🌟 Introduction
Merging multiple sorted linked lists is a very popular problem in data structures and algorithms. If you have several lists where each one is already sorted, the goal is to merge them into one single sorted linked list while keeping the order intact. This problem is common in coding interviews, competitive programming, and real-world applications like combining search results or merging logs in large systems.
In this article, we’ll explore different ways to merge k sorted linked lists. We will explain each method step by step, share examples, discuss its advantages and disadvantages, and finally identify the most efficient solution.
🧮 Method 1. Brute Force (Concatenate and Sort)
How It Works
This is the simplest method. You take all the elements from all k linked lists, put them into one array, sort the array, and then create a new linked list from the sorted elements.
Example
Suppose you have three linked lists:
List1: 1 → 4 → 5
List2: 1 → 3 → 4
List3: 2 → 6
First, combine them into one array → [1, 4, 5, 1, 3, 4, 2, 6].
Then, sort the array → [1, 1, 2, 3, 4, 4, 5, 6].
Finally, build a new linked list → 1 → 1 → 2 → 3 → 4 → 4 → 5 → 6 ✅
Pros and Cons
This method is fine for small datasets but inefficient for larger ones.
🏗️ Method 2/.Compare One by One
How It Works
In this method, you maintain pointers for each linked list. At each step, you compare the first (head) elements of all lists and pick the smallest one to add to the result. You then move the pointer forward in that list.
Example
For lists: (1, 1, 2), the smallest is 1. Add 1 to the result. Next comparison: (4, 1, 2) → pick 1 again. Continue until all lists are empty.
Pros and Cons
✅ No need for extra memory apart from the new linked list.
❌ Very slow if k is large because you compare across all k lists every time.
Time Complexity = O(kN), which becomes inefficient when k is big.
This method is okay when k is very small, but not practical for larger values of k.
⚡ Method 3. Using a Min-Heap (Most Efficient in Practice)
How It Works
A Min-Heap (priority queue) is a data structure that helps you quickly find the smallest element. By using a heap, you can efficiently merge the lists.
Insert the first node (head) of each list into the Min-Heap.
Remove the smallest element from the heap and add it to the merged result.
If the removed element has a next node, insert it into the heap.
Keep repeating until the heap is empty.
Example
For the three lists:
List1: 1 → 4 → 5
List2: 1 → 3 → 4
List3: 2 → 6
Start with heap = [1, 1, 2].
Extract 1 → result = [1], insert 4 → heap = [1, 2, 4].
Extract 1 → result = [1, 1], insert 3 → heap = [2, 4, 3].
Continue until heap is empty.
Final result = 1 → 1 → 2 → 3 → 4 → 4 → 5 → 6 ✅
Pros and Cons
✅ Very efficient for large k.
✅ Time Complexity = O(N log k).
✅ Widely used in coding interview solutions and practical systems.
❌ Requires extra memory for the heap (O(k)).
This method is considered the most practical and efficient.
🏗️ Method 4. Divide and Conquer
How It Works
This method works similar to the merge sort technique:
Pair up the k lists and merge them two at a time.
Repeat the process until only one list remains.
Example
Merge List1 and List2 → Result = [1, 1, 3, 4, 4, 5].
Merge this result with List3 → Final = [1, 1, 2, 3, 4, 4, 5, 6]. ✅
Pros and Cons
✅ Reduces the number of comparisons.
✅ Time Complexity = O(N log k).
✅ Efficient and elegant.
❌ Slightly harder to implement compared to Min-Heap.
This method is also considered one of the most efficient solutions.
📊 Comparison of All Methods
| Method | Time Complexity | Space Complexity | Best Use Case |
|---|
| Brute Force (Sort) | O(N log N) | O(N) | Small datasets, very simple code |
| Compare One by One | O(kN) | O(1) | When k is very small |
| Min-Heap | O(N log k) | O(k) | Best practical method, works for large k |
| Divide and Conquer | O(N log k) | O(1) or O(log k) | Efficient and scalable, good for interviews |
📌 Summary
The most efficient way to merge k sorted linked lists is by using either the Min-Heap method or the Divide and Conquer approach. Both methods achieve a time complexity of O(N log k), making them suitable for large datasets and coding interview problems. While the brute force and one-by-one comparison methods are easier to implement, they are not efficient for bigger inputs.
If you are preparing for coding interviews, learning both the Min-Heap and Divide and Conquer solutions will give you a strong edge. These approaches not only solve this problem but also improve your understanding of priority queues, merging techniques, and divide-and-conquer strategies that are widely used in computer science and real-world applications.