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<html> <head> <title>MayaChemTools:Code:Graph::CyclesDetection.pm</title> <meta http-equiv="content-type" content="text/html;charset=utf-8"> <link rel="stylesheet" type="text/css" href="../../../css/MayaChemToolsCode.css"> </head> <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> <br/> <center> <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> </center> <br/> <pre> <a name="package-Graph::CyclesDetection-"></a> 1 <span class="k">package </span><span class="i">Graph::CyclesDetection</span><span class="sc">;</span> 2 <span class="c">#</span> 3 <span class="c"># $RCSfile: CyclesDetection.pm,v $</span> 4 <span class="c"># $Date: 2015/02/28 20:49:06 $</span> 5 <span class="c"># $Revision: 1.27 $</span> 6 <span class="c">#</span> 7 <span class="c"># Author: Manish Sud <msud@san.rr.com></span> 8 <span class="c">#</span> 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span> 10 <span class="c">#</span> 11 <span class="c"># This file is part of MayaChemTools.</span> 12 <span class="c">#</span> 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span> 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span> 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span> 16 <span class="c"># later version.</span> 17 <span class="c">#</span> 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span> 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span> 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span> 21 <span class="c"># details.</span> 22 <span class="c">#</span> 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span> 24 <span class="c"># along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or</span> 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span> 26 <span class="c"># Boston, MA, 02111-1307, USA.</span> 27 <span class="c">#</span> 28 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span> 30 <span class="k">use</span> <span class="w">Carp</span><span class="sc">;</span> 31 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span> 32 <span class="k">use</span> <span class="w">Graph</span><span class="sc">;</span> 33 <span class="k">use</span> <span class="w">Graph::Path</span><span class="sc">;</span> 34 <span class="k">use</span> <span class="w">Graph::PathGraph</span><span class="sc">;</span> 35 <span class="k">use</span> <span class="w">BitVector</span><span class="sc">;</span> 36 37 <span class="k">use</span> <span class="w">vars</span> <span class="q">qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS)</span><span class="sc">;</span> 38 39 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span> 40 <span class="i">@EXPORT</span> = <span class="q">qw()</span><span class="sc">;</span> 41 <span class="i">@EXPORT_OK</span> = <span class="q">qw()</span><span class="sc">;</span> 42 43 <span class="i">%EXPORT_TAGS</span> = <span class="s">(</span><span class="w">all</span> <span class="cm">=></span> <span class="s">[</span><span class="i">@EXPORT</span><span class="cm">,</span> <span class="i">@EXPORT_OK</span><span class="s">]</span><span class="s">)</span><span class="sc">;</span> 44 45 <span class="c"># Setup class variables...</span> 46 <span class="k">my</span><span class="s">(</span><span class="i">$ClassName</span><span class="s">)</span><span class="sc">;</span> 47 <span class="i">_InitializeClass</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 48 49 <span class="c"># Overload Perl functions...</span> 50 <span class="k">use</span> <span class="w">overload</span> <span class="q">'""'</span> <span class="cm">=></span> <span class="q">'StringifyCyclesDetection'</span><span class="sc">;</span> 51 52 <span class="c"># Class constructor...</span> <a name="new-"></a> 53 <span class="k">sub </span><span class="m">new</span> <span class="s">{</span> 54 <span class="k">my</span><span class="s">(</span><span class="i">$Class</span><span class="cm">,</span> <span class="i">$Graph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 55 56 <span class="c"># Initialize object...</span> 57 <span class="k">my</span> <span class="i">$This</span> = <span class="s">{</span><span class="s">}</span><span class="sc">;</span> 58 <span class="k">bless</span> <span class="i">$This</span><span class="cm">,</span> <span class="k">ref</span><span class="s">(</span><span class="i">$Class</span><span class="s">)</span> || <span class="i">$Class</span><span class="sc">;</span> 59 <span class="i">$This</span><span class="i">->_InitializeCyclesDetection</span><span class="s">(</span><span class="i">$Graph</span><span class="s">)</span><span class="sc">;</span> 60 61 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 62 <span class="s">}</span> 63 64 <span class="c"># Initialize object data...</span> <a name="_InitializeCyclesDetection-"></a> 65 <span class="k">sub </span><span class="m">_InitializeCyclesDetection</span> <span class="s">{</span> 66 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Graph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 67 68 <span class="i">$This</span>->{<span class="w">Graph</span>} = <span class="i">$Graph</span><span class="sc">;</span> 69 70 <span class="c"># Cycles list...</span> 71 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 72 73 <span class="c"># Cyclic paths which are not part of any other cycle...</span> 74 <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}} = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 75 76 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 77 <span class="s">}</span> 78 79 <span class="c"># Initialize class ...</span> <a name="_InitializeClass-"></a> 80 <span class="k">sub </span><span class="m">_InitializeClass</span> <span class="s">{</span> 81 <span class="c">#Class name...</span> 82 <span class="i">$ClassName</span> = <span class="w">__PACKAGE__</span><span class="sc">;</span> 83 <span class="s">}</span> 84 85 <span class="c"># Detect all cycles in graph...</span> 86 <span class="c">#</span> <a name="DetectCycles-"></a> 87 <span class="k">sub </span><span class="m">DetectCycles</span> <span class="s">{</span> 88 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 89 90 <span class="k">return</span> <span class="i">$This</span><span class="i">->DetectCyclesUsingCollapsingPathGraphMethodology</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 91 <span class="s">}</span> 92 93 <span class="c"># Detect all cycles in the graph using collapsing path graph [Ref 31] methodology...</span> 94 <span class="c">#</span> 95 <span class="c"># Note:</span> 96 <span class="c"># . For topologically complex graphs containing large number of cycles,</span> 97 <span class="c"># CollapseVertexAndCollectCyclicPathsDetectCycles method implemented in</span> 98 <span class="c"># PathGraph can time out in which case no cycles are detected or</span> 99 <span class="c"># assigned.</span> 100 <span class="c">#</span> <a name="DetectCyclesUsingCollapsingPathGraphMethodology-"></a> 101 <span class="k">sub </span><span class="m">DetectCyclesUsingCollapsingPathGraphMethodology</span> <span class="s">{</span> 102 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 103 <span class="k">my</span><span class="s">(</span><span class="i">$PathGraph</span><span class="s">)</span><span class="sc">;</span> 104 105 <span class="c"># Create a path graph...</span> 106 <span class="i">$PathGraph</span> = <span class="i">new</span> <span class="i">Graph::PathGraph</span><span class="s">(</span><span class="i">$This</span>->{<span class="w">Graph</span>}<span class="s">)</span><span class="sc">;</span> 107 108 <span class="c"># For a vertex to be in a cycle, its degree must be >=2. So delete vertices recursively</span> 109 <span class="c"># till all vertices with degree less than 2 have been deleted...</span> 110 <span class="i">$PathGraph</span><span class="i">->DeleteVerticesWithDegreeLessThan</span><span class="s">(</span><span class="n">2</span><span class="s">)</span><span class="sc">;</span> 111 112 <span class="c"># Setup a VertexID and EdgeID to index map usage during retrieval of independent cycles to</span> 113 <span class="c"># avoid going over all vertices in all cylic paths later...</span> 114 <span class="c">#</span> 115 <span class="k">my</span><span class="s">(</span><span class="i">$VertexIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestVertexIndex</span><span class="cm">,</span> <span class="i">$EdgeIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestEdgeIDIndex</span><span class="s">)</span><span class="sc">;</span> 116 <span class="s">(</span><span class="i">$VertexIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestVertexIndex</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->_SetupVertexIDsToIndicesMap</span><span class="s">(</span><span class="i">$PathGraph</span><span class="s">)</span><span class="sc">;</span> 117 <span class="s">(</span><span class="i">$EdgeIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestEdgeIDIndex</span><span class="s">)</span> = <span class="i">$This</span><span class="i">->_SetupEdgeIDsToIndicesMap</span><span class="s">(</span><span class="i">$PathGraph</span><span class="s">)</span><span class="sc">;</span> 118 119 <span class="c"># Recursively collapse vertices with lowest degree...</span> 120 <span class="k">my</span><span class="s">(</span><span class="i">$VertexID</span><span class="cm">,</span> <span class="i">$CycleVertexID</span><span class="s">)</span><span class="sc">;</span> 121 <span class="k">while</span> <span class="s">(</span><span class="i">$VertexID</span> = <span class="i">$PathGraph</span><span class="i">->GetVertexWithSmallestDegree</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 122 <span class="k">if</span> <span class="s">(</span>!<span class="i">$PathGraph</span><span class="i">->CollapseVertexAndCollectCyclicPaths</span><span class="s">(</span><span class="i">$VertexID</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 123 <span class="c"># Cycles detection didn't finish...</span> 124 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span> 125 <span class="s">}</span> 126 <span class="s">}</span> 127 128 <span class="c"># Get detected cycles and save 'em sorted by size...</span> 129 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="cm">,</span> <span class="k">sort</span> <span class="s">{</span> <span class="i">$a</span><span class="i">->GetLength</span><span class="s">(</span><span class="s">)</span> <=> <span class="i">$b</span><span class="i">->GetLength</span><span class="s">(</span><span class="s">)</span> <span class="s">}</span> <span class="i">$PathGraph</span><span class="i">->GetCyclicPaths</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 130 131 <span class="c"># Retrieve independent cyclic paths...</span> 132 <span class="k">return</span> <span class="i">$This</span><span class="i">->_RetrieveIndependentCycles</span><span class="s">(</span><span class="i">$VertexIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestVertexIndex</span><span class="cm">,</span> <span class="i">$EdgeIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestEdgeIDIndex</span><span class="s">)</span><span class="sc">;</span> 133 <span class="s">}</span> 134 135 <span class="c"># Retrieve and save independent cyclic paths...</span> 136 <span class="c">#</span> 137 <span class="c"># Set of independent cycles identified using this method doesn't correspond to basis set of</span> 138 <span class="c"># rings or smallest set of smallest rings (SSSR) [ Refs 29-30 ]; instead, set of cycles identified</span> 139 <span class="c"># as independent cycles simply correspond to cycles which contain no other cycle as their</span> 140 <span class="c"># subcycles and can't be described as linear combination of smaller cycles. And it also happen</span> 141 <span class="c"># to contain all the rings in basis set of rings and SSSR. In other words, it's a superset of basis set</span> 142 <span class="c"># of cycles and SSSR. For example, six four membered cycles are identified for cubane which is one</span> 143 <span class="c"># more than the basis set of cycles.</span> 144 <span class="c">#</span> <a name="_RetrieveIndependentCycles-"></a> 145 <span class="k">sub </span><span class="m">_RetrieveIndependentCycles</span> <span class="s">{</span> 146 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$VertexIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestVertexIndex</span><span class="cm">,</span> <span class="i">$EdgeIDsToIndicesRef</span><span class="cm">,</span> <span class="i">$LargestEdgeIDIndex</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 147 148 <span class="c"># Only 1 or 0 cyclic paths...</span> 149 <span class="k">if</span> <span class="s">(</span><span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}} <= <span class="n">1</span><span class="s">)</span> <span class="s">{</span> 150 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}}<span class="cm">,</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="sc">;</span> 151 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 152 <span class="s">}</span> 153 154 <span class="c"># Setup bit vectors for each cyclic path with size of each bit vector corresponding to</span> 155 <span class="c"># maximum vertex index plus one...</span> 156 <span class="k">my</span><span class="s">(</span><span class="i">$CyclicPath</span><span class="cm">,</span> <span class="i">$BitVector</span><span class="cm">,</span> <span class="i">@BitNums</span><span class="cm">,</span> <span class="i">@CyclicPathBitVectors</span><span class="cm">,</span> <span class="i">@CyclicPathEdgeIDsBitVectors</span><span class="s">)</span><span class="sc">;</span> 157 158 <span class="i">@CyclicPathBitVectors</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> <span class="i">@CyclicPathEdgeIDsBitVectors</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 159 160 <span class="c"># Set bits corresponding to VertexIDs EdgeIDs using their indices...</span> 161 <span class="k">for</span> <span class="i">$CyclicPath</span> <span class="s">(</span><span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="s">)</span> <span class="s">{</span> 162 <span class="i">$BitVector</span> = <span class="i">new</span> <span class="i">BitVector</span><span class="s">(</span><span class="i">$LargestVertexIndex</span><span class="s">)</span><span class="sc">;</span> 163 <span class="i">@BitNums</span> = <span class="k">map</span> <span class="s">{</span> <span class="i">$VertexIDsToIndicesRef</span>->{<span class="i">$_</span>} <span class="s">}</span> <span class="i">$CyclicPath</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 164 <span class="i">$BitVector</span><span class="i">->SetBits</span><span class="s">(</span><span class="i">@BitNums</span><span class="s">)</span><span class="sc">;</span> 165 <span class="k">push</span> <span class="i">@CyclicPathBitVectors</span><span class="cm">,</span> <span class="i">$BitVector</span><span class="sc">;</span> 166 167 <span class="i">$BitVector</span> = <span class="i">new</span> <span class="i">BitVector</span><span class="s">(</span><span class="i">$LargestEdgeIDIndex</span><span class="s">)</span><span class="sc">;</span> 168 <span class="i">@BitNums</span> = <span class="k">map</span> <span class="s">{</span> <span class="i">$EdgeIDsToIndicesRef</span>->{<span class="i">$_</span>} <span class="s">}</span> <span class="i">$This</span><span class="i">->_GetPathEdgeIDs</span><span class="s">(</span><span class="i">$CyclicPath</span><span class="s">)</span><span class="sc">;</span> 169 <span class="i">$BitVector</span><span class="i">->SetBits</span><span class="s">(</span><span class="i">@BitNums</span><span class="s">)</span><span class="sc">;</span> 170 <span class="k">push</span> <span class="i">@CyclicPathEdgeIDsBitVectors</span><span class="cm">,</span> <span class="i">$BitVector</span><span class="sc">;</span> 171 <span class="s">}</span> 172 173 <span class="c"># First smallest cyclic path always ends up as an independent cyclic path...</span> 174 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}}<span class="cm">,</span> <span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}[<span class="n">0</span>]<span class="sc">;</span> 175 176 <span class="c"># Retrieve other independent cyclic paths...</span> 177 <span class="k">my</span><span class="s">(</span><span class="i">$CurrentIndex</span><span class="cm">,</span> <span class="i">$PreviousIndex</span><span class="cm">,</span> <span class="i">$CurrentCyclicPath</span><span class="cm">,</span> <span class="i">$PreviousCyclicPath</span><span class="cm">,</span> <span class="i">$CurrentPathLength</span><span class="cm">,</span> <span class="i">$PreviousPathLength</span><span class="cm">,</span> <span class="i">$CurrentBitVector</span><span class="cm">,</span> <span class="i">$PreviousBitVector</span><span class="cm">,</span> <span class="i">$CurrentAndPreviousBitVectpor</span><span class="cm">,</span> <span class="i">$AllPreviousSmallerPathsBitVector</span><span class="cm">,</span> <span class="i">$AllPreviousSmallerPathsEdgeIDsBitVector</span><span class="cm">,</span> <span class="i">$CurrentEdgeIDsBitVector</span><span class="cm">,</span> <span class="i">$AndBitVector</span><span class="cm">,</span> <span class="i">%SmallerPathAlreadyAdded</span><span class="cm">,</span> <span class="i">%SkipPath</span><span class="s">)</span><span class="sc">;</span> 178 179 <span class="i">%SkipPath</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 180 <span class="i">%SmallerPathAlreadyAdded</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 181 <span class="i">$AllPreviousSmallerPathsBitVector</span> = <span class="i">new</span> <span class="i">BitVector</span><span class="s">(</span><span class="i">$LargestVertexIndex</span><span class="s">)</span><span class="sc">;</span> 182 <span class="i">$AllPreviousSmallerPathsEdgeIDsBitVector</span> = <span class="i">new</span> <span class="i">BitVector</span><span class="s">(</span><span class="i">$LargestEdgeIDIndex</span><span class="s">)</span><span class="sc">;</span> 183 184 <span class="j">CURRENT:</span> <span class="k">for</span> <span class="i">$CurrentIndex</span> <span class="s">(</span><span class="n">1</span> .. <span class="i">$#</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="s">)</span> <span class="s">{</span> 185 <span class="k">if</span> <span class="s">(</span><span class="k">exists</span> <span class="i">$SkipPath</span>{<span class="i">$CurrentIndex</span>}<span class="s">)</span> <span class="s">{</span> 186 <span class="k">next</span> <span class="j">CURRENT</span><span class="sc">;</span> 187 <span class="s">}</span> 188 <span class="i">$CurrentCyclicPath</span> = <span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}[<span class="i">$CurrentIndex</span>]<span class="sc">;</span> 189 <span class="i">$CurrentBitVector</span> = <span class="i">$CyclicPathBitVectors</span>[<span class="i">$CurrentIndex</span>]<span class="sc">;</span> 190 <span class="i">$CurrentPathLength</span> = <span class="i">$CurrentCyclicPath</span><span class="i">->GetLength</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 191 192 <span class="j">PREVIOUS:</span> <span class="k">for</span> <span class="i">$PreviousIndex</span> <span class="s">(</span><span class="n">0</span> .. <span class="s">(</span><span class="i">$CurrentIndex</span> - <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 193 <span class="k">if</span> <span class="s">(</span><span class="k">exists</span> <span class="i">$SkipPath</span>{<span class="i">$PreviousIndex</span>}<span class="s">)</span> <span class="s">{</span> 194 <span class="k">next</span> <span class="j">PREVIOUS</span><span class="sc">;</span> 195 <span class="s">}</span> 196 <span class="i">$PreviousCyclicPath</span> = <span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}[<span class="i">$PreviousIndex</span>]<span class="sc">;</span> 197 <span class="i">$PreviousBitVector</span> = <span class="i">$CyclicPathBitVectors</span>[<span class="i">$PreviousIndex</span>]<span class="sc">;</span> 198 199 <span class="c"># Is previous path a subset of current path?</span> 200 <span class="i">$CurrentAndPreviousBitVectpor</span> = <span class="i">$PreviousBitVector</span> & <span class="i">$CurrentBitVector</span><span class="sc">;</span> 201 <span class="k">if</span> <span class="s">(</span><span class="i">$PreviousBitVector</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span> == <span class="i">$CurrentAndPreviousBitVectpor</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 202 <span class="c"># Current path doesn't qualify an independent path...</span> 203 <span class="i">$SkipPath</span>{<span class="i">$CurrentIndex</span>} = <span class="n">1</span><span class="sc">;</span> 204 <span class="k">next</span> <span class="j">CURRENT</span><span class="sc">;</span> 205 <span class="s">}</span> 206 207 <span class="i">$PreviousPathLength</span> = <span class="i">$PreviousCyclicPath</span><span class="i">->GetLength</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 208 <span class="k">if</span> <span class="s">(</span><span class="i">$PreviousPathLength</span> < <span class="i">$CurrentPathLength</span><span class="s">)</span> <span class="s">{</span> 209 <span class="c"># Mark cycle vertices seen in cyclic paths with length smaller than current path...</span> 210 <span class="k">if</span> <span class="s">(</span>! <span class="k">exists</span> <span class="i">$SmallerPathAlreadyAdded</span>{<span class="i">$PreviousIndex</span>}<span class="s">)</span> <span class="s">{</span> 211 <span class="i">$SmallerPathAlreadyAdded</span>{<span class="i">$PreviousIndex</span>} = <span class="n">1</span><span class="sc">;</span> 212 <span class="i">$AllPreviousSmallerPathsBitVector</span> = <span class="i">$AllPreviousSmallerPathsBitVector</span> | <span class="i">$PreviousBitVector</span><span class="sc">;</span> 213 <span class="i">$AllPreviousSmallerPathsEdgeIDsBitVector</span> = <span class="i">$AllPreviousSmallerPathsEdgeIDsBitVector</span> | <span class="i">$CyclicPathEdgeIDsBitVectors</span>[<span class="i">$PreviousIndex</span>]<span class="sc">;</span> 214 <span class="s">}</span> 215 <span class="s">}</span> 216 <span class="s">}</span> 217 <span class="k">if</span> <span class="s">(</span><span class="i">$AllPreviousSmallerPathsBitVector</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 218 <span class="c"># Is current path a linear combination of smaller paths?</span> 219 <span class="i">$AndBitVector</span> = <span class="i">$AllPreviousSmallerPathsBitVector</span> & <span class="i">$CurrentBitVector</span><span class="sc">;</span> 220 <span class="k">if</span> <span class="s">(</span><span class="i">$CurrentBitVector</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span> == <span class="i">$AndBitVector</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 221 <span class="c"># Are all edges in the current path already present in smaller paths?</span> 222 <span class="i">$CurrentEdgeIDsBitVector</span> = <span class="i">$CyclicPathEdgeIDsBitVectors</span>[<span class="i">$CurrentIndex</span>]<span class="sc">;</span> 223 <span class="i">$AndBitVector</span> = <span class="i">$AllPreviousSmallerPathsEdgeIDsBitVector</span> & <span class="i">$CurrentEdgeIDsBitVector</span><span class="sc">;</span> 224 225 <span class="k">if</span> <span class="s">(</span><span class="i">$CurrentEdgeIDsBitVector</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span> == <span class="i">$AndBitVector</span><span class="i">->GetNumOfSetBits</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 226 <span class="c"># Current path doesn't qualify an independent path...</span> 227 <span class="i">$SkipPath</span>{<span class="i">$CurrentIndex</span>} = <span class="n">1</span><span class="sc">;</span> 228 <span class="k">next</span> <span class="j">CURRENT</span><span class="sc">;</span> 229 <span class="s">}</span> 230 <span class="s">}</span> 231 <span class="s">}</span> 232 <span class="c"># It's an independent cyclic path...</span> 233 <span class="k">push</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}}<span class="cm">,</span> <span class="i">$CurrentCyclicPath</span><span class="sc">;</span> 234 <span class="s">}</span> 235 <span class="k">return</span> <span class="i">$This</span><span class="sc">;</span> 236 <span class="s">}</span> 237 238 <span class="c"># Setup a VertexID to index map...</span> 239 <span class="c">#</span> <a name="_SetupVertexIDsToIndicesMap-"></a> 240 <span class="k">sub </span><span class="m">_SetupVertexIDsToIndicesMap</span> <span class="s">{</span> 241 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$PathGraph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 242 <span class="k">my</span><span class="s">(</span><span class="i">$LargestVertexIndex</span><span class="cm">,</span> <span class="i">@VertexIDs</span><span class="cm">,</span> <span class="i">%VertexIDsMap</span><span class="s">)</span><span class="sc">;</span> 243 244 <span class="i">%VertexIDsMap</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> <span class="i">@VertexIDs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> <span class="i">$LargestVertexIndex</span> = <span class="n">0</span><span class="sc">;</span> 245 246 <span class="i">@VertexIDs</span> = <span class="i">$PathGraph</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 247 <span class="k">if</span> <span class="s">(</span>! <span class="i">@VertexIDs</span><span class="s">)</span> <span class="s">{</span> 248 <span class="k">return</span> <span class="s">(</span>\<span class="i">%VertexIDsMap</span><span class="cm">,</span> <span class="i">$LargestVertexIndex</span><span class="s">)</span><span class="sc">;</span> 249 <span class="s">}</span> 250 <span class="i">@VertexIDsMap</span>{ <span class="i">@VertexIDs</span> } = <span class="s">(</span><span class="n">0</span> .. <span class="i">$#VertexIDs</span><span class="s">)</span><span class="sc">;</span> 251 <span class="i">$LargestVertexIndex</span> = <span class="k">scalar</span> <span class="i">@VertexIDs</span><span class="sc">;</span> 252 253 <span class="k">return</span> <span class="s">(</span>\<span class="i">%VertexIDsMap</span><span class="cm">,</span> <span class="i">$LargestVertexIndex</span><span class="s">)</span><span class="sc">;</span> 254 <span class="s">}</span> 255 256 <span class="c"># Setup a Edge to index map using paths associated to egdes in an intial</span> 257 <span class="c"># path graph...</span> 258 <span class="c">#</span> <a name="_SetupEdgeIDsToIndicesMap-"></a> 259 <span class="k">sub </span><span class="m">_SetupEdgeIDsToIndicesMap</span> <span class="s">{</span> 260 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$PathGraph</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 261 <span class="k">my</span><span class="s">(</span><span class="i">$Path</span><span class="cm">,</span> <span class="i">$LargestEdgeIndex</span><span class="cm">,</span> <span class="i">@EdgeIDs</span><span class="cm">,</span> <span class="i">%EdgeIDsMap</span><span class="s">)</span><span class="sc">;</span> 262 263 <span class="i">%EdgeIDsMap</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> <span class="i">@EdgeIDs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> <span class="i">$LargestEdgeIndex</span> = <span class="n">0</span><span class="sc">;</span> 264 265 <span class="i">@EdgeIDs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 266 <span class="k">for</span> <span class="i">$Path</span> <span class="s">(</span><span class="i">$PathGraph</span><span class="i">->GetPaths</span><span class="s">(</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 267 <span class="k">push</span> <span class="i">@EdgeIDs</span><span class="cm">,</span> <span class="i">$This</span><span class="i">->_GetPathEdgeIDs</span><span class="s">(</span><span class="i">$Path</span><span class="s">)</span><span class="sc">;</span> 268 <span class="s">}</span> 269 270 <span class="k">if</span> <span class="s">(</span>! <span class="i">@EdgeIDs</span><span class="s">)</span> <span class="s">{</span> 271 <span class="k">return</span> <span class="s">(</span>\<span class="i">%EdgeIDsMap</span><span class="cm">,</span> <span class="i">$LargestEdgeIndex</span><span class="s">)</span><span class="sc">;</span> 272 <span class="s">}</span> 273 274 <span class="i">@EdgeIDsMap</span>{ <span class="i">@EdgeIDs</span> } = <span class="s">(</span><span class="n">0</span> .. <span class="i">$#EdgeIDs</span><span class="s">)</span><span class="sc">;</span> 275 <span class="i">$LargestEdgeIndex</span> = <span class="k">scalar</span> <span class="i">@EdgeIDs</span><span class="sc">;</span> 276 277 <span class="k">return</span> <span class="s">(</span>\<span class="i">%EdgeIDsMap</span><span class="cm">,</span> <span class="i">$LargestEdgeIndex</span><span class="s">)</span><span class="sc">;</span> 278 <span class="s">}</span> 279 280 <span class="c"># Get path edge IDs or number of edges. The edge IDs are generated from</span> 281 <span class="c"># edge vertices and correpond to VertexID1-VertexID2 where VertexID1 <=</span> 282 <span class="c"># VertexID2.</span> 283 <span class="c">#</span> <a name="_GetPathEdgeIDs-"></a> 284 <span class="k">sub </span><span class="m">_GetPathEdgeIDs</span> <span class="s">{</span> 285 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="cm">,</span> <span class="i">$Path</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 286 <span class="k">my</span><span class="s">(</span><span class="i">@EdgesVertexIDs</span><span class="cm">,</span> <span class="i">@EdgeIDs</span><span class="s">)</span><span class="sc">;</span> 287 288 <span class="i">@EdgesVertexIDs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> <span class="i">@EdgeIDs</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 289 <span class="i">@EdgesVertexIDs</span> = <span class="i">$Path</span><span class="i">->GetEdges</span><span class="s">(</span><span class="s">)</span><span class="sc">;</span> 290 <span class="k">if</span> <span class="s">(</span>!<span class="i">@EdgesVertexIDs</span><span class="s">)</span> <span class="s">{</span> 291 <span class="k">return</span> <span class="k">wantarray</span> ? <span class="i">@EdgeIDs</span> <span class="co">:</span> <span class="s">(</span><span class="k">scalar</span> <span class="i">@EdgeIDs</span><span class="s">)</span><span class="sc">;</span> 292 <span class="s">}</span> 293 294 <span class="c"># Set up edge IDs...</span> 295 <span class="k">my</span><span class="s">(</span><span class="i">$Index</span><span class="cm">,</span> <span class="i">$VertexID1</span><span class="cm">,</span> <span class="i">$VertexID2</span><span class="cm">,</span> <span class="i">$EdgeID</span><span class="s">)</span><span class="sc">;</span> 296 297 <span class="k">for</span> <span class="s">(</span><span class="i">$Index</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$Index</span> < <span class="i">$#EdgesVertexIDs</span><span class="sc">;</span> <span class="i">$Index</span> += <span class="n">2</span><span class="s">)</span> <span class="s">{</span> 298 <span class="i">$VertexID1</span> = <span class="i">$EdgesVertexIDs</span>[<span class="i">$Index</span>]<span class="sc">;</span> <span class="i">$VertexID2</span> = <span class="i">$EdgesVertexIDs</span>[<span class="i">$Index</span> + <span class="n">1</span>]<span class="sc">;</span> 299 <span class="i">$EdgeID</span> = <span class="s">(</span><span class="i">$VertexID1</span> <= <span class="i">$VertexID2</span><span class="s">)</span> ? <span class="q">"$VertexID1-$VertexID2"</span> <span class="co">:</span> <span class="q">"$VertexID2-$VertexID1"</span><span class="sc">;</span> 300 <span class="k">push</span> <span class="i">@EdgeIDs</span><span class="cm">,</span> <span class="i">$EdgeID</span><span class="sc">;</span> 301 <span class="s">}</span> 302 303 <span class="k">return</span> <span class="k">wantarray</span> ? <span class="i">@EdgeIDs</span> <span class="co">:</span> <span class="s">(</span><span class="k">scalar</span> <span class="i">@EdgeIDs</span><span class="s">)</span><span class="sc">;</span> 304 <span class="s">}</span> 305 306 <span class="c"># Return an array containing references to cyclic paths or number of cylic paths...</span> 307 <span class="c">#</span> <a name="GetAllCyclicPaths-"></a> 308 <span class="k">sub </span><span class="m">GetAllCyclicPaths</span> <span class="s">{</span> 309 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 310 311 <span class="k">return</span> <span class="k">wantarray</span> ? <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}} <span class="co">:</span> <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="sc">;</span> 312 <span class="s">}</span> 313 314 <span class="c"># Get cyclic paths which are independent. In otherwords, cycles which don't contain any other</span> 315 <span class="c"># cycle as their subset...</span> 316 <span class="c">#</span> <a name="GetIndependentCyclicPaths-"></a> 317 <span class="k">sub </span><span class="m">GetIndependentCyclicPaths</span> <span class="s">{</span> 318 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 319 320 <span class="k">return</span> <span class="k">wantarray</span> ? <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}} <span class="co">:</span> <span class="k">scalar</span> <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}}<span class="sc">;</span> 321 <span class="s">}</span> 322 323 <span class="c"># Return a string containg data for CyclesDetection object...</span> <a name="StringifyCyclesDetection-"></a> 324 <span class="k">sub </span><span class="m">StringifyCyclesDetection</span> <span class="s">{</span> 325 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 326 <span class="k">my</span><span class="s">(</span><span class="i">$CyclesDetectionString</span><span class="cm">,</span> <span class="i">$CyclesCount</span><span class="cm">,</span> <span class="i">$CyclicPath</span><span class="s">)</span><span class="sc">;</span> 327 328 <span class="i">$CyclesCount</span> = <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="sc">;</span> 329 <span class="i">$CyclesDetectionString</span> = <span class="q">"AllCycles: Count - $CyclesCount"</span><span class="sc">;</span> 330 <span class="k">for</span> <span class="i">$CyclicPath</span> <span class="s">(</span><span class="i">@</span>{<span class="i">$This</span>->{<span class="w">AllCyclicPaths</span>}}<span class="s">)</span> <span class="s">{</span> 331 <span class="i">$CyclesDetectionString</span> .= <span class="q">"; Cycle: "</span> . <span class="k">join</span><span class="s">(</span><span class="q">'-'</span><span class="cm">,</span> <span class="i">$CyclicPath</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span> 332 <span class="s">}</span> 333 334 <span class="i">$CyclesCount</span> = <span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}}<span class="sc">;</span> 335 <span class="i">$CyclesDetectionString</span> .= <span class="q">"\nIndependentCycles: Count - $CyclesCount"</span><span class="sc">;</span> 336 <span class="k">for</span> <span class="i">$CyclicPath</span> <span class="s">(</span><span class="i">@</span>{<span class="i">$This</span>->{<span class="w">IndependentCyclicPaths</span>}}<span class="s">)</span> <span class="s">{</span> 337 <span class="i">$CyclesDetectionString</span> .= <span class="q">"; Cycle: "</span> . <span class="k">join</span><span class="s">(</span><span class="q">'-'</span><span class="cm">,</span> <span class="i">$CyclicPath</span><span class="i">->GetVertices</span><span class="s">(</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span> 338 <span class="s">}</span> 339 340 <span class="k">return</span> <span class="i">$CyclesDetectionString</span><span class="sc">;</span> 341 <span class="s">}</span> 342 343 <span class="c"># Return a reference to new cycle detection object...</span> <a name="Copy-"></a> 344 <span class="k">sub </span><span class="m">Copy</span> <span class="s">{</span> 345 <span class="k">my</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 346 <span class="k">my</span><span class="s">(</span><span class="i">$NewCyclesDetection</span><span class="s">)</span><span class="sc">;</span> 347 348 <span class="i">$NewCyclesDetection</span> = <span class="i">Storable::dclone</span><span class="s">(</span><span class="i">$This</span><span class="s">)</span><span class="sc">;</span> 349 350 <span class="k">return</span> <span class="i">$NewCyclesDetection</span><span class="sc">;</span> 351 <span class="s">}</span> 352 <a name="EOF-"></a></pre> <p> </p> <br /> <center> <img src="../../../images/h2o2.png"> </center> </body> </html>