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{
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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 14 : Weighted Graphs"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 14.1 Page no: 681"
]
},
{
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"collapsed": false,
"input": [
" \n",
"class Edge:\n",
" def __init__(self,sv,dv,d): # constructor\n",
" self.srcVert = sv\n",
" self.destVert = dv\n",
" self.distance = d\n",
"\n",
"class PriorityQ:\n",
" def __init__(self):\n",
" # constructor\n",
" self.queArray = []\n",
" self.size = 0\n",
" def insert(self,item): # insert item in sorted order\n",
" self.queArray.append(item)\n",
" b = self.size\n",
" for j in range(self.size): # find place to insert\n",
" if( item.distance >= self.queArray[j].distance ):\n",
" b = j\n",
" break\n",
" for k in range(self.size-1,b-1,-1):#=self.size-1 k>=j k--) # move items up\n",
" self.queArray[k+1] = self.queArray[k]\n",
" self.queArray[b] = item\n",
" # insert item\n",
" self.size += 1\n",
"\n",
" def removeMin(self): # remove minimum item\n",
" self.size -= 1\n",
" return self.queArray[self.size] \n",
"\n",
" def removeN(self,n): # remove item at n\n",
" for j in range(n,self.size-1): # move items down\n",
" self.queArray[j] = self.queArray[j+1]\n",
" self.size -= 1\n",
"\n",
" def peekMin(self): # peek at minimum item\n",
" return self.self.queArray[self.size-1] \n",
"\n",
" def size(self): # return number of items\n",
" return self.size\n",
"\n",
" def isEmpty(self): # true if queue is empty\n",
" return (self.size==0) \n",
"\n",
" def peekN(self,n): # peek at item n\n",
" return self.queArray[n]\n",
"\n",
" def find(self,findDex): # find item with specified\n",
" # self.destVert value\n",
" for j in range(self.size-1):\n",
" if(self.queArray[j].destVert == findDex):\n",
" return j\n",
" return -1\n",
"\n",
"class Vertex:\n",
" def __init__(self,lab): # constructor\n",
" self.label = lab\n",
" self.isInTree = False\n",
"\n",
"class Graph:\n",
" def __init__(self):\n",
" self.vertexList = [] # adjacency matrix\n",
" self.adjMat = []\n",
" self.nVerts = 0\n",
" for j in range(20): # set adjacency\n",
" l = []\n",
" for k in range(20):\n",
" l.append(1000000)\n",
" self.adjMat.append(l)\n",
" self.thePQ = PriorityQ()\n",
" self.nTree = 0\n",
" self.currentVert = 0\n",
"\n",
" def addVertex(self,lab):\n",
" self.vertexList.append( Vertex(lab))\n",
" self.nVerts += 1\n",
"\n",
" def addEdge(self,start, end,weight):\n",
" self.adjMat[start][end] = weight\n",
" self.adjMat[end][start] = weight\n",
"\n",
"\n",
" def displayVertex(self,v):\n",
" print self.vertexList[v].label ,\n",
"\n",
" def mstw(self):\n",
" self.currentVert = 0 # minimum spanning tree\n",
" # start at 0\n",
" while(self.nTree < self.nVerts-1): # while not all verts in tree\n",
" # put self.currentVert in tree\n",
" self.vertexList[self.currentVert].isInTree = True\n",
" self.nTree += 1\n",
" # insert edges adjacent to self.currentVert into PQ\n",
" for j in range(self.nVerts): # for each vertex,\n",
" if(j==self.currentVert): # skip if its us\n",
" continue\n",
" if(self.vertexList[j].isInTree): # skip if in the tree\n",
" continue\n",
" self.distance = self.adjMat[self.currentVert][j]\n",
" if( self.distance == 1000000): # skip if no edge\n",
" continue\n",
" self.putInPQ(j, self.distance) # put it in PQ (maybe)\n",
" if(self.thePQ.size==0): # no vertices in PQ?\n",
" print 'GRAPH NOT CONNECTED',\n",
" return\n",
" # remove edge with minimum self.distance, from PQ\n",
" theEdge = self.thePQ.removeMin()\n",
" sourceVert = theEdge.srcVert\n",
" self.currentVert = theEdge.destVert\n",
" # display edge from source to current\n",
" print self.vertexList[sourceVert].label ,self.vertexList[self.currentVert].label, \" \",\n",
"\n",
" for j in range(self.nVerts): # unmark vertices\n",
" self.vertexList[j].isIsTree = False\n",
"\n",
" def putInPQ(self,newVert,newDist): # is there another edge with the same destination vertex?\n",
" queueIndex = self.thePQ.find(newVert)\n",
" if(queueIndex != -1): # got edges index\n",
" tempEdge = self.thePQ.peekN(queueIndex) # get edge\n",
" oldDist = tempEdge.distance\n",
" if(oldDist > newDist): # if new edge shorter,\n",
" self.thePQ.removeN(queueIndex) # remove old edge\n",
" theEdge = Edge(self.currentVert, newVert, newDist)\n",
" self.thePQ.insert(theEdge)# insert new edge\n",
" # else no action just leave the old vertex there\n",
" else: # no edge with same destination vertex\n",
" # so insert new one\n",
" theEdge = Edge(self.currentVert, newVert, newDist)\n",
" self.thePQ.insert(theEdge)\n",
"\n",
"\n",
"theGraph = Graph()\n",
"theGraph.addVertex('A') # 0 (start for mst)\n",
"theGraph.addVertex('B') # 1\n",
"theGraph.addVertex('C') # 2\n",
"theGraph.addVertex('D') # 3\n",
"theGraph.addVertex('E') # 4\n",
"theGraph.addVertex('F') # 5\n",
"theGraph.addEdge(0, 1, 16) # AB\n",
"theGraph.addEdge(0, 3, 24) # AD\n",
"\n",
"theGraph.addEdge(1,2,1)\n",
"theGraph.addEdge(1,3,5)\n",
"theGraph.addEdge(1,4,2)\n",
"theGraph.addEdge(2,3,6)\n",
"theGraph.addEdge(2,4,8)\n",
"theGraph.addEdge(2,5,26)\n",
"theGraph.addEdge(3,4,142)\n",
"theGraph.addEdge(4,5,17)\n",
"\n",
"print 'Minimum spanning tree: ',\n",
"theGraph.mstw() # minimum spanning tree"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 14.2 Page 703"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"class DistPar:\n",
" def __init__(self,pv,d): # constructor\n",
" self.distance = d\n",
" self.parentVert = pv\n",
"\n",
"class Vertex:\n",
" def __init__(self,lab): # constructor\n",
" self.label = lab\n",
" self.isInTree = False\n",
"\n",
"class Graph:\n",
" def __init__(self): # constructor\n",
" self.vertexList = [] # adjacency matrix\n",
" self.adjMat = []\n",
" self.nVerts = 0\n",
" self.nTree = 0\n",
" for j in range(20): # set adjacency\n",
" l = []\n",
" for k in range(20):\n",
" l.append(1000000)\n",
" self.adjMat.append(l)\n",
" self.currentVert = 0\n",
" self.sPath = [] # shortest paths\n",
" self.startToCurrent = 0\n",
"\n",
" def addVertex(self,lab):\n",
" self.vertexList.append( Vertex(lab))\n",
" self.nVerts += 1\n",
"\n",
" def addEdge(self,start, end,weight):\n",
" self.adjMat[start][end] = weight\n",
"\n",
"\n",
" def displayVertex(self,v):\n",
" print self.vertexList[v].label ,\n",
"\n",
" def path(self): # find all shortest paths\n",
" startTree = 0 # start at vertex 0\n",
" self.vertexList[startTree].isInTree = True\n",
" self.nTree = 1 # put it in tree\n",
" # transfer row of distances from adjMat to sPath\n",
" for j in range(self.nVerts):\n",
" tempDist = self.adjMat[startTree][j]\n",
" try:\n",
" self.sPath[j] = DistPar(startTree, tempDist)\n",
" except:\n",
" self.sPath.append(DistPar(startTree, tempDist))\n",
" # until all vertices are in the tree\n",
" while(self.nTree < self.nVerts):\n",
" indexMin = self.getMin() # get minimum from sPath\n",
" minDist = self.sPath[indexMin].distance\n",
" if(minDist == 1000000): # if all infinite\n",
" # or in tree,\n",
" print 'There are unreachable vertices'\n",
" break # sPath is complete\n",
" else:\n",
" # reset self.currentVert\n",
" self.currentVert = indexMin # to closest vert\n",
" self.startToCurrent = self.sPath[indexMin].distance\n",
" # minimum distance from startTree is\n",
" # to self.currentVert, and is self.startToCurrent\n",
" # put current vertex in tree\n",
" self.vertexList[self.currentVert].isInTree = True\n",
" self.nTree += 1\n",
" self.adjust_sPath() # update sPath[] array\n",
"\n",
" self.displayPaths() # display sPath[] contents\n",
" self.nTree = 0 # clear tree\n",
" for j in range(self.nVerts):\n",
" self.vertexList[j].isInTree = False \n",
"\n",
" def getMin(self): # get entry from sPath\n",
" minDist = 1000000 # assume minimum\n",
" indexMin = 0\n",
" for j in range(self.nVerts): # for each vertex,\n",
" # if its in tree and\n",
" if( not self.vertexList[j].isInTree and self.sPath[j].distance < minDist ):\n",
" minDist = self.sPath[j].distance\n",
" indexMin = j # update minimum\n",
" return indexMin\n",
"\n",
" def adjust_sPath(self):\n",
" # adjust values in shortest-path array sPath\n",
" column = 1\n",
" # skip starting vertex\n",
" while(column < self.nVerts): # go across columns\n",
" # if this columns vertex already in tree, skip it\n",
" if( self.vertexList[column].isInTree ):\n",
" column += 1\n",
" continue\n",
" # calculate distance for one sPath entry get edge from self.currentVert to column\n",
" currentToFringe = self.adjMat[self.currentVert][column]\n",
" # add distance from start\n",
" startToFringe = self.startToCurrent + currentToFringe\n",
" # get distance of current sPath entry\n",
" sPathDist = self.sPath[column].distance\n",
" # compare distance from start with sPath entry\n",
" if(startToFringe < sPathDist): # if shorter,\n",
" # update sPath\n",
" self.sPath[column].parentVert = self.currentVert\n",
" self.sPath[column].distance = startToFringe\n",
" column += 1\n",
"\n",
" def displayPaths(self):\n",
" for j in range(self.nVerts): # display contents of sPath[]\n",
" print self.vertexList[j].label ,' =' \n",
" if(self.sPath[j].distance == 1000000):\n",
" print 'inf', # inf\n",
" else:\n",
" print self.sPath[j].distance , # 50\n",
" parent = self.vertexList[ self.sPath[j].parentVert ].label\n",
" print '(' , parent , ')' , # (A)\n",
" print ''\n",
" \n",
"theGraph = Graph()\n",
"theGraph.addVertex('A') # 0 (start)\n",
"theGraph.addVertex('C') # 2\n",
"theGraph.addVertex('B') # 1\n",
"theGraph.addVertex('D') # 3\n",
"theGraph.addVertex('E') # 4\n",
"theGraph.addEdge(0,1,50)\n",
"theGraph.addEdge(0,3,80)\n",
"theGraph.addEdge(1,2,60)\n",
"theGraph.addEdge(1,3,90)\n",
"theGraph.addEdge(2,4,40)\n",
"theGraph.addEdge(3,2,20)\n",
"theGraph.addEdge(3,4,70)\n",
"theGraph.addEdge(4,1,50)\n",
"print 'Shortest paths' ,\n",
"theGraph.path() # shortest paths"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Shortest paths A =\n",
"inf ( A ) C =\n",
"50 ( A ) B =\n",
"100 ( D ) D =\n",
"80 ( A ) E =\n",
"140 ( B ) \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
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}
]
}
|
