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

Example 1:

Input: 4->2->1->3
Output: 1->2->3->4

Example 2:

Input: -1->5->3->4->0
Output: -1->0->3->4->5

解法：歸並排序。由於有時間和空間復雜度的要求。把鏈表從中間分開，遞歸下去，都最後兩個node時開始合並，返回上一層繼續合並，直到結束。找中間點的方法可以用快慢指針，快指針走2步，慢指針走1步。也可以求出鏈表長度，再分開鏈表。

Java:

public class Solution {
  
  public ListNode sortList(ListNode head) {
    if (head == null || head.next == null)
      return head;
        
    // step 1. cut the list to two halves
    ListNode prev = null, slow = head, fast = head;
    
    while (fast != null && fast.next != null) {
      prev = slow;
      slow = slow.next;
      fast = fast.next.next;
    }
    
    prev.next = null;
    
    // step 2. sort each half
    ListNode l1 = sortList(head);
    ListNode l2 = sortList(slow);
    
    // step 3. merge l1 and l2
    return merge(l1, l2);
  }
  
  ListNode merge(ListNode l1, ListNode l2) {
    ListNode l = new ListNode(0), p = l;
    
    while (l1 != null && l2 != null) {
      if (l1.val < l2.val) {
        p.next = l1;
        l1 = l1.next;
      } else {
        p.next = l2;
        l2 = l2.next;
      }
      p = p.next;
    }
    
    if (l1 != null)
      p.next = l1;
    
    if (l2 != null)
      p.next = l2;
    
    return l.next;
  }

}

Python:

class Solution(object):
    def merge(self, h1, h2):
        dummy = tail = ListNode(None)
        while h1 and h2:
            if h1.val < h2.val:
                tail.next, tail, h1 = h1, h1, h1.next
            else:
                tail.next, tail, h2 = h2, h2, h2.next
    
        tail.next = h1 or h2
        return dummy.next
    
    def sortList(self, head):
        if not head or not head.next:
            return head
    
        pre, slow, fast = None, head, head
        while fast and fast.next:
            pre, slow, fast = slow, slow.next, fast.next.next
        pre.next = None

        return self.merge(*map(self.sortList, (head, slow)))　

C++:

class Solution {
public:
	ListNode *sortList(ListNode *head) {
		if(!head || !(head->next)) return head;
		
		//get the linked list‘s length
		ListNode* cur = head;
		int length = 0;
		while(cur){
			length++;
			cur = cur->next;
		}
		
		ListNode dummy(0);
		dummy.next = head;
		ListNode *left, *right, *tail;
		for(int step = 1; step < length; step <<= 1){
			cur = dummy.next;
			tail = &dummy;
			while(cur){
				left = cur;
				right = split(left, step);
				cur = split(right,step);
				tail = merge(left, right, tail);
			}
		}
		return dummy.next;
	}
private:
	/**
	 * Divide the linked list into two lists,
     * while the first list contains first n ndoes
	 * return the second list‘s head
	 */
	ListNode* split(ListNode *head, int n){
		//if(!head) return NULL;
		for(int i = 1; head && i < n; i++) head = head->next;
		
		if(!head) return NULL;
		ListNode *second = head->next;
		head->next = NULL;
		return second;
	}
	/**
	  * merge the two sorted linked list l1 and l2,
	  * then append the merged sorted linked list to the node head
	  * return the tail of the merged sorted linked list
	 */
	ListNode* merge(ListNode* l1, ListNode* l2, ListNode* head){
		ListNode *cur = head;
		while(l1 && l2){
			if(l1->val > l2->val){
				cur->next = l2;
				cur = l2;
				l2 = l2->next;
			}
			else{
				cur->next = l1;
				cur = l1;
				l1 = l1->next;
			}
		}
		cur->next = (l1 ? l1 : l2);
		while(cur->next) cur = cur->next;
		return cur;
	}
};

[LeetCode] 148. Sort List 鏈表排序