Merge K Sorted Lists

Merging k sorted linked lists is one of the most discussed problems in coding interviews and system-level data merging tasks. From optimizing search engines to handling massive datasets in real-time, the ability to merge multiple sorted linked lists efficiently can be vital. In this guide, we'll explore multiple approaches including min-heap, divide and conquer, and even brute force—all while solving common Google-searched questions and offering clean Python code.

Introduction to the Merge K Sorted Lists Problem

In the Merge K Sorted Lists problem, you're given k linked lists, each already sorted in ascending order. The goal is to merge them into a single sorted linked list efficiently.

This problem frequently appears in FAANG coding interviews, competitive programming contests, and real-world data integration pipelines. From merging multiple sorted linked lists in log aggregation to building search engines that combine ranked results from different sources, mastering this technique prepares you for both interviews and production-level challenges.

Problem Explanation with Examples

To clarify what it means to merge k linked lists:

Input Example:

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list1: 1 -> 4 -> 5  
list2: 1 -> 3 -> 4  
list3: 2 -> 6

Merged Output:

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1 -> 1 -> 2 -> 3 -> 4 -> 4 -> 5 -> 6

You are expected to return a new sorted linked list that merges all input lists. This example also answers the common search:
"How to merge multiple sorted linked lists into one?"

Edge Cases to Consider:

• Some or all linked lists are empty
• All lists are null
• Lists have duplicated values

Brute Force Solution – Merge and Sort All Nodes

The simplest way to approach this:

1. Extract all nodes from the k lists
2. Store them in an array
3. Sort the array
4. Create a new sorted linked list from the array

Pros:

• Easy to understand and implement

Cons:

• Time-consuming and memory-heavy

This approach directly answers:
"How do you merge k sorted lists using sorting?"

Optimal Approach 1 – Using Min Heap (Priority Queue)

This is the most efficient and scalable way to merge multiple sorted linked lists.

How It Works:

• Insert the first node of each list into a min-heap
• Pop the smallest node, and insert its next into the heap
• Repeat until the heap is empty

Python Code (Using heapq):

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import heapq

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def mergeKLists(lists):
    heap = []
    for i, node in enumerate(lists):
        if node:
            heapq.heappush(heap, (node.val, i, node))

    dummy = ListNode()
    curr = dummy

    while heap:
        val, i, node = heapq.heappop(heap)
        curr.next = node
        curr = curr.next
        if node.next:
            heapq.heappush(heap, (node.next.val, i, node.next))

    return dummy.next

This answers:

• "How to merge k sorted linked lists using heap?"
• "What is the most optimal way to merge multiple linked lists in Python?"

Optimal Approach 2 – Divide and Conquer Strategy

How It Works:

• Recursively split the list of lists into pairs
• Merge each pair of lists using a helper function
• Combine all merged lists

This is essentially a recursive pairwise merging technique.

Python Code:

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def mergeTwoLists(l1, l2):
    if not l1 or not l2:
        return l1 or l2
    if l1.val < l2.val:
        l1.next = mergeTwoLists(l1.next, l2)
        return l1
    else:
        l2.next = mergeTwoLists(l1, l2.next)
        return l2

def mergeKLists(lists):
    if not lists:
        return None
    while len(lists) > 1:
        merged = []
        for i in range(0, len(lists), 2):
            l1 = lists[i]
            l2 = lists[i+1] if i+1 < len(lists) else None
            merged.append(mergeTwoLists(l1, l2))
        lists = merged
    return lists[0]

Answers the questions:

• "Is divide and conquer better than heap for merging?"
• "How do I merge k sorted lists recursively?"

Time and Space Complexity Analysis

Brute Force:

• Time: O(N log N), where N is total number of nodes
• Space: O(N), for array storage

Min Heap:

• Time: O(N log k), where k is number of linked lists
• Space: O(k), for the heap

Divide and Conquer:

• Time: O(N log k)
• Space: O(log k), due to recursive calls

This section addresses search queries like:

• "Merge K sorted lists time and space complexity"
• "Which merge method is fastest for k sorted lists?"

Common Mistakes and Optimization Tips

Avoid these pitfalls:

• Forgetting to check for empty lists
• Not handling None values in the heap
• Building a new list instead of modifying existing nodes
• Ignoring recursion stack limits in large inputs

Tips for better performance:

• Use min-heap when lists are long
• Use divide and conquer when lists are numerous

Real-Life Applications of Merging K Sorted Lists

This problem isn’t just academic. It's widely used in:

• Search engines combining ranked documents
• Merging database query results
• Log aggregation systems that collect real-time data from distributed servers
• Streaming platforms combining sorted data sources

Key Takeaways

• Use brute force for quick prototypes or very small datasets.
• Use min heap when each list is long but k is relatively small.
• Use divide and conquer when you have many small lists.