Merge K Sorted Linked Lists using Min HeapThe efficient merging of Ksorted linked lists is a typical challenge in computer science and software development. This assignment entails integrating various linked lists that have already been sorted in ascending order into a single sorted linked list. Using a Min Heap data structure is one of the more efficient ways to handle this problem. In this article, we'll look at the Min Heap technique for merging Ksorted linked lists, as well as its implementation and time and space difficulties. Merge K Sorted Linked Lists: An IntroductionWhen dealing with Ksorted linked lists, a simple but timeconsuming solution is to merge pairs of lists until they are all merged into a single list. However, this approach exhibits a temporal complexity of O(N^2), where N represents the overall number of nodes across all lists.
Understanding Min Heap: A Min Heap is a complete binary tree wherein each node's value is equal to or smaller than the values of its children. It is frequently expressed as an array, which allows for quick insertion and extraction of the minimal member. In this case, the head nodes of the Klinked lists will be stored in a Min Heap. Algorithm: Merge K Sorted Linked Lists using Min HeapInput: K sorted linked lists. Output: A single sorted linked list containing all elements from the K input lists. Steps: Step 1: Initialize an empty Min Heap.
Step 2: Traverse through all Klinked lists and insert their head nodes into the Min Heap.
Step 3: Initialize an empty resultlinked list to store the merged output.
Step 4: While the Min Heap is not empty:
Step 5: Return the head of the resultlinked list.
Example Let's consider three sorted linked lists: List 1: 1 > 4 > 5 List 2: 1 > 3 > 4 List 3: 2 > 6 We'll apply the merging algorithm using a minheap to combine these linked lists into a single sorted list. Step 1: Initialize a Min Heap We start by creating an empty min heap. Step 2: Populate the Min Heap Insert the head nodes of the three lists into the min heap. Heap: Step 3: Merge Process While the min heap is not empty:
Heap: Continue this process:
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Heap: (Empty) The result linked list after merging the three sorted lists would be: 1 > 1 > 2 > 3 > 4 > 4 > 5 > 6 ImplementationOutput: Explanation ListNode Class:
Custom Comparison Method:
mergeKLists Function:
createLinkedList Function:
Sample Input and Output:
Time Complexity Building the Heap: Inserting the head nodes of all K lists into the min heap takes O(K log K) time. Merging:
Overall: The time complexity for building the heap and merging the lists is O(N log K). Space Complexity Heap Space: The space required for the min heap will be O(K) since, at most, K nodes will be in the heap at any time during the merging process. Output Linked List: The merged linked list will require additional space equivalent to the total number of nodes, which is O(N). Overall: The space complexity will be O(max(N, K)), considering the space required for the heap and the merged linked list. Summary Time Complexity: O(N log K) Space Complexity: O(max(N, K)) ConclusionWhen merging Ksorted linked lists, the Min Heap technique considerably decreases temporal complexity when compared to alternative approaches. We efficiently combine the lists in a sorted way by utilizing the capabilities of the Min Heap data structure, demonstrating the significance of selecting the correct data structures and methods in problemsolving scenarios.
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