Merge k Sorted Lists

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

思路：

二分转化为两个链表的归并，复杂度为（kn）。

代码：

 1     ListNode *merge2Lists(ListNode *l1, ListNode *l2){
 2         if(l1 == NULL)
 3             return l2;
 4         if(l2 == NULL)
 5             return l1;
 6         ListNode *result, *head = NULL;
 7         if(l1->val < l2->val){
 8             head = l1;
 9             l1 = l1->next;
10         }            
11         else{
12             head = l2;
13             l2 = l2->next;
14         }
15         result = head;
16         while(l1 && l2){
17             if(l1->val < l2->val){
18                 result->next = l1;
19                 l1 = l1->next;
20             }
21             else{
22                 result->next = l2; 
23                 l2 = l2->next;
24             }
25             result = result->next;
26         }
27         if(l1 == NULL)
28             result->next = l2;
29         else
30             result->next = l1;
31         return head;
32     }
33     ListNode *mergeKLists(vector<ListNode *> &lists, int start, int end){
34         if(start >= end)
35             return NULL;
36         if(end == start+1)
37             return lists[start];
38         if(end == start+2){
39             ListNode *l1 = lists[start];
40             ListNode *l2 = lists[start+1];
41             return merge2Lists(l1, l2);
42         }
43         else{
44             ListNode *l1 = mergeKLists(lists, start, (start+end)/2);
45             ListNode *l2 = mergeKLists(lists, (start+end)/2, end);
46             return merge2Lists(l1, l2);
47         }
48     }
49     ListNode *mergeKLists(vector<ListNode *> &lists) {
50         // IMPORTANT: Please reset any member data you declared, as
51         // the same Solution instance will be reused for each test case.
52         return mergeKLists(lists, 0, lists.size());
53     }

另外一种方法是使用堆，可是使得复杂度变为O（nlgk）。这里堆可以自己实现，也可以用STL中的priority_queue。

在下面代码，一方面要学习priority_queue的使用，另一方面要注意那个虚头head的使用，这样可以避免对head是否为NULL的判断。另外一种解决的类似方法的手段是用一个**指针指向head，然后不断更新**，最后返回**指针指向的指针。

 1     struct cmp{
 2         bool operator()(ListNode *a, ListNode *b){
 3             return a->val > b->val;
 4         }
 5     };
 6     ListNode *mergeKLists(vector<ListNode *> &lists) {
 7         // IMPORTANT: Please reset any member data you declared, as
 8         // the same Solution instance will be reused for each test case.
 9         priority_queue<ListNode*, vector<ListNode*>, cmp > pq;
10         int i;
11         for(i = 0; i < lists.size(); i++){
12             if(lists[i])
13                 pq.push(lists[i]);
14         }
15         ListNode *head = new ListNode(0), *cur = head;
16         while(!pq.empty()){
17             ListNode *tmp = pq.top();
18             cur->next = tmp;
19             cur = cur->next;
20             pq.pop();
21             if(tmp->next)
22                 pq.push(tmp->next);
23         }
24         return head->next;
25     }