Sort List

Sort a linked list in O(nlogn) time using constant space complexity.

思路：要求常数空间，并且时间复杂度o(nlogn).可以采用归并排序。

#include <iostream>
using namespace std;

struct LinkNode{
	int data;
	LinkNode *next;
	LinkNode(int x):data(x),next(){}
};

//合并两个有序的list
LinkNode* mergeTwoList(LinkNode *l1,LinkNode *l2)
{
	LinkNode *p1 = l1,*p2 = l2,*head,*pre;
	LinkNode *dummy = new LinkNode(-1);
	pre = dummy;
	
	while(p1!=NULL && p2!=NULL)
	{
		if(p1->data < p2->data)
		{
			pre->next = p1;
			p1 = p1->next;			
		}
		else
		{
			pre->next = p2;
			p2 = p2->next;
		}
		pre = pre->next;
	}

	if(p1!=NULL)
	{
		pre->next = p1;
	}

	if(p2!=NULL)
	{
		pre->next = p2;
	}


	head = dummy->next;
	delete dummy;
	return head;
}

//要求常数空间，并且时间复杂度o(nlogn).可以采用归并排序。
LinkNode *sortList(LinkNode *head)
{
	if(head==NULL || head->next == NULL) return head;

	//找到链表的中点。这里可以用快慢指针的方法。
	LinkNode *fast =head,*slow = head;
	while(fast->next !=NULL && fast->next->next!=NULL)
	{
		fast = fast->next->next;
		slow = slow->next;
	}

	//从中点断开成两个List
	fast = slow;
	slow = slow->next;
	fast->next = NULL;

	LinkNode *l1 = sortList(head);//递归，左半部分有序
	LinkNode *l2 = sortList(slow);//递归，右半部分有序
	return mergeTwoList(l1,l2);//合并
}

//对链表初始化
LinkNode *initLink(LinkNode *dummy,int array[],int len)
{
	LinkNode *head,*tmp;//dummy表示哑节点，head一般表示头指针，它指向第一个节点。
	tmp = dummy;
	
	//用尾插法
	for(int i = 0;i < len;i++)
	{
		LinkNode *p = new LinkNode(array[i]);
		tmp->next = p;
		tmp = tmp->next;
	}
	
	head = dummy->next;
	delete dummy;
	return head;
}

//显示list
void showList(LinkNode *head)
{
	while(head)
	{
		printf("%d ",head->data);
		head = head->next;
	}
	printf("\n");
}

//摧毁链表
void destroyList(LinkNode *head)
{
	LinkNode *dummy = new LinkNode(-1);
	dummy->next = head;
	LinkNode *pre,*cur,*tmp;
	pre = dummy;
	cur = pre->next;
	while(cur)
	{
		tmp = cur->next;
		pre->next = tmp;
		delete cur;
		cur = tmp;
	}
	delete dummy;
	printf("The list has been destroyed!\n");
}

void main()
{
	LinkNode *dummy1 = new LinkNode(-1);
	int array1[] = {2,5,1,4,8,12,43,56,15,89,65,120,44,38};
	int len1 = sizeof(array1)/sizeof(int);
	LinkNode *head1 = initLink(dummy1,array1,len1);
	showList(head1);

	head1 = sortList(head1);
	showList(head1);

	destroyList(head1);
}