有序单链表的（交并差）运算

Posted 2021-02-03 tuqunfu

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

// 创建单链表
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指向第一个节点
	if(p!=NULL)
	{
		r = p->next; // r指向第二个节点
		p->next = NULL; // p的后继节点为NULL
		p = r; // p指向第一个节点
		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;
		}
	}
}

// 求两个集合并集
void Union(List *La, List *Lb, List *&Lc)
{
	List *la = La->next, *lb = Lb->next,*tc,*s;
	Lc = (List *)malloc(sizeof(List));
	tc = Lc;
	// 在进行比较
	if (la != NULL && lb != NULL)
	{
		while (la != NULL && lb != NULL)
		{
			s = (List *)malloc(sizeof(List));
			if (la->data > lb->data)
			{
				// la节点大于lb节点
				s->data = lb->data;
				tc->next = s;
				tc = s;
				lb = lb->next;
			}
			else if(la->data<lb->data)
			{
				 // la节点小于lb节点
				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;
			}
		}
	}

	//  剩余节点(la与lb必定有一个是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;
}

// 求两个集合的并集
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;
		// 根据链表为有序链表过滤一部分比较节点
		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链表中与b链表的交集
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;
		// 根据链表为有序链表过滤一部分比较节点
		while (lb!=NULL && lb->data<la->data)
		{
			lb = lb->next;
		}
		// 去掉Lb链表与La链表的交集部分
		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、使用单链表对集合进行交、并、差的运算，重点在于对单链表进行排序，排序后的单链表在进行运算，可以减少节点的比较优化时间复杂度。