数据结构——图的邻接矩阵表示法

  
    

   
     
   
     #include 
   
     <
   
     iostream
   
     >
   
     

   
     using
   
      
   
     namespace
   
      std;
 

   
     #define
   
      MAX_VERTEX_NUM 10 
   
     //
   
     最大顶点个数
   
     
typedef 
   
     char
   
      VERTYPE;
typedef 
   
     struct
   
     
{
 VERTYPE vexs[MAX_VERTEX_NUM]; 
   
     //
   
     顶点向量
   
     

   
      
   
     int
   
      arcs[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; 
   
     //
   
     邻接矩阵
   
     

   
      
   
     int
   
      vexnum,arcnum; 
   
     //
   
     图的当前顶点数和弧数
   
     

   
     }mgraph, 
   
     *
   
      MGraph;


   
     void
   
      init_mgraph(MGraph 
   
     &
   
     g) 
   
     //
   
     初始化图
   
     

   
     {
 g
   
     =
   
     (MGraph)malloc(
   
     sizeof
   
     (mgraph));
 g
   
     ->
   
     vexnum
   
     =
   
     0
   
     ;
 g
   
     ->
   
     arcnum
   
     =
   
     0
   
     ;
 
   
     for
   
     (
   
     int
   
      i
   
     =
   
     0
   
     ;i
   
     <
   
     MAX_VERTEX_NUM;i
   
     ++
   
     )
 g
   
     ->
   
     vexs[i]
   
     =
   
     0
   
     ;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     MAX_VERTEX_NUM;i
   
     ++
   
     )
 
   
     for
   
     (
   
     int
   
      j
   
     =
   
     0
   
     ;j
   
     <
   
     MAX_VERTEX_NUM;j
   
     ++
   
     )
 g
   
     ->
   
     arcs[i][j]
   
     =
   
     0
   
     ;
}


   
     void
   
      add_vexs(MGraph 
   
     &
   
     g) 
   
     //
   
     增加顶点
   
     

   
     {
 cout
   
     <<
   
     "
   
     请输入顶点的个数:
   
     "
   
     <<
   
     endl;
 cin
   
     >>
   
     g
   
     ->
   
     vexnum;
 cout
   
     <<
   
     "
   
     请输入顶点的值
   
     "
   
     <<
   
     endl;
 
   
     for
   
     (
   
     int
   
      i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     vexnum;i
   
     ++
   
     )
 {
 cin
   
     >>
   
     g
   
     ->
   
     vexs[i];
 }
}

   
     void
   
      add_arcs(MGraph 
   
     &
   
     g) 
   
     //
   
     增加边
   
     

   
     {
 cout
   
     <<
   
     "
   
     请输入边的个数:
   
     "
   
     <<
   
     endl;
 cin
   
     >>
   
     g
   
     ->
   
     arcnum;
 VERTYPE ch1,ch2;
 
   
     int
   
      row,col;

 
   
     for
   
     (
   
     int
   
      i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     arcnum;i
   
     ++
   
     )
 { 
 cin
   
     >>
   
     ch1
   
     >>
   
     ch2;
 
   
     for
   
     (
   
     int
   
      j
   
     =
   
     0
   
     ;j
   
     <
   
     g
   
     ->
   
     vexnum;j
   
     ++
   
     )
 {
 
   
     if
   
     (g
   
     ->
   
     vexs[j]
   
     ==
   
     ch1)
 {
 row
   
     =
   
     j;
 }
 
   
     if
   
     (g
   
     ->
   
     vexs[j]
   
     ==
   
     ch2)
 {
 col
   
     =
   
     j;
 }
 }
 g
   
     ->
   
     arcs[row][col]
   
     =
   
     1
   
     ; 
   
     //
   
     有向带权图只需把1改为weight
   
     

   
      g
   
     ->
   
     arcs[col][row]
   
     =
   
     1
   
     ; 
   
     //
   
     无向图加上此行
   
     

   
      }
}


   
     void
   
      creat_mgraph(MGraph 
   
     &
   
     g) 
   
     //
   
     创建图 
   
     

   
     {
 add_vexs(g); 
   
     //
   
     增加顶点
   
     

   
      add_arcs(g); 
   
     //
   
     增加边
   
     

   
     }


   
     void
   
      print_mgraph(MGraph 
   
     &
   
     g) 
   
     //
   
     打印图
   
     

   
     {
 
   
     for
   
     (
   
     int
   
      i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     vexnum;i
   
     ++
   
     )
 cout
   
     <<
   
     "
   
      
   
     "
   
     <<
   
     g
   
     ->
   
     vexs[i];
 cout
   
     <<
   
     endl;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     vexnum;i
   
     ++
   
     )
 {
 cout
   
     <<
   
     g
   
     ->
   
     vexs[i]
   
     <<
   
     "
   
      
   
     "
   
     ;
 
   
     for
   
     (
   
     int
   
      j
   
     =
   
     0
   
     ;j
   
     <
   
     g
   
     ->
   
     vexnum;j
   
     ++
   
     )
 {
 cout
   
     <<
   
     g
   
     ->
   
     arcs[i][j]
   
     <<
   
     "
   
      
   
     "
   
     ;
 }
 cout
   
     <<
   
     endl;
 }
}


   
     //
   
     删除顶点
   
     

   
     void
   
      delete_vex(MGraph 
   
     &
   
     g,VERTYPE ch)
{
 
   
     int
   
      row;
 
   
     int
   
      i,j;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     vexnum;i
   
     ++
   
     )
 {
 
   
     if
   
     (g
   
     ->
   
     vexs[i]
   
     ==
   
     ch)
 {
 row
   
     =
   
     i;
 }
 }

 
   
     int
   
      arcs
   
     =
   
     0
   
     ; 
   
     //
   
     记录删除顶点的弧数，然后总弧数减去此值
   
     

   
      
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     vexnum;i
   
     ++
   
     )
 {
 
   
     if
   
     (g
   
     ->
   
     arcs[row][i] 
   
     ==
   
      
   
     1
   
     )
 arcs
   
     ++
   
     ;
 }
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     g
   
     ->
   
     vexnum;i
   
     ++
   
     )
 {
 
   
     for
   
     (j
   
     =
   
     row;j
   
     <
   
     g
   
     ->
   
     vexnum
   
     -
   
     1
   
     ;j
   
     ++
   
     )
 g
   
     ->
   
     arcs[i][j]
   
     =
   
     g
   
     ->
   
     arcs[i][j
   
     +
   
     1
   
     ]; 
   
     //
   
     把删除顶点右边的数据左移
   
     

   
      g
   
     ->
   
     arcs[i][j
   
     +
   
     1
   
     ]
   
     =
   
     0
   
     ;
 }
 
   
     for
   
     (i
   
     =
   
     row;i
   
     <
   
     g
   
     ->
   
     vexnum
   
     -
   
     1
   
     ;i
   
     ++
   
     )
 {
 
   
     for
   
     (j
   
     =
   
     0
   
     ;j
   
     <
   
     g
   
     ->
   
     vexnum;j
   
     ++
   
     )
 g
   
     ->
   
     arcs[i][j]
   
     =
   
     g
   
     ->
   
     arcs[i
   
     +
   
     1
   
     ][j]; 
   
     //
   
     把删除顶点下边的数据上移
   
     

   
      g
   
     ->
   
     arcs[i
   
     +
   
     1
   
     ][j]
   
     =
   
     0
   
     ;
 }
 
   
     for
   
     (i
   
     =
   
     row;i
   
     <
   
     g
   
     ->
   
     vexnum
   
     -
   
     1
   
     ;i
   
     ++
   
     ) 
   
     //
   
     把顶点数组中右边的顶点左移
   
     

   
      g
   
     ->
   
     vexs[i]
   
     =
   
     g
   
     ->
   
     vexs[i
   
     +
   
     1
   
     ];

 g
   
     ->
   
     vexnum
   
     =
   
     g
   
     ->
   
     vexnum
   
     -
   
     1
   
     ; 
   
     //
   
     顶点个数减1
   
     

   
      g
   
     ->
   
     arcnum
   
     =
   
     g
   
     ->
   
     arcnum
   
     -
   
     arcs; 
   
     //
   
     总弧数减去要删除顶点的弧数
   
     

   
     }


   
     int
   
      main()
{
 MGraph G;
 init_mgraph(G); 
   
     //
   
     初始化图
   
     

   
      creat_mgraph(G); 
   
     //
   
     创建图
   
     

   
      print_mgraph(G); 
   
     //
   
     打印图

 
   
     //
   
     删除顶点
   
     

   
      VERTYPE ch;
 cin
   
     >>
   
     ch;
 delete_vex(G,ch);
 cout
   
     <<
   
     G
   
     ->
   
     arcnum
   
     <<
   
     "
   
      
   
     "
   
     <<
   
     G
   
     ->
   
     vexnum
   
     <<
   
     endl;
 print_mgraph(G);

 
   
     return
   
      
   
     0
   
     ;
}