path: root/Data_Structures_and_Algorithms_in_Java/ch13.ipynb

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  {
   "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": [
      " \n",
      "class 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",
      "\n",
      "class Vertex:\n",
      "    def __init__(self,lab): # constructor\n",
      "        self.label = lab\n",
      "        self.wasVisited = 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(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",
      "\n",
      "theGraph = Graph()\n",
      "theGraph.addVertex('A') # 0 (start for dfs)\n",
      "theGraph.addVertex('B') # 1\n",
      "theGraph.addVertex('C') # 2\n",
      "theGraph.addVertex('D') # 3\n",
      "theGraph.addVertex('E') # 4\n",
      "theGraph.addEdge(0,1)\n",
      "theGraph.addEdge(1,2)\n",
      "theGraph.addEdge(0,3)\n",
      "theGraph.addEdge(3,4)\n",
      "print 'Visits: ',\n",
      "theGraph.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": [
      " \n",
      "class 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",
      "\n",
      "class Vertex:\n",
      "    def __init__(self,lab): # constructor\n",
      "        self.label = lab\n",
      "        self.wasVisited = 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(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",
      "\n",
      "theGraph = Graph()\n",
      "theGraph.addVertex('A') # 0 (start for dfs)\n",
      "theGraph.addVertex('B') # 1\n",
      "theGraph.addVertex('C') # 2\n",
      "theGraph.addVertex('D') # 3\n",
      "theGraph.addVertex('E') # 4\n",
      "theGraph.addEdge(0,1)\n",
      "theGraph.addEdge(1,2)\n",
      "theGraph.addEdge(0,3)\n",
      "theGraph.addEdge(3,4)\n",
      "print 'Visits: ',\n",
      "theGraph.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": [
      " \n",
      "class 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",
      "\n",
      "class Vertex:\n",
      "    def __init__(self,lab): # constructor\n",
      "        self.label = lab\n",
      "        self.wasVisited = 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(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",
      "\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') # 3Topological Sorting with Directed Graphs\n",
      "theGraph.addVertex('E') # 4\n",
      "theGraph.addEdge(0,1) \n",
      "theGraph.addEdge(0,2)\n",
      "theGraph.addEdge(0,3) \n",
      "theGraph.addEdge(0,4) \n",
      "theGraph.addEdge(1,2) \n",
      "theGraph.addEdge(1,3)\n",
      "theGraph.addEdge(1,4) \n",
      "theGraph.addEdge(2,3) \n",
      "theGraph.addEdge(2,4) \n",
      "theGraph.addEdge(3,4) \n",
      "print 'Minimum spanning tree: ',\n",
      "theGraph.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": [
      " \n",
      "class Vertex:\n",
      "    def __init__(self,lab): # constructor\n",
      "        self.label = lab\n",
      "        self.wasVisited = 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(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",
      "\n",
      "theGraph = Graph()\n",
      "theGraph.addVertex('A') # 0\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.addVertex('G') # 6\n",
      "theGraph.addVertex('H') # 7Connectivity in Directed Graphs\n",
      "theGraph.addEdge(0,3)\n",
      "theGraph.addEdge(0,4)\n",
      "theGraph.addEdge(1,4)\n",
      "theGraph.addEdge(2,5)\n",
      "theGraph.addEdge(3,6)\n",
      "theGraph.addEdge(4,6)\n",
      "theGraph.addEdge(5,7)\n",
      "theGraph.addEdge(6,7)\n",
      "theGraph.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": []
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}