1 | #region License Information
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2 |
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3 | /* HeuristicLab
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4 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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5 | *
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6 | * This file is part of HeuristicLab.
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7 | *
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8 | * HeuristicLab is free software: you can redistribute it and/or modify
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9 | * it under the terms of the GNU General Public License as published by
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10 | * the Free Software Foundation, either version 3 of the License, or
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11 | * (at your option) any later version.
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12 | *
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13 | * HeuristicLab is distributed in the hope that it will be useful,
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14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 | * GNU General Public License for more details.
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17 | *
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18 | * You should have received a copy of the GNU General Public License
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19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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20 | */
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21 |
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22 | #endregion License Information
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23 |
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24 | using System;
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25 | using System.Collections.Generic;
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26 | using System.Diagnostics;
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27 | using System.Globalization;
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28 | using System.Linq;
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29 | using HeuristicLab.Common;
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30 | using HeuristicLab.Core;
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31 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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32 | using HeuristicLab.Optimization.Operators;
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33 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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34 |
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35 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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36 |
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37 | [StorableClass]
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38 | [Item("SymbolicExpressionTreeBottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
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39 | public class SymbolicExpressionTreeBottomUpSimilarityCalculator : SolutionSimilarityCalculator {
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40 | private readonly HashSet<string> commutativeSymbols = new HashSet<string> { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };
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41 |
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42 | public SymbolicExpressionTreeBottomUpSimilarityCalculator() {
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43 | }
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44 |
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45 | protected override bool IsCommutative { get { return true; } }
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46 |
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47 | public bool MatchVariableWeights { get; set; }
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48 | public bool MatchConstantValues { get; set; }
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49 |
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50 | [StorableConstructor]
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51 | protected SymbolicExpressionTreeBottomUpSimilarityCalculator(bool deserializing)
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52 | : base(deserializing) {
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53 | }
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54 |
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55 | protected SymbolicExpressionTreeBottomUpSimilarityCalculator(SymbolicExpressionTreeBottomUpSimilarityCalculator original, Cloner cloner)
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56 | : base(original, cloner) {
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57 | }
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58 |
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59 | public override IDeepCloneable Clone(Cloner cloner) {
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60 | return new SymbolicExpressionTreeBottomUpSimilarityCalculator(this, cloner);
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61 | }
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62 |
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63 | public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
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64 | if (t1 == t2)
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65 | return 1;
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66 |
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67 | var map = ComputeBottomUpMapping(t1.Root, t2.Root);
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68 | return 2.0 * map.Count / (t1.Length + t2.Length);
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69 | }
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70 |
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71 | public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
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72 | if (leftSolution == rightSolution)
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73 | return 1.0;
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74 |
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75 | var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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76 | var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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77 |
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78 | if (t1 == null || t2 == null)
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79 | throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
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80 |
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81 | var similarity = CalculateSimilarity(t1, t2);
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82 | if (similarity > 1.0)
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83 | throw new Exception("Similarity value cannot be greater than 1");
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84 |
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85 | return similarity;
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86 | }
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87 |
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88 | public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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89 | var comparer = new SymbolicExpressionTreeNodeComparer(); // use a node comparer because it's faster than calling node.ToString() (strings are expensive) and comparing strings
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90 | var compactedGraph = Compact(n1, n2);
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91 |
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92 | var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
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93 | var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
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94 |
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95 | // visit nodes in order of decreasing height to ensure correct mapping
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96 | var nodes1 = n1.IterateNodesPrefix().OrderByDescending(x => x.GetDepth()).ToList();
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97 | var nodes2 = n2.IterateNodesPrefix().ToList();
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98 | for (int i = 0; i < nodes1.Count; ++i) {
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99 | var v = nodes1[i];
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100 | if (forwardMap.ContainsKey(v))
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101 | continue;
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102 | var kv = compactedGraph[v];
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103 | ISymbolicExpressionTreeNode w = null;
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104 | for (int j = 0; j < nodes2.Count; ++j) {
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105 | var t = nodes2[j];
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106 | if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
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107 | continue;
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108 | w = t;
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109 | break;
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110 | }
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111 | if (w == null) continue;
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112 |
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113 | // at this point we know that v and w are isomorphic, however, the mapping cannot be done directly
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114 | // (as in the paper) because the trees are unordered (subtree order might differ). the solution is
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115 | // to sort subtrees from under commutative labels (this will work because the subtrees are isomorphic!)
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116 | // while iterating over the two subtrees
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117 | var vv = IterateBreadthOrdered(v, comparer).ToList();
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118 | var ww = IterateBreadthOrdered(w, comparer).ToList();
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119 | int len = Math.Min(vv.Count, ww.Count);
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120 | for (int j = 0; j < len; ++j) {
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121 | var s = vv[j];
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122 | var t = ww[j];
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123 | Debug.Assert(!reverseMap.ContainsKey(t));
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124 |
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125 | forwardMap[s] = t;
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126 | reverseMap[t] = s;
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127 | }
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128 | }
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129 |
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130 | return forwardMap;
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131 | }
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132 |
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133 | /// <summary>
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134 | /// Creates a compact representation of the two trees as a directed acyclic graph
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135 | /// </summary>
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136 | /// <param name="n1">The root of the first tree</param>
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137 | /// <param name="n2">The root of the second tree</param>
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138 | /// <returns>The compacted DAG representing the two trees</returns>
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139 | private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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140 | var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K
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141 | var labelMap = new Dictionary<string, GraphNode>(); // L
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142 | var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
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143 |
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144 | var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
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145 | var list = new List<GraphNode>();
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146 | var queue = new Queue<ISymbolicExpressionTreeNode>();
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147 |
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148 | foreach (var n in nodes) {
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149 | if (n.SubtreeCount == 0) {
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150 | var label = GetLabel(n);
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151 | if (!labelMap.ContainsKey(label)) {
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152 | var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
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153 | labelMap[z.Label] = z;
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154 | }
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155 | nodeMap[n] = labelMap[label];
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156 | queue.Enqueue(n);
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157 | } else {
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158 | childrenCount[n] = n.SubtreeCount;
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159 | }
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160 | }
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161 | while (queue.Any()) {
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162 | var n = queue.Dequeue();
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163 | if (n.SubtreeCount > 0) {
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164 | bool found = false;
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165 | var label = n.Symbol.Name;
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166 | var depth = n.GetDepth();
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167 |
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168 | bool sort = n.SubtreeCount > 1 && commutativeSymbols.Contains(label);
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169 | var nSubtrees = n.Subtrees.Select(x => nodeMap[x]).ToList();
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170 | if (sort) nSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
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171 |
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172 | for (int i = list.Count - 1; i >= 0; --i) {
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173 | var w = list[i];
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174 | if (!(n.SubtreeCount == w.SubtreeCount && label == w.Label && depth == w.Depth))
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175 | continue;
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176 |
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177 | // sort V and W when the symbol is commutative because we are dealing with unordered trees
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178 | var m = w.SymbolicExpressionTreeNode;
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179 | var mSubtrees = m.Subtrees.Select(x => nodeMap[x]).ToList();
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180 | if (sort) mSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
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181 |
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182 | found = nSubtrees.SequenceEqual(mSubtrees);
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183 | if (found) {
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184 | nodeMap[n] = w;
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185 | break;
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186 | }
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187 | }
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188 |
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189 | if (!found) {
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190 | var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };
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191 | list.Add(w);
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192 | nodeMap[n] = w;
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193 | }
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194 | }
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195 |
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196 | if (n == n1 || n == n2)
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197 | continue;
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198 |
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199 | var p = n.Parent;
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200 | if (p == null)
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201 | continue;
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202 |
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203 | childrenCount[p]--;
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204 |
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205 | if (childrenCount[p] == 0)
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206 | queue.Enqueue(p);
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207 | }
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208 |
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209 | return nodeMap;
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210 | }
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211 |
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212 | private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {
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213 | var list = new List<ISymbolicExpressionTreeNode> { node };
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214 | int i = 0;
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215 | while (i < list.Count) {
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216 | var n = list[i];
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217 | if (n.SubtreeCount > 0) {
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218 | var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;
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219 | list.AddRange(subtrees);
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220 | }
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221 | i++;
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222 | }
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223 | return list;
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224 | }
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225 |
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226 | private string GetLabel(ISymbolicExpressionTreeNode node) {
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227 | if (node.SubtreeCount > 0)
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228 | return node.Symbol.Name;
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229 |
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230 | var constant = node as ConstantTreeNode;
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231 | if (constant != null)
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232 | return MatchConstantValues ? constant.Value.ToString(CultureInfo.InvariantCulture) : node.Symbol.Name;
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233 |
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234 | var variable = node as VariableTreeNode;
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235 | if (variable != null)
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236 | return MatchVariableWeights ? variable.Weight + variable.VariableName : variable.VariableName;
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237 |
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238 | return node.ToString();
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239 | }
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240 |
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241 | private class GraphNode {
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242 | public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
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243 | public string Label;
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244 | public int Depth;
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245 | public int SubtreeCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }
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246 | }
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247 | }
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248 | } |
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