#include "stdafx.h"
#include "malloc.h"
typedef struct Node
{
	char data;
	Node *next;
}List;

// 創建單鏈表
void CreateList(List *&L, char a[], int n)
{
	List *s,*r;
	L = (List *)malloc(sizeof(List));
	L->next = NULL;
	r = L;
	for (int i = 0; i < n; i++)
	{
		s = (List *)malloc(sizeof(List));
		s->data = a[i];
		r->next = s;
		r = s;
	}
	r->next = NULL;
}

// 使用了排序算法中的插入排序
void Sort(List *&head)
{
	List *p = head->next, *q, *r; // p指向第一個節點
	if(p!=NULL)
	{
		r = p->next; // r指向第二個節點
		p->next = NULL; // p的後繼節點為NULL
		p = r; // p指向第一個節點
		while (p!=NULL)
		{
			r = p->next; 
			q = head;
			while (q->next!=NULL &&q->next->data<p->data)
			{
				q = q->next;
			}
			p->next = q->next;
			q->next = p;
			p = r;
		}
	}
}

// 求兩個集合並集
void Union(List *La, List *Lb, List *&Lc)
{
	List *la = La->next, *lb = Lb->next,*tc,*s;
	Lc = (List *)malloc(sizeof(List));
	tc = Lc;
	// 在進行比較
	if (la != NULL && lb != NULL)
	{
		while (la != NULL && lb != NULL)
		{
			s = (List *)malloc(sizeof(List));
			if (la->data > lb->data)
			{
				// la節點大於lb節點
				s->data = lb->data;
				tc->next = s;
				tc = s;
				lb = lb->next;
			}
			else if(la->data<lb->data)
			{
				 // la節點小於lb節點
				s->data = la->data;
				tc->next = s;
				tc = s;
				la = la->next;
			}
			else
			{
				s->data = la->data;
				tc->next = s;
				tc = s;
				la = la->next;
				lb = lb->next;
			}
		}
	}

	//  剩余節點(la與lb必定有一個是NULL)
	if (lb != NULL)
	{
		la = lb;
	}
	while (la!=NULL)
	{
		s = (List *)malloc(sizeof(List));
		s->data = la->data;
		tc->next = s;
		tc = s;
		la = la->next;
	}
	tc->next = NULL;
}

// 求兩個集合的並集
void  InterSect(List *La, List *Lb, List *&Lc)
{
	List *la = La->next, *lb,*tc, *s;
	Lc = (List *)malloc(sizeof(List));
	tc = Lc;
	while (la!=NULL)
	{
		lb = Lb->next;
		// 根據鏈表為有序鏈表過濾一部分比較節點
		while (lb!=NULL && lb->data<la->data)
		{
			lb = lb->next;
		}
		if (lb != NULL && lb->data == la->data)
		{
			s = (List *)malloc(sizeof(List));
			s->data = la->data;
			tc->next = s;
			tc = s;
		}
		la = la->next;
	}
	tc->next = NULL;
}

// 求差集，即a-b，去掉a鏈表中與b鏈表的交集
void Subs(List *La, List *Lb, List *&Lc)
{
	List *la = La->next, *lb, *tc, *s;
	Lc = (List *)malloc(sizeof(List));
	tc = Lc;
	while (la!=NULL)
	{
		lb = Lb->next;
		// 根據鏈表為有序鏈表過濾一部分比較節點
		while (lb!=NULL && lb->data<la->data)
		{
			lb = lb->next;
		}
		// 去掉Lb鏈表與La鏈表的交集部分
		if (!(lb != NULL &&la->data == lb->data))
		{
			s = (List *)malloc(sizeof(List));
			s->data = la->data;
			tc->next = s;
			tc = s;
		}
		la = la->next;
	}
	tc->next = NULL;
}

　　1、使用單鏈表對集合進行交、並、差的運算，重點在於對單鏈表進行排序，排序後的單鏈表在進行運算，可以減少節點的比較優化時間復雜度。

有序單鏈表的（交、並、差）運算