148. Sort List (List)

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(0);
        ListNode* dummyHead2 = new ListNode(0);
        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(0);
        ListNode* dummyHead2 = new ListNode(0);
        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;
    }

};