23 || Merge k Sorted Lists || Leetcode Daily Problem

Problem Link :- leetcode-23

Problem statement

You are 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.

Significance of problem

The significance of the "Merge k Sorted Lists" problem lies in its representation of a common real-world scenario—merging multiple sorted datasets efficiently. This problem addresses a common computational task encountered in various domains, such as database management, data processing pipelines, and sorting algorithms. The solution involves merging k linked-lists, each sorted in ascending order, into a single sorted linked-list.

Firstly, the problem delves into the realm of linked-list manipulation, emphasizing the importance of recursive merging. The code solution elegantly handles the merging process by recursively comparing and linking nodes, providing learners with insights into recursive algorithms for linked-list operations.

Secondly, the problem underscores the significance of algorithmic efficiency. Merging k linked-lists efficiently requires a strategic approach to avoid unnecessary comparisons and traversals. The code solution optimizes this process by merging pairs of lists iteratively, demonstrating the importance of minimizing operations for enhanced computational performance.

Moreover, the problem promotes a deeper understanding of data structures and their applications. Merging sorted linked-lists aligns with scenarios where maintaining sorted order is essential for subsequent operations, such as searching or iterating through the data. This aspect showcases the practical implications of data structure design and manipulation in real-world computational tasks.

Furthermore, the problem cultivates adaptability in algorithmic design. The code solution provides a flexible approach that accommodates varying numbers of input linked-lists, demonstrating the importance of scalable solutions capable of handling dynamic datasets.

In essence, mastering the "Merge k Sorted Lists" problem equips developers with essential skills in linked-list manipulation, recursive algorithms, and algorithmic efficiency. These skills are transferable to a myriad of computational scenarios, reflecting the universal importance of merging and sorting operations in diverse domains where efficient data processing is paramount.

Easiest Explanation

Imagine you have some books, and each book has some pages. Now, you want to combine all the pages from all the books into one big book, but you want to keep the pages in order.

So, you start with the first page of the first book, and you put it in the big book. Then, you look at the first page of the second book, and compare it with the page you just added. If it's smaller, you add it after the first page of the first book. If it's bigger, you add it after the first page of the second book.

You keep doing this for every page in every book, always making sure to add the pages in the correct order. When you're done, you have one big book with all the pages in order from smallest to largest.

This is similar to the problem of merging k sorted linked-lists. Each linked-list is like a book, and each node in the linked-list is like a page. You need to combine all the nodes from all the linked-lists into one big linked-list, but keep them in order.

I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.

Python Code :

import heapq
# implementationusing priority queue
class Solution:
    def mergeKLists(self, lists: List[ListNode]) -> ListNode:
        heap = []
        for i, lst in enumerate(lists):
            if lst:
                heapq.heappush(heap, (lst.val, i, lst))
        
        dummy = ListNode(0)
        curr = dummy
        while heap:
            _, i, node = heapq.heappop(heap)
            curr.next = node
            curr = curr.next
            if node.next:
                heapq.heappush(heap, (node.next.val, i, node.next))
                
        return dummy.next

CPP Code

class Solution {
public:

    ListNode* merge_list(ListNode* l1,ListNode* l2){
        if(!l1) return l2;
        if(!l2) return l1;

        ListNode* head ;
        if(l1->val<=l2->val) head = l1;
        else head = l2;

        if(l1->val<=l2->val) head->next =  merge_list(l1->next,l2);
        else head->next = merge_list(l1,l2->next);

        return head;
    }

    ListNode* mergeKLists(vector<ListNode*>& lists) {
        if(lists.size()==0) return NULL;
        ListNode* head = lists[0];
        for(int i =1;i<lists.size();i++)
            head = merge_list(head,lists[i]);

        return head;
    }
};
    

Here's how the function works:

1. The merge_list function takes two linked-lists as input, l1 and l2, and returns a single merged linked-list.

2. In the merge_list function, first we check if either of the input linked-lists are empty. If one of the lists is empty, we return the other list.

3. Next, we create a pointer head to point to the merged linked-list. We check which of the two input linked-lists has a smaller first node value, and set head to that linked-list.

4. If l1 has the smaller first node value, we set its next pointer to the result of merging the remaining nodes of l1 and all the nodes of l2. If l2 has the smaller first node value, we set its next pointer to the result of merging the remaining nodes of l2 and all the nodes of l1. This is done recursively until we reach the end of both l1 and l2.

5. Finally, the mergeKLists function takes an input vector of k linked-lists, iterates over them one by one, and merges them into a single sorted linked-list using the merge_list function. It returns the head of the merged linked-list.

Overall, this code uses a divide-and-conquer approach to merge the linked-lists. The merge_list function merges two linked-lists at a time, and the mergeKLists function combines these merged linked-lists one by one until all the input linked-lists have been merged into a single sorted linked-list.

Learning Outcomes

Solving the "Merge k Sorted Lists" problem yields a spectrum of valuable learning outcomes, enriching one's skill set in algorithmic design, data structure manipulation, and efficiency optimization. Firstly, learners develop a nuanced understanding of linked-list operations, particularly recursive merging. The recursive approach employed in the code solution illuminates the elegance and effectiveness of recursive algorithms in the context of linked-list manipulation, a skill applicable in various scenarios requiring sophisticated data structuring.

Secondly, the problem enhances expertise in algorithmic efficiency. The iterative merging of pairs of lists demonstrates the significance of minimizing comparisons and traversals, offering practical insights into streamlining operations for improved computational performance. This skill is transferable to scenarios where large datasets demand optimized algorithms to ensure swift and resource-efficient processing.

Moreover, learners gain insights into the practical applications of data structures. Merging sorted linked-lists mirrors real-world scenarios where maintaining ordered datasets is crucial for subsequent operations like searching or analysis. This aspect underscores the practical implications of thoughtful data structure design and manipulation in solving complex computational challenges.

Furthermore, the problem cultivates adaptability in algorithmic design. The code solution provides a flexible approach capable of handling varying numbers of input linked-lists, encouraging learners to develop scalable solutions applicable to dynamic datasets. This adaptability is a key trait in designing algorithms that can accommodate diverse and evolving computational scenarios.

Conclusion

In conclusion, solving the "Merge k Sorted Lists" problem unfolds as a pivotal learning experience, imparting fundamental skills in algorithmic design and data manipulation. The recursive merging of linked-lists underscores the elegance of recursive algorithms, contributing to a nuanced understanding of linked-list operations. Furthermore, the emphasis on algorithmic efficiency highlights the importance of minimizing comparisons and traversals for optimized performance, a skill indispensable in scenarios with extensive datasets.

The problem's practical applications in managing ordered datasets reinforce the significance of thoughtful data structure design. The adaptable approach to handle varying numbers of input linked-lists cultivates flexibility in algorithmic design, emphasizing the development of scalable solutions for dynamic datasets. Mastering this problem equips learners with essential tools applicable in various computational contexts, solidifying their ability to tackle challenges involving efficient data processing and manipulation. Overall, the "Merge k Sorted Lists" problem serves as a cornerstone in building a well-rounded skill set essential for proficient algorithmic problem-solving.

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