Algorithm – Merge K Sorted Lists

Introduction

Merging multiple sorted lists efficiently is a common problem encountered in various scenarios, such as merging sorted arrays or combining sorted linked lists. In this blog post, we will explore an optimized algorithm for merging K sorted lists. This algorithm provides an efficient solution with a time complexity of O(N log K), where N represents the total number of elements across all lists.

Merge Process

Combining Two Sorted Lists

The merge process is a crucial step within the algorithm for merging K sorted lists efficiently. This process combines two sorted lists into a single sorted list. Let’s dive into the steps involved!

Java Implementation

public ListNode mergeKLists(ListNode[] lists) {
        int amount = lists.length;
        int interval = 1;
        while (interval < amount) {
            for (int i = 0; i < amount - interval; i += interval * 2) {
                lists[i] = merge2Lists(lists[i], lists[i + interval]);
            }
            interval *= 2;
        }
        return amount > 0 ? lists[0] : null;
    }

    private ListNode merge2Lists(ListNode l1, ListNode l2) {
        ListNode head = new ListNode(0);
        ListNode point = head;
        while (l1 != null && l2 != null) {
            if (l1.val <= l2.val) {
                point.next = l1;
                l1 = l1.next;
            } else {
                point.next = l2;
                l2 = l2.next;
            }
            point = point.next;
        }
        if (l1 != null) {
            point.next = l1;
        } else {
            point.next = l2;
        }
        return head.next;
    }

In this implementation, the merge2Lists method takes two sorted lists, l1 and l2, as input and merges them into a single sorted list. Here’s how the merge process works:

Initialization

• A new list head is initialized with a dummy node.
• The point pointer is set to head to keep track of the current position.

Value Comparison

• The algorithm compares the values at the current positions of the two pointers, l1 and l2.
• If l1.val is less than or equal to l2.val, it means the element in l1 should come before or at the same position as the element in l2 in the merged list.
• The smaller value is appended to the point.next in the merged list.

Advancing Pointers

• The point pointer is moved to the next position in the merged list.
• The corresponding pointer (l1 or l2) is advanced to the next element.

Iteration

• Steps 2 and 3 are repeated until one of the lists is exhausted, i.e., reaches the end.

Appending Remaining Elements

• After exiting the while loop, the algorithm appends the remaining elements from the non-exhausted list (l1 or l2) to the merged list.

Returning the Result:

• initial dummy node, is returned as the merged result.

This merge process serves as the core operation within the mergeKLists algorithm. By efficiently merging pairs of lists using this process recursively, the algorithm achieves an optimal time complexity of O(N log K) for merging K sorted lists.

Conclusion

In conclusion, the algorithm for merging K sorted lists efficiently provides a powerful solution for combining multiple sorted lists into a single sorted list. By leveraging the merge process and its steps, developers can achieve an optimal time complexity of O(N log K), where N represents the total number of elements across all lists. This algorithm proves to be valuable in various scenarios where merging sorted arrays or linked lists is required. Its optimized approach ensures improved performance and scalability. By understanding the merge process and its implementation, developers can efficiently tackle the challenge of merging K sorted lists, saving time and computational resources. Incorporate this algorithm into your codebase to enhance your applications with efficient merging capabilities.

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