一、写在前面

数据结构线性表可以用来模拟集合，通过线性表的各种操作实现集合的基本运算。例如已知集合A和B，求A和B的并集A∪B。这里分无序集和有序集分别讨论。无论无序集和有序集，都可以用顺序表或者链表描述。下面是详细讨论。

二、无序集合求并集

1.用顺序表描述

/*-----合并顺序表La Lb-----*/ 
void mergeList(List &La, List &Lb)
{
	for (int i=1; i<=Lb.length; ++i)	//遍历Lb 
	{
		ElemType e = Lb.elem[i-1];		//取出Lb中第i个元素 
		int j, k;
		
		for (j=1; j<=La.length; ++j)	//La中查找e 查到则跳出循环 
			if (e == La.elem[j-1])	break;
	
		if (j == La.length+1)			//如果不在La中
		{								
			La.elem[j-1] = e; 			//在La表尾插入 e
			++La.length;	
		}
	}
} 

2.用链表描述

/*-----合并链表La Lb-----*/
void mergeList(List &La, List &Lb)
{
	List pa = La->next;
	List pb = Lb->next; 
	List pre = Lb; 			//辅助指针 
	
	while (pb)				//遍历Lb 
	{	
		while (pa->next && pa->data != pb->data)	//pa未到达La表尾 La未找到与pb的值相等的结点 
			pa = pa->next;							//La中查找与b相同的元素
		

		if(pa->data != pb->data)			//*p是表尾结点 pb链接pa后面
		{
			pre->next = pb->next;			//临时保存结点*pb后继 
			pa->next = pb;					//更新当前结点*pa后继为*pb 
			pb->next = NULL;	 			//标记为表尾 
			pb = pre->next;					//Lb工作指针后移 
		} 
		
		else								//释放pb
		{
			pre->next = pb->next;			//临时保存结点*pb后继 
			delete pb; 						//释放pb 
			pb = pre->next; 				//工作指针后移 
		} 
		pa = La->next;						//pa回溯到首元结点 以备下一次查找 
	}
	delete Lb;				//释放Lb表头 
} 

三、有序集合求并集

1.用顺序表描述

/*-----合并非递减顺序表La Lb-----*/ 
void mergeList(List &La, List &Lb, List &Lc)
{
	// 初始化
	Lc.length = La.length+Lb.length;		//新表长度为A、B之和 
	Lc.elem = new ElemType[Lc.length];	
	 
	ElemType *pa = La.elem;	
	ElemType *pb = Lb.elem;
	ElemType *pc = Lc.elem;
	ElemType *pa_last = La.elem+La.length-1;	//La表尾 
	ElemType *pb_last = Lb.elem+Lb.length-1;	//Lb表尾 
	
	while (pa<=pa_last && pb<=pb_last)	//La Lb均为到达表尾 
	{
		if(*pa <= *pb) *pc++=*pa++;
		else *pc++ = *pb++;
	}
	
	while (pa <= pa_last) *pc++=*pa++;	//Lb先到达表尾 处理La剩余元素 
	while (pb <= pb_last) *pc++=*pb++;	//La先到达表尾 处理Lb剩余元素 
	 
} 

2.用链表描述

/*-----合并有序链表La Lb-----*/
void mergeList(List &La, List &Lb, List &Lc)
{
	List pa = La->next;
	List pb = Lb->next; 
	List pc = Lc = La;
	List prea = La;		//辅助指针 pa前驱 
	List preb = Lb;		//辅助指针 pb前驱 
	
	
	while (pa && pb) //pa pb 均未到达表尾 
	{
		if(pa->data <= pb->data)
		{
			cout << "正在插入" << pa->data <<endl;
			pc->next = pa;	//pa链接到pc表尾 
			pc = pc->next;	//pc后移 
			pa = pa->next;	//pa后移
		} 
		
		else
		{
			cout << "正在插入" << pb->data <<endl;
			pc->next = pb;
			pc = pc->next;	//pc后移 
			pb = pb->next;	//pb后移 
		}
	}
	
	while (pa)
	{
		cout << "正在插入" << pa->data <<endl;
		pc->next = pa;	//pa链接到pc表尾 
		pc = pc->next;	//pc后移 
		pa = pa->next;	//pa后移 
	}
	
	while (pb)
	{
		cout << "正在插入" << pb->data <<endl;
		pc->next = pb;
		pc = pc->next;	//pc后移 
		pb = pb->next;	//pb后移 
	}
	
	delete Lb;
}

总结