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

法I:快排。快排的难点在于切分序列。从头扫描,碰到>=target的元素,停止;从第二个字串扫描,碰到<=target的元素停止;交换这两个元素。这样的好处是:当数据元素都相同时,也能控制在logn次递归(否则需要O(n))。另外,要注意避免子序列只剩两个相等元素时的死循环。

/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
ListNode* sortList(ListNode* head) {
if(head == NULL || head->next==NULL) return head; //only one element ListNode* dummyHead1 = new ListNode();
ListNode* dummyHead2 = new ListNode();
ListNode* fastNode = dummyHead1;
ListNode* slowNode = dummyHead1;
ListNode* cur1, *cur2;
int tmp;
dummyHead1->next = head; //fast, slow pointer to find the middle point
while(fastNode->next){
fastNode = fastNode->next;
if(fastNode->next) fastNode = fastNode->next;
else break;
slowNode = slowNode->next; //slowNode always point to the element before center(odd number)
// or the left center (even number)
} //partition the sequence into two halves
dummyHead2->next = slowNode->next;
slowNode->next=NULL;
cur1 = dummyHead1;
cur2 = dummyHead2->next;
while(cur1->next&&cur2->next){
//stop when find an element in first half, value of whihch >= target
while(cur1->next && cur1->next->val < dummyHead2->next->val) cur1 = cur1->next;
//stop when find an element in second half, value of which <= target
while(cur2->next && cur2->next->val > dummyHead2->next->val) cur2 = cur2->next;
if(!cur1->next || !cur2->next ) break;
tmp = cur1->next->val;
cur1->next->val = cur2->next->val;
cur2->next->val = tmp;
cur1 = cur1->next;
cur2 = cur2->next; }
while(cur1->next){
//stop when find an element in first half, value of which > target
//>= may lead to endless recursion if two equal elements left
while(cur1->next && cur1->next->val <= dummyHead2->next->val) cur1 = cur1->next;
if(!cur1->next) break;
cur2->next = cur1->next;
cur1->next = cur1->next->next;
cur2 = cur2->next;
cur2->next = NULL;
}
while(cur2->next){
//stop when find an element in second half, value of which < target
//<= may lead to endless recursion if two equal elements left
while(cur2->next && cur2->next->val >= dummyHead2->next->val) cur2 = cur2->next;
if(!cur2->next) break;
cur1->next = cur2->next;
cur2->next = cur2->next->next;
cur1 = cur1->next;
cur1->next = NULL;
} //cascade two halves
head = sortList(dummyHead1->next);
cur2 = sortList(dummyHead2->next);
if(head==NULL) return cur2;
cur1 = head;
while(cur1->next){
cur1 = cur1->next;
}
cur1->next = cur2;
return head;
} };

法II: 归并排序。由于是List,归并排序的好处是不用额外申请O(n)的空间

/**
* Definition for singly-linked list.
* struct ListNode {
* int val;
* ListNode *next;
* ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
ListNode* sortList(ListNode* head) {
if(head == NULL || head->next==NULL) return head; //only one element ListNode* dummyHead1 = new ListNode();
ListNode* dummyHead2 = new ListNode();
ListNode* fastNode = dummyHead1;
ListNode* slowNode = dummyHead1;
ListNode* cur1, *cur2, *cur;
dummyHead1->next = head; //fast, slow pointer to find the middle point
while(fastNode->next){
fastNode = fastNode->next;
if(fastNode->next) fastNode = fastNode->next;
else break;
slowNode = slowNode->next; //slowNode always point to the element before center(odd number)
// or the left center (even number)
}
dummyHead2->next = slowNode->next;
slowNode->next = NULL; //recursion
cur1 = sortList(dummyHead1->next);
cur2 = sortList(dummyHead2->next); //merge
cur = dummyHead1;
while(cur1 && cur2){
if(cur1->val <= cur2->val){
cur->next = cur1;
cur1 = cur1->next;
}
else{
cur->next = cur2;
cur2 = cur2->next;
}
cur = cur->next;
}
if(cur1){
cur->next = cur1;
}
else{
cur->next = cur2;
}
return dummyHead1->next;
} };

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