Merge k Sorted Linked Lists

You are given an array of k sorted linked lists. Your task is to merge all these sorted lists into one single sorted linked list. This is a common problem in data structure and algorithm design, often encountered when dealing with large datasets that are partitioned and sorted independently. Efficiently merging these lists is crucial for maintaining order and facilitating further processing.

Problem Description

Given an array lists containing k linked lists, where each linked list is already sorted in ascending order, merge all the linked lists into a single sorted linked list and return it.

Key Requirements:

• The output linked list must be sorted in ascending order.
• The merged list should contain all nodes from the original k lists.
• You should handle empty input lists gracefully.

Expected Behavior:

The function should take an array of linked lists as input and return the head of the newly merged, sorted linked list.

Edge Cases to Consider:

• The input array lists might be empty.
• Some of the linked lists within the input array might be empty.
• All linked lists might be empty.
• There might be only one linked list in the input array.

Examples

Example 1:

Input: lists = [[1,4,5],[1,3,4],[2,6]]
Output: [1,1,2,3,4,4,5,6]
Explanation:
The three 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: []
Explanation: An empty input array results in an empty merged list.

Example 3:

Input: lists = [[]]
Output: []
Explanation: An array containing only an empty linked list results in an empty merged list.

Example 4:

Input: lists = [[10]]
Output: [10]
Explanation: Merging a single list simply returns that list.

Constraints

• k will be the number of linked lists in the input array.
• 0 <= k <= 10^4
• The number of nodes in each linked list will be between 0 and 500.
• The total number of nodes across all linked lists will not exceed 10^4.
• The value of each node will be within the range -10^4 <= Node.val <= 10^4.
• Each linked list is sorted in ascending order.

Notes

• A linked list node typically has a value (or data) and a next pointer. For pseudocode, we can assume a structure like ListNode { value: Integer, next: ListNode }.
• Consider the time and space complexity of your solution. How can you efficiently merge multiple sorted lists without resorting to simply concatenating and then sorting?
• Think about data structures that can help you efficiently find the smallest element among the current heads of all k lists.