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

sort_list.cpp

/**
 * 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) {
            return head;
        }
        return sortList(head, NULL);
    }
private:
    ListNode *sortList(ListNode *head, ListNode *sentinel) {
        if (head->next == sentinel) { // only 1 node presents
            head->next = NULL;
            return head;
        }
        
        ListNode *mid;
        ListNode *end;
        mid = end = head;
        while (end != sentinel) {
            mid = mid->next;
            end = end->next;
            if (end == sentinel) {
                break;
            } else {
                end = end->next;
            }
        }
        
        ListNode *a = sortList(head, mid);
        ListNode *b = sortList(mid, sentinel);
        
        // INVARIANT: [head, current] are all in order
        // TERMINATION: a == NULL && b == NULL
        head = new ListNode(-1);
        ListNode *current = head;
        while (a != NULL || b != NULL) {
            if (a == NULL || (b != NULL && b->val < a->val)) {
                current->next = b;
                b = b->next;
            } else {
                current->next = a;
                a = a->next;
            }
            current = current->next;
        }
        current->next = NULL;
        
        return head->next;
    }
};