# [Leetcode C++] Merge k Sorted Lists

## Problem

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

## Analysis

We can recursively merge two lists into one list

Let k denote the number of lists
Let n denote the average length of each list
Time complexity: T(k) = 2T(k/2) + O(nk), thus we have O(nk*log k)
Space complexity:

## Solution

```/**
* struct ListNode {
*     int val;
*     ListNode *next;
*     ListNode(int x) : val(x), next(NULL) {}
* };
*/
class Solution {
public:
ListNode* mergeKLists(vector<ListNode*>& lists) {
if(lists.size() == 0) return NULL;
if(lists.size() == 1) return lists[0];

//merge each two lists into one
vector<ListNode*> newLists;
int n = lists.size();
for(int i=0; i<n/2; i++){
ListNode* currList = helper(lists[i], lists[n-1-i]);
newLists.push_back(currList);
}
if(n%2 != 0){
newLists.push_back(lists[n/2]);
}

//recursively merge all the lists
return mergeKLists(newLists);
}

//merge two lists
ListNode* helper(ListNode* l1, ListNode* l2){
while(l1 && l2){
if(l1->val <= l2->val){
l->next = l1;
l1 = l1->next;
}else{
l->next = l2;
l2 = l2->next;
}
l = l->next;
}
l->next = l1? l1 : l2;