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图的邻接矩阵表示

Posted on 2012-04-30 12:52 eryar 阅读(3275) 评论(2)  编辑 收藏 引用

图的邻接矩阵表示

Adjacency Matrix of the Graph

一、邻接矩阵定义

图的邻接矩阵定义:设图G=(V, E)的顶点集为V(G)={v1, v2,v3,…,vp},用aij表示G中顶点vivj之间的边数,则n阶方阵M(G)=(aij)pxp称为G的邻接矩阵(Adjacency Matrix)。

Graph

上图所示的图的邻接矩阵如下:

Adjacency Matrix

图的邻接矩阵有以下明显的性质:

l 邻接矩阵是一个对称矩阵;

l 若图G为无环图,则M(G)中第i行(列)的元素之和等于顶点的度数;

一般说来,图的邻接矩阵比它的关联矩阵小得多,通常图就以其邻接矩阵的形式存贮在计算机中。

二、图的邻接矩阵表示法的程序实现

图的邻接矩阵表示法的数据结构为:

   1:  typedef struct SArc
   2:  {
   3:      double  dWeight;
   4:  }AdjMatrix[VERTEX_NUM][VERTEX_NUM];
   5:   
   6:  typedef struct SGraph
   7:  {
   8:      int         iVertexNum;
   9:      int         iArcNum;
  10:      int         aVertex[VERTEX_NUM];
  11:      AdjMatrix   mArcs;
  12:  }Graph;
 
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在此基础上实现图的创建:

程序代码如下:

   1:  //------------------------------------------------------------------------------
   2:  //    Copyright (c) 2012 eryar All Rights Reserved.
   3:  //
   4:  //        File    : Main.cpp
   5:  //        Author  : eryar@163.com
   6:  //        Date    : 2012-4-11 20:33
   7:  //        Version : 1.0v
   8:  //
   9:  //    Description : Use adjacency matrix of a graph.
  10:  //
  11:  //==============================================================================
  12:   
  13:  #include <IOSTREAM>
  14:  using namespace std;
  15:   
  16:  const int INFINIY       = INT_MAX;
  17:  const int VERTEX_NUM    = 20;
  18:   
  19:  typedef struct SArc
  20:  {
  21:      double  dWeight;
  22:  }AdjMatrix[VERTEX_NUM][VERTEX_NUM];
  23:   
  24:  typedef struct SGraph
  25:  {
  26:      int         iVertexNum;
  27:      int         iArcNum;
  28:      int         aVertex[VERTEX_NUM];
  29:      AdjMatrix   mArcs;
  30:  }Graph;
  31:   
  32:  void    CreateGraph(Graph& graph);
  33:  int     LocateVertex(const Graph& graph, int vertex);
  34:  void    ShowGraph(const Graph& graph);
  35:   
  36:  ///////////////////////////////////////////////////////////////////////////////
  37:  // Main function.
  38:   
  39:  int main(int argc, char* argv[])
  40:  {
  41:      Graph   graph;
  42:   
  43:      CreateGraph(graph);
  44:   
  45:      ShowGraph(graph);
  46:   
  47:      return 0;
  48:  }
  49:   
  50:  ///////////////////////////////////////////////////////////////////////////////
  51:  /*
  52:  * Create a graph.
  53:  */
  54:  void    CreateGraph(Graph& graph)
  55:  {
  56:      cout<<"Create the graph"<<endl;
  57:      cout<<"Input vertex number:"; 
  58:      cin>>graph.iVertexNum;
  59:   
  60:      cout<<"Input arc number:";
  61:      cin>>graph.iArcNum;
  62:   
  63:      // Input vertex
  64:      for (int iVertex = 0; iVertex < graph.iVertexNum; iVertex++)
  65:      {
  66:          cout<<"Input "<<iVertex+1<<" vertex value:";
  67:          cin>>graph.aVertex[iVertex];
  68:      }
  69:   
  70:      // Initialize adjacency matrix.
  71:      for (int i = 0; i < graph.iVertexNum; i++)
  72:      {
  73:          for (int j = 0; j < graph.iVertexNum; j++)
  74:          {
  75:              graph.mArcs[i][j].dWeight   = 0;
  76:          }
  77:      }
  78:   
  79:      // Build adjacency matrix.
  80:      int     iFirst  = 0;
  81:      int     iSecond = 0;
  82:      int     xPos    = 0;
  83:      int     yPos    = 0;
  84:      double  dWeight = 0;
  85:   
  86:      for (int k = 0; k < graph.iArcNum; k++)
  87:      {
  88:          cout<<"Input edge first vertex:";
  89:          cin>>iFirst;
  90:   
  91:          cout<<"Input edge second vertex:";
  92:          cin>>iSecond;
  93:   
  94:          cout<<"Input the weight:";
  95:          cin>>dWeight;
  96:   
  97:          xPos  = LocateVertex(graph, iFirst);
  98:          yPos  = LocateVertex(graph, iSecond);
  99:   
 100:          // 
 101:          graph.mArcs[xPos][yPos].dWeight = dWeight;
 102:          graph.mArcs[yPos][xPos].dWeight = dWeight;
 103:      }
 104:  }
 105:   
 106:  /**
 107:  * Show a graph.
 108:  */
 109:  void    ShowGraph(const Graph& graph)
 110:  {
 111:      cout<<"Show the graph represented by adjacency matrix:"<<endl;
 112:   
 113:      // Output adjacency matrix.
 114:      for (int m = 0; m < graph.iVertexNum; m++)
 115:      {
 116:          for (int n = 0; n < graph.iVertexNum; n++)
 117:          {
 118:              cout<<graph.mArcs[m][n].dWeight<<"\t";
 119:          }
 120:   
 121:          cout<<endl;
 122:      }
 123:  }
 124:   
 125:  /**
 126:  * Locate vertex position in the adjacency matrix.
 127:  */
 128:  int LocateVertex( const Graph& graph, int vertex )
 129:  {
 130:      for (int i = 0; i < graph.iVertexNum; i++)
 131:      {
 132:          if (graph.aVertex[i] == vertex)
 133:          {
 134:              return i;
 135:          }
 136:      }
 137:   
 138:      return -1;
 139:  }
.csharpcode, .csharpcode pre { font-size: small; color: black; font-family: consolas, "Courier New", courier, monospace; background-color: #ffffff; /*white-space: pre;*/ } .csharpcode pre { margin: 0em; } .csharpcode .rem { color: #008000; } .csharpcode .kwrd { color: #0000ff; } .csharpcode .str { color: #006080; } .csharpcode .op { color: #0000c0; } .csharpcode .preproc { color: #cc6633; } .csharpcode .asp { background-color: #ffff00; } .csharpcode .html { color: #800000; } .csharpcode .attr { color: #ff0000; } .csharpcode .alt { background-color: #f4f4f4; width: 100%; margin: 0em; } .csharpcode .lnum { color: #606060; }

程序运行效果如下图所示:

Run the program

Feedback

# re: 图的邻接矩阵表示[未登录]  回复  更多评论   

2012-05-21 08:45 by jack
大哥,你这是用mfc编的?

# re: 图的邻接矩阵表示  回复  更多评论   

2012-05-22 14:04 by eryar
不是, 控制台的小程序@jack

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