Introduction

Merge K Sorted Lists means:

  • combining multiple sorted linked lists into one sorted list

Goal:

  • efficiently merge all list while maintaining order

Example:

List 1:1 → 4 → 5

List 2:
1 → 3 → 4

List 3:
2 → 6

Output:
1 → 1 → 2 → 3 → 4 → 4 → 5 → 6

Explanation:

Smallest node is always selected first using Min Heap.

This problem is one of the most important applications of:

Priority Queue (Min Heap)

Constraints

0 <= K <= 10^40 <= Total Nodes <= 10^5

Approach : Min Heap

Explanations:

Explanation:

The idea is:

  • store first node of every list inside Min Heap
  • always pick smallest node
  • push next node from same list

Steps:

  1. Insert heads of all lists.
  2. Create Min Heap.
  3. Remove smallest node.
  4. Add node to answer list.
  5. Insert next node.
  6. Continue until heap becomes empty.

Observation:

Heap always contains smallest available node from each list.

This approach:

  • avoids repeated scanning
  • efficiently merges
    all sorted lists

Dry Run

Lists:1→4→5
1→3→4
2→6

Heap:
1,1,2

Remove:
1

Insert:
4

Heap:
1,2,4

Remove:
1

Insert:
3

Heap:
2,3,4

Continue...

Answer:
1→1→2→3→4→4→5→6

Practice :

Complexity Analysis :

Time Complexity:- O(N log K)Explanation :
N = total nodes
K = number of lists
Each heap operationtakes log K time.

Space Complexity:- O(K)
Explanation :
Heap stores at most one node from each list.

Why This Problem is Important

This problem builds the foundation for:

  • Priority Queues
  • K-way Merge
  • Linked Lists
  • Heap Optimization
  • Efficient Sorting

Real-World Applications

This pattern is used in:

  • External Sorting
  • Search Engines
  • Log Aggregation
  • Database Systems
  • Data Stream Processing

Common Beginner Mistakes

  • Merging lists one by one
  • Ignoring heap optimization
  • Forgetting next node insertion
  • Using full sorting
  • Incorrect linked list handling

Interview Tip

Interviewers often expect:

  • Min Heap explanation
  • K-way merge discussion
  • Linked List handling
  • Complexity analysis

Always explain:

  • why heap stores one node per list
  • why heap size remains K
  • why complexity becomes O(N log K)

Related Questions

  • Top K Frequent Elements
  • Kth Largest Element
  • Last Stone Weight
  • Find Median from Data Stream
  • K Closest Points to Origin

Final Takeaway

The Merge K Sorted Lists problem is one of the most important Priority Queue interview questions.

It teaches:

  • Min Heap usage
  • K-way merging
  • Linked List processing
  • Heap optimization

Understanding this problem builds a strong foundation for:

  • advanced heap problems
  • external sorting
  • interview-level data structures.