23

23. Merge k Sorted Lists (Hard)

You are given an array of k linked-lists lists, each linked-list is sorted in ascending order.

Merge all the linked-lists into one sorted linked-list and return it.

 

Example 1:

Input: lists = [[1,4,5],[1,3,4],[2,6]]
Output: [1,1,2,3,4,4,5,6]
Explanation: The linked-lists are:
[
  1->4->5,
  1->3->4,
  2->6
]
merging them into one sorted list:
1->1->2->3->4->4->5->6

Example 2:

Input: lists = []
Output: []

Example 3:

Input: lists = [[]]
Output: []

 

Constraints:

• k == lists.length
• 0 <= k <= 10^4
• 0 <= lists[i].length <= 500
• -10^4 <= lists[i][j] <= 10^4
• lists[i] is sorted in ascending order.
• The sum of lists[i].length won't exceed 10^4.

Companies:
Facebook, Amazon, Microsoft, Google, ByteDance, Yandex, Apple, Adobe, VMware, Bloomberg, eBay, tiktok, Indeed, Oracle, Walmart Labs, Qualtrics, Sprinklr, Cruise Automation

Related Topics:
Linked List, Divide and Conquer, Heap (Priority Queue), Merge Sort

Similar Questions:

• Merge Two Sorted Lists (Easy)
• Ugly Number II (Medium)

Solution 1. Heap

// OJ: https://leetcode.com/problems/merge-k-sorted-lists/
// Author: github.com/lzl124631x
// Time: O(NlogK)
// Space: O(K)
class Solution {
public:
    ListNode* mergeKLists(vector<ListNode*>& lists) {
        ListNode dummy, *tail = &dummy;
        auto cmp = [](auto a, auto b) { return a->val > b->val; };
        priority_queue<ListNode*, vector<ListNode*>, decltype(cmp)> q(cmp);
        for (auto list : lists) {
            if (list) q.push(list); // avoid pushing NULL list.
        }
        while (q.size()) {
            auto node = q.top();
            q.pop();
            if (node->next) q.push(node->next);
            tail->next = node;
            tail = node;
        }
        return dummy.next;
    }
};

Solution 2. Divide And Conquer (Merge Sort)

// OJ: https://leetcode.com/problems/merge-k-sorted-lists/
// Author: github.com/lzl124631x
// Time: O(NlogK)
// Space: O(1)
class Solution {
private:
    ListNode* mergeTwoLists(ListNode* a, ListNode* b) {
        ListNode head, *tail = &head;
        while (a && b) {
            if (a->val < b->val) { tail->next = a; a = a->next; }
            else { tail->next = b; b = b->next; }
            tail = tail->next;
        }
        tail->next = a ? a : b;
        return head.next;
    }
public:
    ListNode* mergeKLists(vector<ListNode*>& lists) {
        if (lists.empty()) return nullptr;
        for (int N = lists.size(); N > 1; N = (N + 1) / 2) {
            for (int i = 0; i < N / 2; ++i) {
                lists[i] = mergeTwoLists(lists[i], lists[N - 1 - i]);
            }
        }
        return lists[0];
    }
};