How do you solve Merge k Sorted Lists on LeetCode?

Merge k Sorted Lists (LeetCode #23) can be solved using Brute Force or Optimal Solution (Heap). The optimal approach is Optimal Solution (Heap) with O(n log k) time complexity and O(k) space complexity. Key insight: Using a min-heap allows us to efficiently merge multiple sorted lists by always extracting the smallest element, which is a common pattern in problems involving merging sorted data.

What is the brute force solution for Merge k Sorted Lists?

The brute force approach for Merge k Sorted Lists is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves merging all the linked lists into a single list and then sorting that list. This is straightforward but inefficient, especially as the number of lists increases. The optimal Optimal Solution (Heap) approach improves this to O(n log k).

What algorithm or data structure is used to solve Merge k Sorted Lists?

Merge k Sorted Lists uses the following concepts: Linked List, Divide and Conquer, Heap (Priority Queue), Merge Sort. The recommended patterns to study are: Heap, Linked List, Divide and Conquer.

What are the interview tips for Merge k Sorted Lists?

When you first see this problem, clarify the input format and constraints, and consider edge cases like empty lists. Communicate your thought process clearly, explaining why you would choose a particular approach and how it optimally solves the problem. Mention edge cases such as all lists being empty or having only one list, as these can affect your implementation.

What are common mistakes when solving Merge k Sorted Lists?

Students often forget to handle edge cases, such as when one or more lists are empty, which can lead to null pointer exceptions. Another common mistake is not properly managing the heap, leading to incorrect order of elements in the merged list.

#23

Merge k Sorted Lists

Hard

Linked ListDivide and ConquerHeap (Priority Queue)Merge SortHeapLinked ListDivide and Conquer

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution (Heap)★
Time	O(n²)	O(n log k)
Space	O(1)	O(k)

💡

Intuition

Time O(n log k)Space O(k)

Using a min-heap (or priority queue) allows us to efficiently merge the k sorted lists by always extracting the smallest element. This approach is much faster than the brute force method.

⚙️

Algorithm

3 steps

1Step 1: Initialize a min-heap and add the head of each linked list to it.
2Step 2: While the heap is not empty, extract the smallest element, add it to the merged list, and if the extracted element has a next node, add that next node to the heap.
3Step 3: Continue until all elements from all lists have been processed.

solution.py24 lines

1# Full working Python code with comments
2import heapq
3
4class ListNode:
5    def __init__(self, val=0, next=None):
6        self.val = val
7        self.next = next
8
9def mergeKLists(lists):
10    min_heap = []
11    # Step 1: Initialize the heap
12    for l in lists:
13        if l:
14            heapq.heappush(min_heap, (l.val, l))
15    dummy = ListNode(0)
16    current = dummy
17    # Step 2: Process the heap
18    while min_heap:
19        val, node = heapq.heappop(min_heap)
20        current.next = ListNode(val)
21        current = current.next
22        if node.next:
23            heapq.heappush(min_heap, (node.next.val, node.next))
24    return dummy.next

ℹ

Complexity note: The time complexity is O(n log k) because we are processing n elements and for each insertion and extraction from the heap, it takes log k time. The space complexity is O(k) due to the storage of the heap containing at most k elements.

1Using a min-heap allows us to efficiently merge multiple sorted lists by always extracting the smallest element, which is a common pattern in problems involving merging sorted data.
2Understanding the trade-offs between time and space complexity is crucial; sometimes a more efficient time complexity can be achieved at the cost of increased space usage.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.