图的邻接表表示与无环图的拓扑排序

#include <iostream>
using namespace std;
 

//////////////////////列队的相关定义//////////////////////
typedef struct QueueRecord *Queue;
#define MinQueueSize  10
struct QueueRecord
{
   int Capacity;    //队的容量
   int Front;       //队头
   int Rear;        //队尾
   int Size;        //队中元素的个数
   int *Array;       //数组
};
/////////////////////邻接表的相关定义//////////////////////
typedef struct EdgeNode *position;
typedef struct Led_table* Table; 


 struct EdgeNode     //边表结点  
{  
    int adjvex;    // 邻接点域,存储该顶点对应的下标  
    int weight;     // 对应边的权值 
    position next; // 链域,指向下一个邻接点
}; 

struct Led_table       // 邻接表结构  
{  
    int data;                //邻接表的大小
    position *firstedge;       //边表头指针，可以理解为数组
};  

///////////////////列队相关函数声明////////////////////////
int IsEmpty(Queue Q);    //判断队列是否为空
int IsFull(Queue Q);     //判断队列是否满了
void MakeEmpty(Queue Q);   //构造一个空列队
Queue CreateQueue(int MaxElements);  //创建一个列队
void DisposeQueue(Queue Q);      //释放一个列队
void Enqueue(int x, Queue Q);    //入队
int Dequeue(Queue Q);      //出队
int Front(Queue Q);     //返回队首值，不出队
 
 
///////////////////列队相关函数定义////////////////////////
int IsEmpty(Queue Q)
{
   return Q->Size == 0;
}
 
int IsFull(Queue Q)
{
    if(Q->Size > Q->Capacity )
    {
       cout << "queue full" << endl;
       return -1;
    }
    else
    {
       return 0;
    }
}
 
void MakeEmpty(Queue Q)
{
   Q->Size = 0;
   Q->Front = 1;
   Q->Rear = 0;
}
 
Queue CreateQueue(int MaxElements)
{
   Queue Q;
   if (MaxElements < MinQueueSize)
   {
      cout << "queue size is too small" << endl;
   }
   Q = static_cast<Queue> (malloc(sizeof(struct QueueRecord)));
   if(Q == NULL)
   {
      cout << "out of space!!!";
   }
   Q->Array =static_cast<int*>(malloc(sizeof(int)*MaxElements));
   if(Q->Array == NULL)
   {
     cout << "out of space!!!";
   }
   Q->Capacity = MaxElements;
   MakeEmpty(Q);
   return Q;
}
 
void DisposeQueue(Queue Q)
{
    if (Q != NULL)
   {
      free(Q->Array );
      free(Q);
   }
}
 
 
static int Succ(int Value, Queue Q)  //循环数组，用于回绕
{
   if(++Value == Q->Capacity )
       Value = 0;
   return Value;
}
void Enqueue(int x, Queue Q)
{
    if(IsFull(Q))
    {
       cout << "Full queue" << endl;
    }
    else
    {
       Q->Size ++;
       Q->Rear = Succ(Q->Rear, Q);
       Q->Array [Q->Rear] = x;
    }
}
 
 
int Dequeue(Queue Q)
{
    if(IsEmpty(Q))
    {
       cout << "Empty Queue" << endl;
       return false;    //仅表示错误
    }
    else
    {
       Q->Size --;
       Q->Front = Succ(Q->Front, Q);
       return Q->Array[(Q->Front)-1];
    }
}
 
int Front(Queue Q)
{
    if(IsEmpty(Q))
    {
       cout << "Empty Queue" << endl;
       return false;    //仅表示错误
    }
    else
    return Q->Array[Q->Front];
}
 

//////////////////////////邻接表相关函数定义///////////////
Table Creat_Lable (int MaxElements)    //MaxElements参数为希望创建的节点数
{
	
	Table table1 = static_cast<Table> (malloc(sizeof(struct Led_table)));
	table1->data = MaxElements;
	if (table1 == NULL)
	{
	   cout << "out of space!!!";
	}

	table1->firstedge  = static_cast<position*>(malloc(sizeof(position)*(table1->data))); 
	if (table1->firstedge  == NULL)
	{
	   cout << "out of space!!!";
	}

	//给每个表头赋值，从0开始
	for (int i = 0; i <= table1->data - 1; ++i)
	{
	    table1->firstedge [i] = static_cast<position>(malloc(sizeof(position)));   //申请一个节点
		if (table1->firstedge [i]  == NULL)
			{
			   cout << "out of space!!!";
			}
		table1->firstedge [i]->adjvex = 0;   //表头这个参数存储入度
		table1->firstedge [i]->weight = 0;   //此参数在此时没有意义
		table1->firstedge [i]->next = NULL;

	}
	return table1;

}


void Insert (Table table1, int v, int w, int weig)   //表示存在一条边为<v,w>,且权重为weig
{
    position p = static_cast<position>(malloc(sizeof(position)));   //申请一个节点
	if(p == NULL)
	{
	   cout << "out of space!!!";
	}
	p->adjvex = w;
    p->weight = weig;
	p->next = table1->firstedge [v]->next;
	table1->firstedge [v]->next = p;
		
}

void CountIndegree(Table table1)      //计算顶点的入度，存在头结点中
{
   for(int i = 0; i <= table1->data - 1; ++i)
   {
       position p = table1->firstedge [i]->next;
        while (p != NULL) 
		{
           ++(table1->firstedge [p->adjvex]->adjvex) ;
            p = p->next;
        }
   }
}

int* Topsort(Table table1)          //拓扑排序
{
   Queue queue_1 = CreateQueue(15);   //创建一个列队
   int Counter = 0;
   int *TopNum = static_cast<int*>( malloc (sizeof(int)*(table1->data )));  //此数组用来存储结果
   int v;
   for(int i = 0; i != table1->data; ++i)
   {
      if(table1->firstedge[i]->adjvex == 0)
	  {
	     Enqueue(i,queue_1);  //如果顶点i的入度为0，就入队
	  }
   }

   while(!IsEmpty(queue_1))
   {
       v = Dequeue(queue_1);
	   TopNum[v] = ++Counter;   //若TopNum[5] = 3， 则排第三的为v5

	    position p = table1->firstedge [v]->next;

		while (p != NULL)   //把这个节点删除后，更新入度
		{
		  --(table1->firstedge [p->adjvex]->adjvex);
		  if(table1->firstedge [p->adjvex]->adjvex == 0) Enqueue(p->adjvex,queue_1);
		   p = p->next;
		}
	   
   }
   if(Counter != table1->data )
   {
       cout << "the graph has a cycle" << endl;
   }
   DisposeQueue(queue_1);
   return TopNum;
}

void print_Topsort_result(int *TopNum,Table table1)   //打印拓扑排序结果
{
   for(int i = 1; i != table1->data+1 ; ++i)
   {
      for (int j = 0; j != table1->data ; ++j)
	  {
	     if (TopNum[j] == i)
		 {
			 if(i == table1->data)
			 {
			    cout << "v" << j;
			 }
			 else
			 {
			    cout << "v" << j << "->";
			 }
		    
		 }
	  }
   }
   cout << endl;
}
 
int main ()
{
  Table table_1 = Creat_Lable (7);    //创建一个大小为7的邻接表

  //根据图来为邻接表插入数据
  Insert (table_1, 0, 1, 2);Insert (table_1, 0, 2, 4);Insert (table_1, 0, 3, 1);
  Insert (table_1, 1, 3, 3);Insert (table_1, 1, 4, 10);
  Insert (table_1, 2, 5, 5);
  Insert (table_1, 3, 2, 2);Insert (table_1, 3, 5, 8);Insert (table_1, 3, 6, 4);
  Insert (table_1, 4, 3, 2);Insert (table_1, 4, 6, 6);
  Insert (table_1, 6, 5, 1);

   CountIndegree(table_1);  //计算入度

   int* TopNum = Topsort(table_1);  //拓扑排序
   print_Topsort_result(TopNum,table_1);   //打印拓扑排序结果
   delete TopNum;
   delete table_1;
   while(1);
   return 0;
}