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+{
+ "metadata": {
+  "name": "ch13"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": "Chapter 13 : Graphs"
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": "Example 13.1  Page no: 631"
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": "'''\nexample 13.1\ndemonstrates depth-first search\n'''\nclass StackX:\n    def __init__(self):\n        self.st = [] # make array\n        self.top = -1\n\n    def push(self,j): # put item on stack\n        self.top += 1\n        self.st.append(j)\n\n    def pop(self): # take item off stack\n        self.top -= 1\n        return self.st.pop()\n\n    def peek(self): # peek at top of stack\n        return self.st[self.top]\n    \n    def isEmpty(self): # true if nothing on stack-\n        return self.top == -1\n\nclass Vertex:\n    def __init__(self,lab): # constructor\n        self.label = lab\n        self.wasVisited = False\n\nclass 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(0)\n            self.adjMat.append(l)\n        self.theStack = StackX()\n\n    def addVertex(self,lab):\n        self.vertexList.append( Vertex(lab))\n        self.nVerts += 1\n\n    def addEdge(self,start, end):\n        self.adjMat[start][end] = 1\n        self.adjMat[end][start] = 1\n\n    def displayVertex(self,v):\n        print self.vertexList[v].label ,\n\n    def dfs(self): # depth-first search # begin at vertex 0\n        self.vertexList[0].wasVisited = True # mark it\n        self.displayVertex(0)     # display it\n        self.theStack.push(0) # push it\n        while( not self.theStack.isEmpty() ): # until stack empty,\n            # get an unvisited vertex adjacent to stack top\n            v = self.getAdjUnvisitedVertex( self.theStack.peek() )\n            if(v == -1): # if no such vertex,\n                self.theStack.pop()\n            else: # if it exists,\n                self.vertexList[v].wasVisited = True # mark it\n                self.displayVertex(v) # display it\n                self.theStack.push(v) # push it\n\n        # stack is empty, so we're done\n        for j in range(self.nVerts): # reset flags\n            self.vertexList[j].wasVisited = False  # end dfs\n\n    def getAdjUnvisitedVertex(self,v):\n        for j in range(self.nVerts):\n            if(self.adjMat[v][j]==1 and self.vertexList[j].wasVisited==False):\n                return j\n        return -1\n\ntheGraph = Graph()\ntheGraph.addVertex('A') # 0 (start for dfs)\ntheGraph.addVertex('B') # 1\ntheGraph.addVertex('C') # 2\ntheGraph.addVertex('D') # 3\ntheGraph.addVertex('E') # 4\ntheGraph.addEdge(0,1)\ntheGraph.addEdge(1,2)\ntheGraph.addEdge(0,3)\ntheGraph.addEdge(3,4)\nprint 'Visits: ',\ntheGraph.dfs() # depth-first search",
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": "Visits:  A B C D E\n"
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": "Example 13.2  Page no : 639"
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": "'''\nExample 13.2\ndemonstrates breadth-first search\n'''\nclass Queue:\n    def __init__(self): # constructor\n        self.SIZE = 20\n        self.queArray = []\n        for i in range(20):\n            self.queArray.append(0)\n        self.front = 0\n        self.rear = -1\n\n    def insert(self,j): # put item at self.rear of queue\n        if(self.rear == self.SIZE-1):\n            self.rear = -1\n        self.rear += 1\n        self.queArray[self.rear] = j\n\n    def remove(self): # take item from front of queue\n        temp = self.queArray[self.front]\n        self.front += 1\n        if(self.front == self.SIZE):\n            self.front = 0\n        return temp\n\n    def isEmpty(self): # true if queue is empty\n        return ( self.rear+1==self.front or (self.front+self.SIZE-1==self.rear) )\n\nclass Vertex:\n    def __init__(self,lab): # constructor\n        self.label = lab\n        self.wasVisited = False\n\nclass 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(0)\n            self.adjMat.append(l)\n        self.theQueue = Queue()\n\n    def addVertex(self,lab):\n        self.vertexList.append( Vertex(lab))\n        self.nVerts += 1\n\n    def addEdge(self,start, end):\n        self.adjMat[start][end] = 1\n        self.adjMat[end][start] = 1\n\n    def displayVertex(self,v):\n        print self.vertexList[v].label ,\n\n    def bfs(self): # breadth-first search\n        # begin at vertex 0\n        self.vertexList[0].wasVisited = True # mark it\n        self.displayVertex(0) # display it\n        self.theQueue.insert(0)  # insert at tail\n        while( not self.theQueue.isEmpty() ): # until queue empty,\n            v1 = self.theQueue.remove() # remove vertex at head\n            # until it has no unvisited neighbors\n            while( self.getAdjUnvisitedVertex(v1) != -1 ):\n                v2 = self.getAdjUnvisitedVertex(v1)\n                self.vertexList[v2].wasVisited = True # mark it\n                self.displayVertex(v2) # display it\n                self.theQueue.insert(v2) # insert it\n        for j in range(self.nVerts): # reset flags\n            self.vertexList[j].wasVisited = False\n\n    def getAdjUnvisitedVertex(self,v):\n        for j in range(self.nVerts):\n            if(self.adjMat[v][j]==1 and self.vertexList[j].wasVisited==False):\n                return j\n        return -1\n\n\ntheGraph = Graph()\ntheGraph.addVertex('A') # 0 (start for dfs)\ntheGraph.addVertex('B') # 1\ntheGraph.addVertex('C') # 2\ntheGraph.addVertex('D') # 3\ntheGraph.addVertex('E') # 4\ntheGraph.addEdge(0,1)\ntheGraph.addEdge(1,2)\ntheGraph.addEdge(0,3)\ntheGraph.addEdge(3,4)\nprint 'Visits: ',\ntheGraph.bfs() # breadth-first search",
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": "Visits:  A B D C E\n"
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": "Example 13.3 Page no : 645"
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": "'''\nexample 13.3\ndemonstrates minimum spanning tree\n'''\nclass StackX:\n    def __init__(self):\n        self.st = [] # make array\n        self.top = -1\n\n    def push(self,j): # put item on stack\n        self.top += 1\n        self.st.append(j)\n\n    def pop(self): # take item off stack\n        self.top -= 1\n        return self.st.pop()\n\n    def peek(self): # peek at top of stack\n        return self.st[self.top]\n    \n    def isEmpty(self): # true if nothing on stack-\n        return self.top == -1\n\nclass Vertex:\n    def __init__(self,lab): # constructor\n        self.label = lab\n        self.wasVisited = False\n\nclass 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(0)\n            self.adjMat.append(l)\n        self.theStack = StackX()\n\n    def addVertex(self,lab):\n        self.vertexList.append( Vertex(lab))\n        self.nVerts += 1\n\n    def addEdge(self,start, end):\n        self.adjMat[start][end] = 1\n        self.adjMat[end][start] = 1\n\n    def displayVertex(self,v):\n        print self.vertexList[v].label ,\n\n    def mst(self): # minimum spanning tree (depth first)\n        # start at 0\n        self.vertexList[0].wasVisited =True\n        # mark it\n        self.theStack.push(0)\n        # push it\n        while(not self.theStack.isEmpty() ):\n            # until stack empty\n            # get stack top\n            currentVertex = self.theStack.peek()\n            # get next unvisited neighbor       \n            v = self.getAdjUnvisitedVertex(currentVertex)\n            if(v == -1):\n                # if no more neighbors\n                self.theStack.pop()\n            else:\n                # got a neighbor\n                self.vertexList[v].wasVisited = True # mark it\n                self.theStack.push(v)\n                # push it\n                # display edge\n                self.displayVertex(currentVertex)\n                # from currentV\n                self.displayVertex(v)\n                # to v\n                print ' ',\n        for j in range(self.nVerts):\n            # reset flags\n            self.vertexList[j].wasVisited = False\n\n    def getAdjUnvisitedVertex(self, v):\n        for j in range(self.nVerts):\n            if(self.adjMat[v][j]==1 and self.vertexList[j].wasVisited==False):\n                return j\n        return -1\n\ntheGraph = Graph()\ntheGraph.addVertex('A') # 0 (start for mst)\ntheGraph.addVertex('B') # 1\ntheGraph.addVertex('C') # 2\ntheGraph.addVertex('D') # 3Topological Sorting with Directed Graphs\ntheGraph.addVertex('E') # 4\ntheGraph.addEdge(0,1) \ntheGraph.addEdge(0,2)\ntheGraph.addEdge(0,3) \ntheGraph.addEdge(0,4) \ntheGraph.addEdge(1,2) \ntheGraph.addEdge(1,3)\ntheGraph.addEdge(1,4) \ntheGraph.addEdge(2,3) \ntheGraph.addEdge(2,4) \ntheGraph.addEdge(3,4) \nprint 'Minimum spanning tree: ',\ntheGraph.mst() # minimum spanning tree",
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": "Minimum spanning tree:  A B   B C   C D   D E  \n"
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": "Example 13.4  page No : 657"
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": "'''\nExample 13.4\ndemonstrates topological sorting\n'''\nclass Vertex:\n    def __init__(self,lab): # constructor\n        self.label = lab\n        self.wasVisited = False\n\nclass 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(0)\n            self.adjMat.append(l)\n\n    def addVertex(self,lab):\n        self.vertexList.append( Vertex(lab))\n        self.nVerts += 1\n\n    def addEdge(self,start, end):\n        self.adjMat[start][end] = 1\n        self.adjMat[end][start] = 1\n\n    def displayVertex(self,v):\n        print self.vertexList[v].label ,\n\n    def topo(self): # topological sort\n        orig_nVerts = self.nVerts # remember how many verts\n        while(self.nVerts > 0): # while vertices remain,\n            # get a vertex with no successors, or -1\n            currentVertex = self.noSuccessors()\n            if(currentVertex == -1):\n                # must be a cycleTopological Sorting with Directed Graphs\n                print 'ERROR: Graph has cycles'\n                return\n\n            # insert vertex label in sorted array (start at end)\n            self.sortedArray[nVerts-1] = self.vertexList[currentVertex].label\n            self.deleteVertex(currentVertex)\n        print 'Topologically sorted order: '\n        for j in range(orig_nVerts):\n            print sortedArray[j] ,\n        print ''\n\n    def noSuccessors(self): # returns vert with no successors\n        # (or -1 if no such verts)\n        isEdge = None\n        for row in range(self.nVerts): # for each vertex,\n            isEdge = False\n            # check edges\n            for col in range(self.nVerts):\n                if( self.adjMat[row][col] > 0 ): # if edge to\n                    # another,\n                    isEdge = True\n                    break\n            if( not isEdge ):\n                # if no edges,\n                return row\n        return -1\n\n    def deleteVertex(self,delVert):\n        if(delVert != self.nVerts-1):\n            # if not last vertex,\n            # delete from vertexList\n            for j in range(self.nVerts-1):\n                self.vertexList[j] = self.vertexList[j+1]\n            # delete row from adjMat\n        for row in range(self.nVerts-1):\n            self.moveRowUp(row, nVerts)\n            # delete col from adjMat\n        for col in range(self.nVerts-1):\n            self.moveColLeft(col, nVerts-1)\n        self.nVerts -= 1\n\n    def moveRowUp(self,row,length):\n        for col in range(length):\n            self.adjMat[row][col] = self.adjMat[row+1][col]\n\n    def moveColLeft(self,col, length):\n        for row in range(self.length):\n            self.adjMat[row][col] = self.adjMat[row][col+1]\n\ntheGraph = Graph()\ntheGraph.addVertex('A') # 0\ntheGraph.addVertex('B') # 1\ntheGraph.addVertex('C') # 2\ntheGraph.addVertex('D') # 3\ntheGraph.addVertex('E') # 4\ntheGraph.addVertex('F') # 5\ntheGraph.addVertex('G') # 6\ntheGraph.addVertex('H') # 7Connectivity in Directed Graphs\ntheGraph.addEdge(0,3)\ntheGraph.addEdge(0,4)\ntheGraph.addEdge(1,4)\ntheGraph.addEdge(2,5)\ntheGraph.addEdge(3,6)\ntheGraph.addEdge(4,6)\ntheGraph.addEdge(5,7)\ntheGraph.addEdge(6,7)\ntheGraph.topo() # do the sort",
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": "ERROR: Graph has cycles\n"
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": "",
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file