source not in G: |
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333 raise nx.NodeNotFound(f"Source {source} not in G") |
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334 |
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335 def join(p1, p2): |
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336 return p1 + p2 |
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337 |
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338 if cutoff is None: |
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339 cutoff = float("inf") |
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340 nextlevel = {source: 1} # list of nodes to check at next level |
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341 paths = {source: [source]} # paths dictionary (paths to key from source) |
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342 return dict(_single_shortest_path(G.adj, nextlevel, paths, cutoff, join)) |
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343 |
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344 |
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345 def _single_shortest_path(adj, firstlevel, paths, cutoff, join): |
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346 """Returns shortest paths |
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347 |
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348 Shortest Path helper function |
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349 Parameters |
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350 ---------- |
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351 adj : dict |
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352 Adjacency dict or view |
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353 firstlevel : dict |
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354 starting nodes, e.g. {source: 1} or {target: 1} |
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355 paths : dict |
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356 paths for starting nodes, e.g. {source: [source]} |
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357 cutoff : int or float |
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358 level at which we stop the process |
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359 join : function |
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360 function to construct a path from two partial paths. Requires two |
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361 list inputs `p1` and `p2`, and returns a list. Usually returns |
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362 `p1 + p2` (forward from source) or `p2 + p1` (backward from target) |
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363 """ |
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364 level = 0 # the current level |
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365 nextlevel = firstlevel |
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366 while nextlevel and cutoff > level: |
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367 thislevel = nextlevel |
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368 nextlevel = {} |
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369 for v in thislevel: |
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370 for w in adj[v]: |
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371 if w not in paths: |
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372 paths[w] = join(paths[v], [w]) |
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373 nextlevel[w] = 1 |
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374 level += 1 |
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375 return paths |
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376 |
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377 |
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378 def single_target_shortest_path(G, target, cutoff=None): |
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379 """Compute shortest path to target from all nodes that reach target. |
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380 |
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381 Parameters |
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382 ---------- |
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383 G : NetworkX graph |
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384 |
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385 target : node label |
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386 Target node for path |
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387 |
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388 cutoff : integer, optional |
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389 Depth to stop the search. Only paths of length <= cutoff are returned. |
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390 |
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391 Returns |
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392 ------- |
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393 lengths : dictionary |
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394 Dictionary, keyed by target, of shortest paths. |
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395 |
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396 Examples |
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397 -------- |
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398 >>> G = nx.path_graph(5, create_using=nx.DiGraph()) |
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399 >>> path = nx.single_target_shortest_path(G, 4) |
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400 >>> path[0] |
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401 [0, 1, 2, 3, 4] |
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402 |
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403 Notes |
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404 ----- |
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405 The shortest path is not necessarily unique. So there can be multiple |
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406 paths between the source and each target node, all of which have the |
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407 same 'shortest' length. For each target node, this function returns |
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408 only one of those paths. |
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409 |
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410 See Also |
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411 -------- |
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412 shortest_path, single_source_shortest_path |
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413 """ |
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414 if target not in G: |
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415 raise nx.NodeNotFound(f"Target {target} not in G") |
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416 |
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417 def join(p1, p2): |
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418 return p2 + p1 |
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419 |
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420 # handle undirected graphs |
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421 adj = G.pred if G.is_directed() else G.adj |
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422 if cutoff is None: |
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423 cutoff = float("inf") |
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424 nextlevel = {target: 1} # list of nodes to check at next level |
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425 paths = {target: [target]} # paths dictionary (paths to key from source) |
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426 return dict(_single_shortest_path(adj, nextlevel, paths, cutoff, join)) |
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427 |
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428 |
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429 def all_pairs_shortest_path(G, cutoff=None): |
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430 """Compute shortest paths between all nodes. |
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431 |
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432 Parameters |
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433 ---------- |
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434 G : NetworkX graph |
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435 |
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436 cutoff : integer, optional |
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437 Depth at which to stop the search. Only paths of length at most |
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438 `cutoff` are returned. |
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439 |
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440 Returns |
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441 ------- |
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442 lengths : dictionary |
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443 Dictionary, keyed by source and target, of shortest paths. |
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444 |
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445 Examples |
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446 -------- |
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447 >>> G = nx.path_graph(5) |
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448 >>> path = dict(nx.all_pairs_shortest_path(G)) |
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449 >>> print(path[0][4]) |
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450 [0, 1, 2, 3, 4] |
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451 |
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452 See Also |
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453 -------- |
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454 floyd_warshall() |
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455 |
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456 """ |
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457 # TODO This can be trivially parallelized. |
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458 for n in G: |
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459 yield (n, single_source_shortest_path(G, n, cutoff=cutoff)) |
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460 |
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461 |
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462 def predecessor(G, source, target=None, cutoff=None, return_seen=None): |
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463 """Returns dict of predecessors for the path from source to all nodes in G |
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464 |
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465 |
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466 Parameters |
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467 ---------- |
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468 G : NetworkX graph |
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469 |
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470 source : node label |
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471 Starting node for path |
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472 |
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473 target : node label, optional |
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474 Ending node for path. If provided only predecessors between |
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475 source and target are returned |
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476 |
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477 cutoff : integer, optional |
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478 Depth to stop the search. Only paths of length <= cutoff are returned. |
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479 |
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480 |
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481 Returns |
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482 ------- |
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483 pred : dictionary |
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484 Dictionary, keyed by node, of predecessors in the shortest path. |
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485 |
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486 Examples |
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487 -------- |
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488 >>> G = nx.path_graph(4) |
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489 >>> list(G) |
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490 [0, 1, 2, 3] |
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491 >>> nx.predecessor(G, 0) |
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492 {0: [], 1: [0], 2: [1], 3: [2]} |
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493 |
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494 """ |
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495 if source not in G: |
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496 raise nx.NodeNotFound(f"Source {source} not in G") |
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497 |
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498 level = 0 # the current level |
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499 nextlevel = [source] # list of nodes to check at next level |
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500 seen = {source: level} # level (number of hops) when seen in BFS |
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501 pred = {source: []} # predecessor dictionary |
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502 while nextlevel: |
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503 level = level + 1 |
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504 thislevel = nextlevel |
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505 nextlevel = [] |
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506 for v in thislevel: |
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507 for w in G[v]: |
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508 if w not in seen: |
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509 pred[w] = [v] |
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510 seen[w] = level |
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511 nextlevel.append(w) |
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512 elif seen[w] == level: # add v to predecessor list if it |
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513 pred[w].append(v) # is at the correct level |
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514 if cutoff and cutoff <= level: |
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515 break |
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516 |
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517 if target is not None: |
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518 if return_seen: |
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519 if target not in pred: |
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520 return ([], -1) # No predecessor |
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521 return (pred[target], seen[target]) |
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522 else: |
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523 if target not in pred: |
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524 return [] # No predecessor |
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525 return pred[target] |
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526 else: |
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527 if return_seen: |
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528 return (pred, seen) |
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529 else: |
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530 return pred |