Merge k Sorted Lists

Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity.

算法一，自底至頂遞歸。

時間復雜度為O(nlogk)。

空間復雜度為O(k)。

此算法在leetcode上實際執行時間為 144ms (130 test cases)。

/**
 * Definition for singly-linked list.
 * struct ListNode {
 *     int val;
 *     ListNode *next;
 *     ListNode(int x) : val(x), next(NULL) {}
 * };
 */
class Solution {
public:
    ListNode *mergeKLists(vector &lists) {
        if (lists.empty()) return 0;
        if (lists.size() == 1) return lists.back();

        vector l;
        while (!lists.empty()) {
                if (lists.size() == 1) {
                        l.push_back(lists.back());
                        lists.pop_back();
                }
                else {
                        ListNode *p = lists.back();
                        lists.pop_back();
                        ListNode *q = lists.back();
                        lists.pop_back();

                        l.push_back(merge(p, q));
                }
        }

        return mergeKLists(l);
    }

    ListNode *merge(ListNode *p,ListNode *q) {
        ListNode fake(0);
        ListNode *m = &fake;

        while (p && q) {
                if (p->val < q->val) {
                        m->next = p;
                        p = p->next;
                }
                else {
                        m->next = q;
                        q = q->next;
                }
                m = m->next;
        }

        m->next  = p ? p : q;
        return fake.next;
    }
};