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annotate war/scripts/sti/kruskal.js @ 86:ed444173aef0 trimmed_data

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author Sebastian Kruse <skruse@mpiwg-berlin.mpg.de>
date Thu, 07 Mar 2013 14:47:36 +0100
parents cf06b77a8bbd
children
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3
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1 var infinity = 100000000000; // !!! beware, not allowable for many applications
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3 function Edge2(a, b, w) { this.v1=a; this.v2=b; this.wt=w; }
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4
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5 function setEdgeAdjMatrix(i, j, w)
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6 { if(j > i) { var t=i; i=j; j=t; }//swap so that i >= j
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7 this.matrix[i][j] = w;
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8 }
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11 function randomAdjMatrix(pr) // allocate random edges with probability 'pr'; LA
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12 { var i, j;
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13 for(i=0; i < this.Vertices; i++)
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14 { for(j=0; j < i; j++)
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15 { if(Math.random() <= pr)//LAllison, roll dice
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16 this.setEdge(i, j, 1+Math.round(Math.random()*8)); // wt in [1..9]
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17 } } }//randomAdjMatrix
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20 function edgeWeightAdjMatrix(i,j)
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21 { return i >= j ? this.matrix[i][j] : this.matrix[j][i]; }
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23 function adjacentAdjMatrix(i, j)
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24 { return this.edgeWeight(i,j) < infinity; }
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26
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27 function AdjMatrix(Vrtcs) // constructor for a Graph as an Adjacency Matrix
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28 { this.Vertices = Vrtcs; // Vertices [0..Vrtcs-1]
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29 this.edgeWeight = edgeWeightAdjMatrix; // These functions
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30 this.adjacent = adjacentAdjMatrix; // and values
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31 this.random = randomAdjMatrix;
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32 this.setEdge = setEdgeAdjMatrix;
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34 this.matrix = new Array(Vrtcs); // the Graph representation...
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35 var i, j;
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36 for(i=0; i < Vrtcs; i++) // undirected graph so...
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37 { this.matrix[i] = new Array(i+1); // symmetric => triangular !!!
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38 for(j=0; j <= i; j++)
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39 this.setEdge(i, j, infinity); // no edges, yet
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40 }
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41 }//AdjMatrix
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42
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43 //-----------------------------------------------------------------------------
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44
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45 function AdjListCell(vert, w, next)
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46 { this.v = vert; this.wt = w; this.tl = next; }
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47
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48 function AdjListFromAdjMatrix(GbyMatrix)
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49 { var v1, v2;
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50 this.Vertices = GbyMatrix.Vertices;
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51
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52 for(v1=0; v1 < this.Vertices; v1++)
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53 { this.vertex[v1] = null; // clear
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54
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55 for(v2=this.Vertices-1; v2 >= v1; v2--) // v1 <= v2
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56 { if(GbyMatrix.adjacent(v1, v2))
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57 { var wt = GbyMatrix.edgeWeight(v1, v2);
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58 this.vertex[v1] = new AdjListCell(v2, wt, this.vertex[v1]);
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59 }
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60 }
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61 }
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62 }//AdjListFromAdjMatrix
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63
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64 function AdjList(Vrtcs) // Constructor for a Graph by Adjacency Lists C
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65 { this.Vertices = Vrtcs; // o
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66 this.fromAdjMatrix = AdjListFromAdjMatrix; // m
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67 // p
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68 this.vertex = new Array(Vrtcs); // set up the adjacency lists .
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69 var i; // S
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70 for(i=0; i < Vrtcs; i++) this.vertex[i]=null; // c
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71 }//AdjList i
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72
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73 //-----------------------------------------------------------------------------
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74
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75 function Prim(G)
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76 // Post: T[] is a minimum spanning tree of G and
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77 // T[i-1] is the edge linking Vertex i into the tree
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78 // Time complexity is O(|V|**2)
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79 { var T = new Array(G.Vertices-1);
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80 var i;
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81 var done = new Array(G.Vertices);
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82
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83 done[0] = true; // initially T=<{0},{ }>
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84 for(i = 1; i < G.Vertices; i++)
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85 { T[i-1] = new Edge2(0, i, G.edgeWeight(0,i));
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86 done[i]=false;
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87 }
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88
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89 var dontCare;
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90 for(dontCare = 1; dontCare < G.Vertices; dontCare++)// |V|-1 times... L
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91 // Invariant: T is a min' spanning sub-Tree of vertices in done A
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92 { // find the undone vertex that is closest to the Spanning (sub-)Tree l
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93 var minDist = infinity, closest = -1; // l
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94 for(i = 1; i < G.Vertices; i++) // i
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95 if(! done[i] && T[i-1].wt <= minDist) // s
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96 { minDist = T[i-1].wt; closest = i; } // o
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97 done[closest] = true; // n
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98
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99 for(i=1; i < G.Vertices; i++) // recompute undone proximities to T
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100 if(! done[i])
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101 { var Gci = G.edgeWeight(closest, i);
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102 if(Gci < T[i-1].wt)
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103 { T[i-1].wt = Gci;
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104 T[i-1].v1 = closest;
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105 } } }
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106
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107 return T;
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108 }//Prim
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109
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110 // ----------------------------------------------------------------------------
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111
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112 function PartitionMerge(s1, s2)
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113 // merge the smaller of subsets s1 and s2 into the larger of them. M
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114 { var drop, keep; // o
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115 if(this.subset[s1].nElts < this.subset[s2].nElts) // drop the smaller n
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116 { drop=s1; keep=s2; } // a
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117 else // s
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118 { drop=s2; keep=s1; } // h
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119
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120 var dropElt = this.subset[drop].firstElt; // each element in smaller subset
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121 var done=false;
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122 while(! done)
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123 { this.elt[dropElt].setNumber = keep; // move the element to larger subset
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124 if( this.elt[dropElt].nextElt < 0)
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125 done = true;
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126 else
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127 dropElt = this.elt[dropElt].nextElt;
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128 }//end while
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129
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130 this.elt[dropElt].nextElt = this.subset[keep].firstElt; // join lists
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131 this.subset[keep].firstElt = this.subset[drop].firstElt;
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132 this.subset[keep].nElts += this.subset[drop].nElts;
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133
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134 this.subset[drop].firstElt = -1; // clear smaller subset
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135 this.subset[drop].nElts = 0;
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136
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137 this.size --; // one less subset in the partition
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138 }//PartitionMerge
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139
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140
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141 function PartitionEltCell(sn, nxt) { this.setNumber = sn; this.nextElt = nxt; }
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142
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143 function PartitionSetCell(ne, fst) { this.nElts = ne; this.firstElt = fst; }
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144
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145
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146 function PartitionSingletons() // make {{0}, {1}, {2}, ...}
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147 { var i;
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148 this.size = (this.elt).length; // # of subsets in the partition
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149 for(i=0; i < this.size; i++)
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150 { this.elt[i] = new PartitionEltCell(i, -1);
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151 this.subset[i] = new PartitionSetCell(1, i); // i.e. i is in {i}
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152 } }
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153
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154
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155 function Partition(N) // A
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156 { this.elt = new Array(N); // elements -> subsets l
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157 this.subset = new Array(N); // subsets -> elements l
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158 // i
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159 this.singletons = PartitionSingletons; // s
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160 this.merge = PartitionMerge; // o
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161 }//Partition constructor n
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162
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163
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164 function upHeap(e) // see PriorityQ L
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165 // add e to the (smallest on top) heap, arr[1..size] A
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166 // PRE: arr[1..size] is a (smallest at top) heap / priority Q l
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167 // POST: arr[1..size] is a (bigger) heap, with e added l
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168 { this.size++; // i
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169 var child = this.size, parent; // s
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170 while(child > 1)//i.e. not top of heap // o
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171 { parent = Math.floor(child / 2); // n
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172
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173 if(this.arr[parent].wt > e.wt)
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174 this.arr[child] = this.arr[parent]; // move parent down
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175 else
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176 break; // found a place for e
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177 child = parent;
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178 }
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179
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180 // either child==1, i.e. parentless, or parent is less than or eq to e
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181 this.arr[child] = e;
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182 }//upHeap, L.Allison, Comp Sci and Software Engineering, Monash University
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183
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184
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185 function downHeap(e)
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186 // add e to the (smallest on top) heap, arr[2..size]
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187 // PRE: arr[2..size] is a heap
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188 // POST: arr[1..size] is a heap
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189 { var parent = 1, child; // A
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190 while(2*parent <= this.size) // U
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191 { child = 2*parent; // left child is 2*parent, right is 2*parent+1 // S
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192 // T
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193 if(child < this.size && this.arr[child+1].wt < this.arr[child].wt) // R
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194 child++; // right child is smaller then left child // A
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195 // L
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196 if(this.arr[child].wt < e.wt) // I
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197 this.arr[parent] = this.arr[child]; // move the child up // I
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198 else // A
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199 break; // found a place for e
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200 parent = child;
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201 }
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202
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203 // either parent childless or child(ren) of parent are greater or eq to e
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204 this.arr[parent] = e;
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205 }//downHeap, L.Allison, Comp Sci and Software Engineering, Monash University
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206
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207
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208 function topHeap()
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209 // PRE: this.size > 0
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210 { var ans = this.arr[1]; // C
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211 this.size--; // S
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212 if(this.size <= 0) return ans; // S
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213 //else // E
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214 this.downHeap(this.arr[this.size+1]);
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215 return ans;
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216 }
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217
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218
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219 function PriorityQ() // A
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220 { this.arr = new Array(); // NB. never use arr[0] l
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221 this.size = 0; // so far l
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222 // i
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223 this.pushq = upHeap; // s
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224 this.popq = topHeap; this.downHeap = downHeap; // o
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225 }//constructor n
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226
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227
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228 function Kruskal(G) // L
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229 // G is a graph implemented by adjacency lists! A
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230 // return a minimum spanning tree, T l
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231 { var i; // l
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232 var T = new Array(); // to be the min' spanning tree i
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233 // s
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234 var Q = new PriorityQ(); // o
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235 // n
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236 for(i=0; i < G.Vertices; i++)//first make a PriorityQ of all the edges of G
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237 { var Gi = G.vertex[i];
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238 while(Gi != null) // i.e. for each edge {i,v}
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239 { Q.pushq(new Edge2(i, Gi.v, Gi.wt));
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240 Gi = Gi.tl;
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241 }
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242 }
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243
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244 var n = 0; // Computer Science
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245 var P = new Partition(G.Vertices); // M
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246 P.singletons(); // o
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247 while(P.size > 1) // the min' spanning tree algorithm proper n
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248 { if(Q.size <= 0) // G disconnected a
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249 break; // s
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250 // h
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251 var e = Q.popq(); // shortest edge
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252 if(P.elt[e.v1].setNumber != P.elt[e.v2].setNumber) // U
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253 { T[n] = e; n++; // n
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254 P.merge(P.elt[e.v1].setNumber, P.elt[e.v2].setNumber); // i
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255 }
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256 }
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257
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258 return T;
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259 }//Kruskal, NB. can work on adjacency matrix, but is best on sparse graphs.