因为题目要求复杂度为O(nlogn),故可以考虑归并排序的思想。
归并排序的一般步骤为:
1)将待排序数组(链表)取中点并一分为二;
2)递归地对左半部分进行归并排序;
3)递归地对右半部分进行归并排序;
4)将两个半部分进行合并(merge),得到结果。
所以对应此题目,可以划分为三个小问题:
1)找到链表中点 (快慢指针思路,快指针一次走两步,慢指针一次走一步,快指针在链表末尾时,慢指针恰好在链表中点);
2)写出merge函数,即如何合并链表。 (见merge-two-sorted-lists 一题解析)
3)写出mergesort函数,实现上述步骤
class Solution {
public:
ListNode* findMiddle(ListNode* head){
ListNode* chaser = head;
ListNode* runner = head->next;
while(runner != NULL && runner->next != NULL){
chaser = chaser->next;
runner = runner->next->next;
}
return chaser;
}
ListNode* mergeTwoLists(ListNode* l1, ListNode* l2) {
if(l1 == NULL){
return l2;
}
if(l2 == NULL){
return l1;
}
ListNode* dummy = new ListNode(0);
ListNode* head = dummy;
while(l1 != NULL && l2 != NULL){
if(l1->val > l2->val){
head->next = l2;
l2 = l2->next;
}
else{
head->next = l1;
l1 = l1->next;
}
head = head->next;
}
if(l1 == NULL){
head ->next = l2;
}
if(l2 == NULL){
head->next = l1;
}
return dummy->next;
}
ListNode* sortList(ListNode* head) {
if(head == NULL || head ->next == NULL){
return head;
}
ListNode* middle = findMiddle(head);
ListNode* right = sortList(middle->next);
middle -> next = NULL;
ListNode* left = sortList(head);
return mergeTwoLists(left, right);
}
};