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1 package Graph::Path;
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2 #
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3 # $RCSfile: Path.pm,v $
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4 # $Date: 2015/02/28 20:49:06 $
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5 # $Revision: 1.25 $
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6 #
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7 # Author: Manish Sud <msud@san.rr.com>
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8 #
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9 # Copyright (C) 2015 Manish Sud. All rights reserved.
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10 #
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11 # This file is part of MayaChemTools.
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12 #
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13 # MayaChemTools is free software; you can redistribute it and/or modify it under
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14 # the terms of the GNU Lesser General Public License as published by the Free
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15 # Software Foundation; either version 3 of the License, or (at your option) any
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16 # later version.
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17 #
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18 # MayaChemTools is distributed in the hope that it will be useful, but without
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19 # any warranty; without even the implied warranty of merchantability of fitness
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20 # for a particular purpose. See the GNU Lesser General Public License for more
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21 # details.
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22 #
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23 # You should have received a copy of the GNU Lesser General Public License
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24 # along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or
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25 # write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,
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26 # Boston, MA, 02111-1307, USA.
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27 #
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28
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29 use strict;
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30 use Carp;
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31 use Exporter;
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32 use Storable ();
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33 use Scalar::Util ();
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34
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35 use vars qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS);
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36
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37 @ISA = qw(Exporter);
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38 @EXPORT = qw();
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39 @EXPORT_OK = qw();
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40
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41 %EXPORT_TAGS = (all => [@EXPORT, @EXPORT_OK]);
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42
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43 # Setup class variables...
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44 my($ClassName, $ObjectID);
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45 _InitializeClass();
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46
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47 # Overload Perl functions...
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48 use overload '""' => 'StringifyPath',
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49
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50 '==' => '_PathEqualOperator',
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51 'eq' => '_PathEqualOperator',
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52
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53 'fallback' => undef;
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54
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55 # Class constructor...
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56 sub new {
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57 my($Class, @VertexIDs) = @_;
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58
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59 # Initialize object...
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60 my $This = {};
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61 bless $This, ref($Class) || $Class;
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62 $This->_InitializePath();
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63
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64 if (@VertexIDs) { $This->AddVertices(@VertexIDs); }
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65
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66 return $This;
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67 }
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68
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69 # Initialize object data...
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70 #
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71 sub _InitializePath {
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72 my($This) = @_;
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73
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74 @{$This->{Vertices}} = ();
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75 }
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76
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77 # Initialize class ...
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78 sub _InitializeClass {
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79 #Class name...
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80 $ClassName = __PACKAGE__;
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81 }
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82
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83 # Add a vertex to path after the end vertex...
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84 #
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85 sub AddVertex {
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86 my($This, $VertexID) = @_;
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87
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88 if (!defined $VertexID ) {
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89 carp "Warning: ${ClassName}->AddVertex: No vertex added: Vertex ID must be specified...";
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90 return undef;
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91 }
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92 push @{$This->{Vertices}}, $VertexID;
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93
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94 return $This;
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95 }
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96
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97 # Add vertices to the path after the end vertex...
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98 #
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99 sub AddVertices {
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100 my($This, @VertexIDs) = @_;
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101
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102 if (!@VertexIDs) {
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103 carp "Warning: ${ClassName}->AddVertices: No vertices added: Vertices list is empty...";
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104 return undef;
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105 }
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106 push @{$This->{Vertices}}, @VertexIDs;
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107
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108 return $This;
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109 }
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110
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111 # Add a vertex to path after the end vertex...
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112 #
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113 sub PushVertex {
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114 my($This, $VertexID) = @_;
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115
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116 return $This->AddVertex($VertexID);
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117 }
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118
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119 # Add vertices to the path after the end vertex...
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120 #
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121 sub PushVertices {
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122 my($This, @VertexIDs) = @_;
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123
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124 return $This->AddVertices(@VertexIDs);
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125 }
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126
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127 # Remove end vertex from path...
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128 #
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129 sub PopVertex {
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130 my($This) = @_;
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131
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132 if (!@{$This->{Vertices}}) {
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133 carp "Warning: ${ClassName}->PopVertex: No vertex removed: Path is empty...";
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134 return undef;
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135 }
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136 pop @{$This->{Vertices}};
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137
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138 return $This;
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139 }
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140
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141 # Remove start vertex from path...
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142 #
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143 sub ShiftVertex {
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144 my($This) = @_;
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145
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146 if (!@{$This->{Vertices}}) {
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147 carp "Warning: ${ClassName}->ShiftVertex: No vertex removed: Path is empty...";
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148 return undef;
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149 }
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150 shift @{$This->{Vertices}};
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151
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152 return $This;
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153 }
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154
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155 # Add a vertex to path before the start vertex...
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156 #
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157 sub UnshiftVertex {
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158 my($This, $VertexID) = @_;
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159
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160 if (!defined $VertexID ) {
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161 carp "Warning: ${ClassName}->UnshiftVertex: No vertex added: Vertex ID must be specified...";
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162 return undef;
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163 }
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164 unshift @{$This->{Vertices}}, $VertexID;
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165
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166 return $This;
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167 }
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168
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169 # Add vertices to the path before the start vertex...
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170 #
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171 sub UnshiftVertices {
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172 my($This, @VertexIDs) = @_;
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173
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174 if (!@VertexIDs) {
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175 carp "Warning: ${ClassName}->UnshiftVertices: No vertices added: Vertices list is empty...";
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176 return undef;
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177 }
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178 unshift @{$This->{Vertices}}, @VertexIDs;
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179
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180 return $This;
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181 }
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182
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183 # Get length...
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184 #
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185 sub GetLength {
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186 my($This) = @_;
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187
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188 return scalar @{$This->{Vertices}};
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189 }
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190
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191 # Get start vertex...
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192 #
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193 sub GetStartVertex {
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194 my($This) = @_;
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195
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196 if (!$This->GetLength()) {
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197 return undef;
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198 }
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199 my($Index) = 0;
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200 return $This->_GetVertex($Index);
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201 }
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202
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203 # Get end vertex...
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204 #
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205 sub GetEndVertex {
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206 my($This) = @_;
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207
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208 if (!$This->GetLength()) {
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209 return undef;
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210 }
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211 my($Index);
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212
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213 $Index = $This->GetLength() - 1;
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214 return $This->_GetVertex($Index);
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215 }
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216
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217 # Get start and end vertices...
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218 #
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219 sub GetTerminalVertices {
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220 my($This) = @_;
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221
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222 return ( $This->GetStartVertex(), $This->GetEndVertex() ),
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223 }
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224
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225 # Get path vertices...
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226 #
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227 sub GetVertices {
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228 my($This) = @_;
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229
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230 return wantarray ? @{$This->{Vertices}} : scalar @{$This->{Vertices}};
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231 }
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232
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233 # Get a specific vertex from path with indicies starting from 0...
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234 #
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235 sub GetVertex {
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236 my($This, $Index) = @_;
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237
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238 if ($Index < 0) {
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239 croak "Error: ${ClassName}->GetValue: Index value must be a positive number...";
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240 }
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241 if ($Index >= $This->GetLength()) {
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242 croak "Error: ${ClassName}->GetValue: Index vaue must be less than length of path...";
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243 }
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244 if (!$This->GetLength()) {
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245 return undef;
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246 }
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247 return $This->_GetVertex($Index);
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248 }
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249
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250 # Get a vertex...
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251 #
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252 sub _GetVertex {
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253 my($This, $Index) = @_;
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254
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255 return $This->{Vertices}[$Index];
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256 }
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257
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258 # Get path edges as pair of vertices or number of edges...
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259 #
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260 sub GetEdges {
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261 my($This) = @_;
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262
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263 if ($This->GetLength < 1) {
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264 return undef;
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265 }
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266 # Set up edges...
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267 my($Index, $VertexID1, $VertexID2, @Vertices, @Edges);
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268
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269 @Edges = ();
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270 for $Index (0 .. ($#{$This->{Vertices}} - 1) ) {
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271 $VertexID1 = $This->{Vertices}[$Index];
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272 $VertexID2 = $This->{Vertices}[$Index + 1];
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273 push @Edges, ($VertexID1, $VertexID2);
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274 }
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275
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276 return wantarray ? @Edges : ((scalar @Edges)/2);
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277 }
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278
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279 # Is it a cycle?
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280 #
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281 sub IsCycle {
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282 my($This) = @_;
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283 my($StartVertex, $EndVertex);
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284
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285 ($StartVertex, $EndVertex) = $This->GetTerminalVertices();
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286
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287 return ($StartVertex == $EndVertex) ? 1 : 0;
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288 }
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289
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290 # For a path to be an independent path, it must meet the following conditions:
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291 # . All other vertices are unique.
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292 #
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293 sub IsIndependentPath {
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294 my($This) = @_;
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295
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296 # Make sure it has at least two vertices...
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297 if ($This->GetLength() < 2) {
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298 return 0;
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299 }
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300
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301 # Check frequency of occurence for non-terminal vertices...
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302 my($VertexID, $IndependenceStatus, @Vertices, %VerticesMap);
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303
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304 @Vertices = $This->GetVertices();
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305 shift @Vertices; pop @Vertices;
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306
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307 %VerticesMap = ();
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308 $IndependenceStatus = 1;
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309
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310 VERTEXID: for $VertexID (@Vertices) {
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311 if (exists $VerticesMap{$VertexID} ) {
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312 $IndependenceStatus = 0;
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313 last VERTEXID;
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314 }
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315 $VerticesMap{$VertexID} = $VertexID;
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316 }
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317 return $IndependenceStatus;
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318 }
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319
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320 # For a path to be an independent cyclic path, it must meet the following conditions:
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321 # . Termimal vertices are the same
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322 # . All other vertices are unique.
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323 #
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324 sub IsIndependentCyclicPath {
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325 my($This) = @_;
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326
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327 # Make sure it's a cycle...
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328 if (!($This->GetLength() >= 3 && $This->IsCycle())) {
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329 return 0;
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330 }
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331 return $This->IsIndependentPath();
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332 }
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333
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334 # Is it a path object?
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335 sub IsPath ($) {
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336 my($Object) = @_;
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337
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338 return _IsPath($Object);
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339 }
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340
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341 # Copy path...
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342 #
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343 sub Copy {
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344 my($This) = @_;
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345 my($NewPath);
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346
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347 $NewPath = Storable::dclone($This);
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348
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349 return $NewPath;
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350 }
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351
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352 # Reverse order of vertices in path...
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353 #
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354 sub Reverse {
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355 my($This) = @_;
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356 my(@VertexIDs);
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357
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358 @VertexIDs = (); push @VertexIDs, @{$This->{Vertices}};
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359
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360 @{$This->{Vertices}} = (); push @{$This->{Vertices}}, reverse @VertexIDs;
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361
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362 return $This;
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363 }
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364
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365 # Get vertices common between two paths...
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366 #
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367 sub GetCommonVertices {
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368 my($This, $Other) = @_;
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369 my($VertexID, @CommonVertices, %OtherVerticesMap);
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370
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371 # Setup a vertices hash for a quick look up...
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372 %OtherVerticesMap = ();
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373 for $VertexID ($Other->GetVertices()) {
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374 $OtherVerticesMap{$VertexID} = $VertexID;
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375 }
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376
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377 @CommonVertices = ();
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378 for $VertexID ($This->GetVertices()) {
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379 if ($OtherVerticesMap{$VertexID}) {
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380 push @CommonVertices, $VertexID
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381 }
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382 }
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383 return wantarray ? @CommonVertices : scalar @CommonVertices;
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384 }
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385
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386 # Join the existing path with a new path specifed using a path object of a list of
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387 # verticies.
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388 #
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389 sub Join {
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390 my($This, @Values) = @_;
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391
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392 return $This->_Join(@Values);
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393 }
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394
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395 # Join the existing path with a new path specifed using a path object at a specified
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396 # vertex.
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397 #
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398 sub JoinAtVertex {
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399 my($This, $Other, $CenterVertexID) = @_;
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400
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401 # Make sure CenterVertexID is end vertex in This and start vertex in Other before
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402 # joining them...
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403 if ($This->GetEndVertex() != $CenterVertexID) {
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404 $This->Reverse();
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405 }
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406 if ($Other->GetStartVertex() != $CenterVertexID) {
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407 $Other->Reverse();
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408 }
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409 return $This->_Join($Other);
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410 }
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411
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412 # Join the existing path with a new path specifed using a path object of a list of
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413 # verticies.
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414 #
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415 # Notes:
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416 # . Paths must have a common terminal vertex.
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417 # . Based on the common terminal vertex found, new path vertices are added to the
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418 # current path in one of the four ways:
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419 # . New path at end of current path with same vertices order : EndVertex = NewStartVertex
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420 # . New path at end of current path with reversed vertices order: EndVertex = NewEndVertex
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421 # . New path at front of current path with same vertices order: StartVertex = NewEndVertex
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422 # . New path at front of current path with reversed vertices order: StartVertex = NewStartVertex
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423 #
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424 sub _Join {
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425 my($This, @Values) = @_;
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426
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427 if (!@Values) {
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428 return;
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429 }
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430
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431 # Get a list of new vertex IDs..
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432 my($NewPath, $FirstValue, $TypeOfFirstValue, @NewVertexIDs);
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433
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434 $NewPath = $This->Copy();
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435
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436 @NewVertexIDs = ();
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437 $FirstValue = $Values[0];
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438 $TypeOfFirstValue = ref $FirstValue;
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439 if ($TypeOfFirstValue =~ /^(SCALAR|HASH|CODE|REF|GLOB)/) {
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440 croak "Error: ${ClassName}->JoinPath: Trying to add vertices to path object with a reference to unsupported value format...";
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441 }
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442
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443 if (_IsPath($FirstValue)) {
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444 # It's another path object...
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445 push @NewVertexIDs, @{$FirstValue->{Vertices}};
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446 }
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447 elsif ($TypeOfFirstValue =~ /^ARRAY/) {
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448 # It's array reference...
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449 push @NewVertexIDs, @{$FirstValue};
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450 }
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451 else {
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452 # It's a list of values...
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453 push @NewVertexIDs, @Values;
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454 }
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455 my($StartVertex, $EndVertex, $NewStartVertex, $NewEndVertex);
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456
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457 ($StartVertex, $EndVertex) = $NewPath->GetTerminalVertices();
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458 ($NewStartVertex, $NewEndVertex) = ($NewVertexIDs[0], $NewVertexIDs[$#NewVertexIDs]);
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459
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460 if (!($EndVertex == $NewStartVertex || $EndVertex == $NewEndVertex || $StartVertex == $NewEndVertex || $StartVertex == $NewStartVertex)) {
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461 carp "Warning: ${ClassName}->JoinPath: Paths can't be joined: No common terminal vertex found...";
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462 return undef;
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463 }
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464
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465 if ($EndVertex == $NewStartVertex) {
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466 # Take out EndVertex and add new path at the end...
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467 pop @{$NewPath->{Vertices}};
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468 push @{$NewPath->{Vertices}}, @NewVertexIDs;
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469 }
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470 elsif ($EndVertex == $NewEndVertex) {
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471 # Take out EndVertex and add new path at the end with reversed vertex order...
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472 pop @{$NewPath->{Vertices}};
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473 push @{$NewPath->{Vertices}}, reverse @NewVertexIDs;
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474 }
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475 elsif ($StartVertex == $NewEndVertex) {
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476 # Take out NewEndVertex and add new path at the front...
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477 pop @NewVertexIDs;
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478 unshift @{$NewPath->{Vertices}}, @NewVertexIDs;
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479 }
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480 elsif ($StartVertex == $NewStartVertex) {
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481 # Take out NewStartVertex and add new path at the front...
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482 shift @NewVertexIDs;
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483 unshift @{$NewPath->{Vertices}}, reverse @NewVertexIDs;
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484 }
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485
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486 return $NewPath,
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487 }
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488
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489 # Compare two paths...
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490 #
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491 sub _PathEqualOperator {
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492 my($This, $Other) = @_;
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493
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494 if (!(defined($This) && _IsPath($This) && defined($Other) && _IsPath($Other))) {
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495 croak "Error: ${ClassName}->_PathEqualOperator: Path equal comparison failed: Both object must be paths...";
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496 }
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497
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498 if ($This->GetLength() != $Other->GetLength()) {
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499 return 0;
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500 }
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501 my($ThisID, $OtherID, $ReverseOtherID);
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502
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503 $ThisID = join('-', @{$This->{Vertices}});
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504 $OtherID = join('-', @{$Other->{Vertices}});
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505 $ReverseOtherID = join('-', reverse(@{$Other->{Vertices}}));
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506
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507 return ($ThisID =~ /^($OtherID|$ReverseOtherID)$/) ? 1 : 0;
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508 }
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509
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510 # Return a string containing vertices in the path...
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511 sub StringifyPath {
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512 my($This) = @_;
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513 my($PathString);
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514
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515 $PathString = "Path: " . join('-', @{$This->{Vertices}});
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516
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517 return $PathString;
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518 }
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519
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520 # Is it a path object?
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521 sub _IsPath {
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522 my($Object) = @_;
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523
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524 return (Scalar::Util::blessed($Object) && $Object->isa($ClassName)) ? 1 : 0;
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525 }
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526
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527 1;
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528
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529 __END__
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530
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531 =head1 NAME
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532
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533 Path - Path class
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534
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535 =head1 SYNOPSIS
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536
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537 use Graph::Path;
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538
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539 use Graph::Path qw(:all);
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540
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541 =head1 DESCRIPTION
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542
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543 B<Path> class provides the following methods:
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544
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545 new, AddVertex, AddVertices, Copy, GetCommonVertices, GetEdges, GetEndVertex,
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546 GetLength, GetStartVertex, GetTerminalVertices, GetVertex, GetVertices, IsCycle,
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547 IsIndependentCyclicPath, IsIndependentPath, IsPath, Join, JoinAtVertex, PopVertex,
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548 PushVertex, PushVertices, Reverse, ShiftVertex, StringifyPath, UnshiftVertex,
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549 UnshiftVertices
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550
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551 Path is a sequential list of vertices with an edge between two successive vertices. The path
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552 becomes a cycle when start vertex and end vertex are the same.
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553
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554 The following operators are overloaded:
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555
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556 "" == eq
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557
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558 =head2 METHODS
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559
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560 =over 4
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561
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562 =item B<new>
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563
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564 $NewPath = new Path();
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565 $NewPath = new Path(@VertexIDs);
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566
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567 Using specified I<VertexIDs>, B<new> method creates a new B<Path> object and returns
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568 newly created B<Path> object.
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569
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570 =item B<AddVertex>
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571
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572 $Path->AddVertex($VertexID);
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573
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574 Adds I<VertexID> to I<Path> and returns I<Path>.
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575
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576 =item B<AddVertices>
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577
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578 $Path->AddVertices(@VertexIDs);
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579
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580 Adds vertices using I<VertexIDs> to I<Path> and returns I<Graph>.
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581
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582 =item B<Copy>
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583
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584 $Return = $Path->Copy();
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585
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586 Copies I<Path> and its associated data using B<Storable::dclone> and returns a new
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587 B<Path> object.
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588
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589 =item B<GetCommonVertices>
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590
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591 @CommonVertices = $Path->GetCommonVertices($OtherPath);
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592 $NumOfCommonVertices = $Path->GetCommonVertices($OtherPath);
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593
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594 Returns an array containing common vertex IDs between two paths. In scalar context, number
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595 of common vertices is returned.
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596
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597 =item B<GetEdges>
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598
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599 @EdgesVertexIDs = $Path->GetEdges();
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600 $NumOfEdges = $Path->GetEdges();
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601
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602 Returns an array containg successive paris of vertex IDs corresponding to all edges in I<Path>.
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603 In scalar context, the number of edges is returned.
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604
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605 =item B<GetEndVertex>
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606
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607 $VertexID = $Path->GetEndVertex();
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608
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609 Returns B<VertexID> of end vertex in I<Path>.
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610
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611 =item B<GetLength>
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612
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613 $Length = $Path->GetLength();
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614
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615 Returns B<Length> of I<Path> corresponding to number of vertices in I<Path>.
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616
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617 =item B<GetStartVertex>
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618
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619 $VertexID = $Path->GetStartVertex();
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620
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621 Returns B<VertexID> of start vertex in I<Path>.
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622
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623 =item B<GetTerminalVertices>
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624
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625 ($StartVertexID, $EndVertexID) = $Path->GetTerminalVertices();
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626
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627 Returns vertex IDs of start and end vertices in I<Path>.
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628
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629 =item B<GetVertex>
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630
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631 $VertexID = $Path->GetVertex($Index);
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632
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633 Returns specific vertex ID from I<Path> corresponding to I<Index> with indicies starting from 0.
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634
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635 =item B<GetVertices>
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636
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637 @Vertices = $Path->GetVertices();
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638 $NumOfVertices = $Path->GetVertices();
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639
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640 Returns an array containing all vertex IDs in I<Path>. In scalar context, number of vertices
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641 is returned.
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642
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643 =item B<IsCycle>
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644
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645 $Status = $Path->IsCycle();
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646
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647 Returns 1 or 0 based on whether I<Path> is a B<CyclicPath> which has the same start and
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648 end vertex IDs.
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649
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650 =item B<IsIndependentCyclicPath>
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651
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652 $Status = $Path->IsIndependentCyclicPath();
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653
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654 Returns 1 or 0 based on whether I<Path> is an independent B<CyclicPath>. For a I<Path> to be
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655 an independent cyclic path, it must be a cyclic path and have unique vertices.
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656
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657 =item B<IsIndependentPath>
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658
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659 $Status = $Path->IsIndependentPath();
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660
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661 Returns 1 or 0 based on whether I<Path> is an independent B<Path>. For a I<Path> to be
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662 an independent path, it must have unique vertices.
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663
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664 =item B<IsPath>
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665
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666 $Status = Graph::Path::IsPath();
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667
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668 Returns 1 or 0 based on whether I<Object> is a B<Path> object
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669
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670 =item B<Join>
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671
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672 $NewPath = $Path->Join($OtherPath);
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673 $NewPath = $Path->Join(@VertexIDs);
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674
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675 Joins existing I<Path> with a new path specified as a I<OtherPath> object or an array of I<VertexIDs>
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676 and returns I<NewPath>.
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677
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678 In order to successfully join two paths, terminal vertices must have a common vertex. Based on the
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679 common terminal vertex found, additional path vertices are added to the current I<Path> in one of
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680 the following four ways:
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681
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682 . EndVertex = NewStartVertex: New path at end of current path with
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683 same vertices order
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684
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685 . EndVertex = NewEndVertex: New path at end of current path with
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686 reversed vertices order
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687
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688 . StartVertex = NewEndVertex: New path at front of current path
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689 with same vertices order
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690
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691 . StartVertex = NewStartVertex: New path at front of current path
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692 with reversed vertices order
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693
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694 =item B<JoinAtVertex>
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695
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696 $NewPath = $Path->JoinAtVertex($OtherPath, $CenterVertexID);
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697
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698 Joins existing I<Path> with I<OtherPath> at a specified I<CeterVertexID> and returns a I<NewPath>.
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699
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700 =item B<PopVertex>
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701
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702 $Path->PopVertex();
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703
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704 Removes end vertex from I<Path> and returns I<Path>.
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705
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706 =item B<PushVertex>
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707
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708 $Path->PushVertex($VertexID);
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709
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710 Adds I<VertexID> to I<Path> after end vertex and returns I<Path>.
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711
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712 =item B<PushVertices>
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713
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714 $Path->PushVertices(@VertexIDs);
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715
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716 Adds I<VertexIDs> to I<Path> after end vertex and returns I<Path>.
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717
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718 =item B<Reverse>
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719
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720 $Path->Reverse();
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721
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722 Reverses order of vertices in I<Path> and returns I<Path>.
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723
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724 =item B<ShiftVertex>
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725
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726 $Path->ShiftVertex();
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727
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728 Removes start vertex from I<Path> and returns I<Path>.
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729
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730 =item B<StringifyPath>
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731
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732 $String = $Path->StringifyPath();
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733
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734 Returns a string containing information about I<Path> object.
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735
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736 =item B<UnshiftVertex>
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737
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738 $Path->UnshiftVertex($VertexID);
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739
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740 Adds I<VertexID> to I<Path> before start vertex and returns I<Path>.
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741
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742 =item B<UnshiftVertices>
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743
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744 $Path->UnshiftVertices(@VertexIDs);
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745
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746 Adds I<VertexIDs> to I<Path> before start vertex and returns I<Path>.
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747
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748 =back
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749
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750 =head1 AUTHOR
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751
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752 Manish Sud <msud@san.rr.com>
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753
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754 =head1 SEE ALSO
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755
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756 PathGraph.pm, PathsTraversal.pm
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757
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758 =head1 COPYRIGHT
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759
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760 Copyright (C) 2015 Manish Sud. All rights reserved.
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761
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762 This file is part of MayaChemTools.
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763
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764 MayaChemTools is free software; you can redistribute it and/or modify it under
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765 the terms of the GNU Lesser General Public License as published by the Free
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766 Software Foundation; either version 3 of the License, or (at your option)
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767 any later version.
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768
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769 =cut
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