# How to Merge K Sorted Linked Lists: Efficient Min-Heap Methods Explained

> Learn efficient methods to merge k sorted linked lists using a min-heap for O(N log k) time complexity. Discover how to extract smallest nodes and optimize merging.

- Repository: [Kevin Naughton Jr./interviews](https://github.com/kdn251/interviews)
- Tags: how-to-guide
- Published: 2026-03-04

---

**The most efficient way to merge k sorted linked lists uses a min-heap (priority queue) to achieve O(N log k) time complexity by always extracting the smallest available node and pushing its successor back onto the heap.**

Merging k sorted linked lists is a fundamental algorithmic challenge frequently encountered in technical interviews at major tech companies. The **kdn251/interviews** repository provides a battle-tested Java implementation that leverages a priority queue to solve this problem with optimal complexity. This guide breaks down the efficient methods for merging k sorted linked lists, analyzing the source code directly from the repository's solutions.

## Min-Heap (Priority Queue) Approach

The optimal solution utilizes a **min-heap** to track the smallest available node across all k lists simultaneously. This approach ensures that each insertion and extraction operation costs O(log k), avoiding the repeated linear scans required by naive comparison methods.

### Algorithm Implementation

The implementation in [`leetcode/linked-list/MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/leetcode/linked-list/MergeKSortedLists.java) follows this exact strategy:

1. Initialize a `PriorityQueue` ordered by node value with capacity `k`
2. Seed the heap with the head node of each non-null list
3. Repeatedly extract the minimum node and append it to the result list
4. If the extracted node has a successor, push that next node into the heap
5. Continue until no nodes remain in the heap

### Complexity Analysis

- **Time Complexity**: **O(N log k)**, where N is the total number of nodes across all lists. Each node is pushed and popped exactly once, with each heap operation costing O(log k).
- **Space Complexity**: **O(k)** for the heap storage, since at most one node from each of the k lists resides in the queue at any time. The output list reuses existing nodes, requiring only O(1) auxiliary space.

### Source Code from kdn251/interviews

```java
// File: leetcode/linked-list/MergeKSortedLists.java
public class MergeKSortedLists {
    public ListNode mergeKLists(ListNode[] lists) {
        if (lists == null || lists.length == 0) {
            return null;
        }

        // Min-heap ordered by node value
        PriorityQueue<ListNode> queue = new PriorityQueue<>(lists.length,
            (o1, o2) -> Integer.compare(o1.val, o2.val));

        ListNode dummy = new ListNode(0);
        ListNode tail = dummy;

        // Seed heap with the first node of each list
        for (ListNode node : lists) {
            if (node != null) {
                queue.add(node);
            }
        }

        // Extract min, attach to result, and push next node from the same list
        while (!queue.isEmpty()) {
            tail.next = queue.poll();
            tail = tail.next;
            if (tail.next != null) {
                queue.add(tail.next);
            }
        }

        return dummy.next;
    }
}

```

## Divide-and-Conquer Alternative

While the kdn251/interviews repository implements the heap solution, a **divide-and-conquer** method offers another O(N log k) approach. This technique recursively merges pairs of lists using the standard linear-time merge routine for two sorted lists.

Although asymptotically equivalent, the divide-and-conquer method typically incurs higher constant factors due to repeated traversal of intermediate lists and recursive overhead. The min-heap solution is generally preferred in production Java code because `PriorityQueue` provides a concise, highly optimized implementation with better cache locality.

## Edge Case Handling

The repository's implementation demonstrates robust handling of boundary conditions common in interview scenarios:

- **Empty Input Arrays**: The method returns `null` immediately when `lists` is null or `lists.length == 0`
- **Null List Heads**: The seeding loop checks `if (node != null)` before adding to the queue, preventing `NullPointerException` when individual lists are empty
- **Dummy Node Pattern**: The `ListNode dummy = new ListNode(0)` technique simplifies pointer manipulation and eliminates special-case logic for initializing the result list's head

## Practical Usage Examples

### Example 1: Merging Three Sorted Lists

```java
// Build three sorted lists: [1→4→5], [1→3→4], [2→6]
ListNode l1 = new ListNode(1);
l1.next = new ListNode(4);
l1.next.next = new ListNode(5);

ListNode l2 = new ListNode(1);
l2.next = new ListNode(3);
l2.next.next = new ListNode(4);

ListNode l3 = new ListNode(2);
l3.next = new ListNode(6);

// Merge them
MergeKSortedLists merger = new MergeKSortedLists();
ListNode[] lists = new ListNode[]{l1, l2, l3};
ListNode merged = merger.mergeKLists(lists);

// Print merged list: 1 → 1 → 2 → 3 → 4 → 4 → 5 → 6
while (merged != null) {
    System.out.print(merged.val + (merged.next != null ? " → " : ""));
    merged = merged.next;
}

```

### Example 2: Handling Empty or Null Lists

```java
ListNode[] lists = new ListNode[]{null, null};
ListNode result = new MergeKSortedLists().mergeKLists(lists);
// result is null (no nodes to merge)

```

## Repository File Locations

The min-heap implementation appears consistently across multiple company-specific interview packages in the kdn251/interviews repository:

- [`leetcode/linked-list/MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/leetcode/linked-list/MergeKSortedLists.java) — Core LeetCode solution
- [`company/uber/MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/company/uber/MergeKSortedLists.java) — Uber interview preparation variant  
- [`company/linkedin/MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/company/linkedin/MergeKSortedLists.java) — LinkedIn-style problem set
- [`company/twitter/MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/company/twitter/MergeKSortedLists.java) — Twitter interview package

Each file contains identical algorithmic logic, demonstrating the universal applicability of the priority queue approach for efficiently merging k sorted linked lists across different interview contexts.

## Summary

- The **min-heap approach** provides the optimal **O(N log k)** time complexity for merging k sorted linked lists, making it the standard solution for this interview problem.
- The `mergeKLists` method in [`leetcode/linked-list/MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/leetcode/linked-list/MergeKSortedLists.java) implements this pattern using Java's `PriorityQueue` with a lambda comparator `(o1, o2) -> Integer.compare(o1.val, o2.val)`.
- **Space efficiency** is maintained at **O(k)** by storing at most one node from each list in the heap at any given time, reusing existing list nodes for the output.
- Robust **edge-case handling** ensures the solution gracefully manages empty inputs, null lists, and varying list lengths without throwing exceptions.
- The **dummy node pattern** simplifies result list construction by eliminating special-case checks for the head pointer.

## Frequently Asked Questions

### What is the time complexity of merging k sorted linked lists?

The optimal time complexity is **O(N log k)**, where N represents the total number of nodes across all lists and k is the number of lists. This is achieved by using a min-heap to track the smallest available node, ensuring each of the N nodes is inserted and extracted exactly once with O(log k) cost per operation.

### Why use a min-heap instead of merging lists sequentially one by one?

A min-heap avoids the **O(N * k)** time complexity of naive sequential merging, where repeatedly merging the accumulated result with the next list requires re-scanning previously processed elements. The heap maintains O(log k) access to the global minimum across all active lists, providing significant performance improvements when k grows large.

### How does the code handle empty or null input lists?

According to the source code in [`MergeKSortedLists.java`](https://github.com/kdn251/interviews/blob/main/MergeKSortedLists.java), the method first validates `if (lists == null || lists.length == 0)` and returns `null` immediately. When seeding the priority queue, the implementation verifies `if (node != null)` before adding each head node, ensuring null entries do not cause `NullPointerException`.

### Can this approach be adapted for merging k sorted arrays instead of linked lists?

Yes, the same min-heap logic applies to arrays, though implementation details differ. Instead of pushing `tail.next`, you would track array indices and push the next element from the same array when extracting the minimum. The time complexity remains **O(N log k)**, but array-based solutions may offer better cache performance than pointer-chasing through linked list nodes.