Introduction

Merge K Sorted Lists means combining multiple sorted linked lists into one sorted linked list.

The task is to:

  • compare nodes from all lists
  • select smallest node
  • maintain sorted order

Example:

Input:
List1:
1 -> 4 -> 7

List2:
2 -> 5 -> 8

List3:
3 -> 6 -> 9

Output:
1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9

Explanation:

Smallest node is selected from all lists at every step.Final linked list remains sorted.

This problem is one of the most important applications of:

 Min Heap / Priority Queue

Constraints

0 <= Total Nodes <= 10^5
-10^9 <= Node Value <= 10^9

Approach 1 : Brute Force (Using Array)

Explanations:

Explanation:

The idea is:

  • store all linked list values
  • sort entire array
  • rebuild linked list

Steps:

  1. Traverse all lists.
  2. Store all values.
  3. Sort array.
  4. Create merged list.

This approach works but:

  • sorting becomes expensive

So Min Heap approach is preferred.

Dry Run

Input:1 -> 4 -> 7
2 -> 5 -> 8
3 -> 6 -> 9

Array:
[1,4,7,2,5,8,3,6,9]

Sorted:
[1,2,3,4,5,6,7,8,9]

Output:
1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9

Practice :

Complexity Analysis :

Time Complexity:- O(n log n)Explanation :
Sorting all elements takes extra time.

Space Complexity:- O(n)
Explanation :
Extra array is used.

Approach 2 : Optimal Solution(Using Min Heap)

Explanations:

Explanation:

This is the most optimized and interview-preferred solution.

The idea is:

  • insert first node from each list
  • use Min Heap to get smallest node
  • insert next node from selected list

This keeps merged list sorted efficiently.

Dry Run

Input:
1 -> 4 -> 7
2 -> 5 -> 8
3 -> 6 -> 9

Heap:
1 2 3

Pick:
1

Insert:
4

Heap:
2 3 4

Continue process.

Output:
1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9

Practice :

Complexity Analysis :

Time Complexity:- O(n log k)
Explanation :
Heap operations are performed efficiently.

Space Complexity:- O(k)
Explanation :
Heap stores k elements.

Why This Problem is Important

This problem builds the foundation for:

  • Min Heap
  • Priority Queue
  • Efficient merging
  • Divide & Conquer
  • Advanced linked list operations

Real-World Applications

Merge operations are used in:

  • External sorting systems
  • Database merging
  • Search engines
  • Streaming systems
  • File processing systems

Common Beginner Mistakes

  • Incorrect heap operations
  • Forgetting next node insertion
  • Wrong sorting logic
  • Infinite loops
  • Heap overflow issues

Interview Tip

Interviewers often expect:

  • Min Heap optimization
  • efficient merging logic
  • O(n log k) solution
  • proper heap usage

Always explain:

  • why heap stores smallest nodes
  • how merging remains sorted efficiently

Related Questions

  • Merge Two Sorted Lists
  • Sort Linked List
  • Kth Largest Element
  • Priority Queue Problems
  • Merge Intervals

Final Takeaway

The Merge K Sorted Lists problem is one of the most important heap-based linked list interview problems.

It teaches:

  • Min Heap usage
  • efficient merging
  • priority queue operations
  • sorted traversal

Understanding this problem builds a strong foundation for:

  • heap algorithms
  • advanced linked list problems
  • interview-level data structure questions.