Solving Merge k Sorted Lists: Combining Multiple Sorted Lists

The "Merge k Sorted Lists" problem is about combining multiple sorted linked lists into one single sorted list.

Problem Statement

Given an array of k linked-lists lists, each linked-list is sorted in ascending order. Merge all the linked-lists into one sorted linked list and return it.

Example

Consider k sorted linked lists:

Example 1

• Input: lists = [[1,4,5],[1,3,4],[2,6]]
• Output: [1,1,2,3,4,4,5,6]
• Explanation: The linked-lists are:

Merging them into one sorted list results in 1 -> 1 -> 2 -> 3 -> 4 -> 4 -> 5 -> 6.

Example 2

• Input: lists = []
• Output: []
• Explanation: No lists to merge, so the output is an empty list.

Example 3

• Input: lists = [[]]
• Output: []
• Explanation: A single empty list results in an empty merged list.

Solution Approach

A popular approach to solving this problem is using a Min Heap or a Priority Queue to efficiently find and merge the smallest elements of the lists.

Solution Approach - Min Heap

Breaking Down the Solution

The provided TypeScript solution for merging k sorted linked lists implements a custom Min Heap class and uses it to efficiently merge the lists. Here's a breakdown of how the solution works:

ListNode Class

• Represents a node in a linked list.
• Contains a value (val) and a reference to the next node (next).

MinHeap Class

• A min heap is a binary tree where the parent node is always less than or equal to its children.
• The class maintains a heap in an array (heap), where each element is a ListNode or null.

Key Methods and Properties:

• getLeftChildIndex, getRightChildIndex, getParentIndex: Calculate the indices of a node's left child, right child, and parent.
• hasLeftChild, hasRightChild, hasParent: Check if the node at the given index has a left child, right child, or parent.
• leftChild, rightChild, parent: Get the left child, right child, or parent of the node at the given index.
• swap: Swap two nodes in the heap.
• isEmpty: Check if the heap is empty.
• insert: Add a new node to the heap and reorganize the heap to maintain the min heap property (heapify up).
• extract: Remove and return the smallest node from the heap and reorganize the heap (heapify down).

mergeKLists Function

• Merges k sorted linked lists into one sorted linked list.
• Uses the Min Heap to efficiently find the smallest current node among all the lists.
• Iteratively extracts the smallest node from the heap and adds it to the merged list.
• If the extracted node has a next node, inserts the next node into the heap.

Process:

1. Initialize Min Heap: All head nodes of the k lists are inserted into the min heap.
2. Merging: Continuously extract the smallest node from the heap and attach it to the merged list.
3. Insert Next Nodes: If the extracted node has a next node, insert that next node into the heap to be considered in subsequent extractions.
4. Completion: The process continues until the heap is empty, meaning all nodes have been merged into the new list.

The result is a new linked list, pointed to by dummy.next, which is a sorted merge of all the input linked lists. This approach efficiently handles the merging process, making it suitable for a large number of lists or lists with a large number of nodes.

Conclusion

Merging k sorted lists is a classic problem that demonstrates the practical application of heap data structures in sorting and merging operations.

Rust Solution

Rust's BinaryHeap is a max-heap, so the Item wrapper implements Ord with the operands flipped — o.0.cmp(&self.0) — to invert the ordering and pop the smallest val first. Because next is an Option<Box<ListNode>>, advancing a list uses node.next.take(), which moves the tail out of the box and leaves None behind so ownership passes cleanly into the next heap.push. The while let Some(Item(_, mut node)) = heap.pop() binding destructures the tuple struct and takes ownership of the boxed node in a single step, avoiding any borrow of the heap's interior.

Go Solution

Go's container/heap isn't a ready-made heap but an algorithm over any type satisfying its interface, so PQ (a []Item slice) must supply Len, Less, Swap, Push, and Pop itself. Less returns p[i].val < p[j].val directly, giving a min-heap with no comparator inversion — the opposite of Rust's flipped Ord. The pre-generics interface hands elements around as interface{}, so Push recovers the concrete type with x.(Item) and Pop peels the last slice element via old[:n-1], with callers re-asserting through heap.Pop(pq).(Item).