# Merge k sorted linked lists | Set 2 (Using Min Heap)

• Difficulty Level : Medium
• Last Updated : 28 Mar, 2022

Given k linked lists each of size n and each list is sorted in non-decreasing order, merge them into a single sorted (non-decreasing order) linked list and print the sorted linked list as output.
Examples:

```Input: k = 3, n =  4
list1 = 1->3->5->7->NULL
list2 = 2->4->6->8->NULL
list3 = 0->9->10->11->NULL

Output: 0->1->2->3->4->5->6->7->8->9->10->11
Merged lists in a sorted order
where every element is greater
than the previous element.

Input: k = 3, n =  3
list1 = 1->3->7->NULL
list2 = 2->4->8->NULL
list3 = 9->10->11->NULL

Output: 1->2->3->4->7->8->9->10->11
Merged lists in a sorted order
where every element is greater
than the previous element.```

An efficient solution for the problem has been discussed in Method 3 of this post.

Approach: This solution is based on the MIN HEAP approach used to solve the problem ‘merge k sorted arrays’ which is discussed here.
MinHeap: A Min-Heap is a complete binary tree in which the value in each internal node is smaller than or equal to the values in the children of that node. Mapping the elements of a heap into an array is trivial: if a node is stored at index k, then its left child is stored at index 2k + 1 and its right child at index 2k + 2.

1. Create a min-heap and insert the first element of all the ‘k’ linked lists.
2. As long as the min-heap is not empty, perform the following steps:
• Remove the top element of the min-heap (which is the current minimum among all the elements in the min-heap) and add it to the result list.
• If there exists an element (in the same linked list) next to the element popped out in previous step, insert it into the min-heap.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to merge k``// sorted linked lists``// | Using MIN HEAP method``#include ``using` `namespace` `std;` `struct` `Node``{``    ``int` `data;``    ``struct` `Node* next;``};` `// Utility function to create``// a new node``struct` `Node* newNode(``int` `data)``{``    ``// Allocate node``    ``struct` `Node* new_node = ``new` `Node();` `    ``// Put in the data``    ``new_node->data = data;``    ``new_node->next = NULL;` `    ``return` `new_node;``}` `// 'compare' function used to build``// up the priority queue``struct` `compare``{``    ``bool` `operator()(``         ``struct` `Node* a, ``struct` `Node* b)``    ``{``        ``return` `a->data > b->data;``    ``}``};` `// Function to merge k sorted linked lists``struct` `Node* mergeKSortedLists(``             ``struct` `Node* arr[], ``int` `k)``{``    ``// Priority_queue 'pq' implemented``    ``// as min heap with the help of``    ``// 'compare' function``    ``priority_queue, compare> pq;` `    ``// Push the head nodes of all``    ``// the k lists in 'pq'``    ``for` `(``int` `i = 0; i < k; i++)``        ``if` `(arr[i] != NULL)``            ``pq.push(arr[i]);``    ` `      ``// Handles the case when k = 0``      ``// or lists have no elements in them   ``      ``if` `(pq.empty())``        ``return` `NULL;``  ` `      ``struct` `Node *dummy = newNode(0);``      ``struct` `Node *last = dummy;``  ` `    ``// Loop till 'pq' is not empty``    ``while` `(!pq.empty()) ``    ``{``        ``// Get the top element of 'pq'``        ``struct` `Node* curr = pq.top();``        ``pq.pop();` `        ``// Add the top element of 'pq'``        ``// to the resultant merged list``        ``last->next = curr;``        ``last = last->next; ``      ` `        ``// Check if there is a node``         ``// next to the 'top' node``        ``// in the list of which 'top'``        ``// node is a member``        ``if` `(curr->next != NULL)``            ` `        ``// Push the next node of top node``        ``// in 'pq'``        ``pq.push(curr->next);``    ``}` `    ``// Address of head node of the required``    ``// merged list``    ``return` `dummy->next;``}` `// Function to print the singly``// linked list``void` `printList(``struct` `Node* head)``{``    ``while` `(head != NULL)``    ``{``        ``cout << head->data << " ";``        ``head = head->next;``    ``}``}` `// Driver code``int` `main()``{``    ``// Number of linked lists``    ``int` `k = 3;` `    ``// Number of elements in each list``    ``int` `n = 4;` `    ``// An array of pointers storing the``    ``// head nodes of the linked lists``    ``Node* arr[k];` `    ``// Creating k = 3 sorted lists``    ``arr = newNode(1);``    ``arr->next = newNode(3);``    ``arr->next->next = newNode(5);``    ``arr->next->next->next = newNode(7);` `    ``arr = newNode(2);``    ``arr->next = newNode(4);``    ``arr->next->next = newNode(6);``    ``arr->next->next->next = newNode(8);` `    ``arr = newNode(0);``    ``arr->next = newNode(9);``    ``arr->next->next = newNode(10);``    ``arr->next->next->next = newNode(11);` `    ``// Merge the k sorted lists``    ``struct` `Node* head = mergeKSortedLists(arr, k);` `    ``// Print the merged list``    ``printList(head);` `    ``return` `0;``}`

## Java

 `/*package whatever //do not write package name here */` `import` `java.io.*;``import` `java.util.*;` `class` `Node {``    ``int` `data;``    ``Node next;` `    ``Node(``int` `key)``    ``{``        ``data = key;``        ``next = ``null``;``    ``}``}``// Class implements Comparator to compare Node data``class` `NodeComparator ``implements` `Comparator {` `    ``public` `int` `compare(Node k1, Node k2)``    ``{``        ``if` `(k1.data > k2.data)``            ``return` `1``;``        ``else` `if` `(k1.data < k2.data)``            ``return` `-``1``;``        ``return` `0``;``    ``}``}``class` `GFG {``    ``// Function to merge k sorted linked lists``    ``static` `Node mergeKList(Node[] arr, ``int` `K)``    ``{``        ``// Priority_queue 'queue' implemented``        ``// as min heap with the help of``        ``// 'compare' function``        ``PriorityQueue queue``            ``= ``new` `PriorityQueue<>(``new` `NodeComparator());``        ``Node at[] = ``new` `Node[K];``        ``Node head = ``new` `Node(``0``);``        ``Node last = head;``        ``// Push the head nodes of all``        ``// the k lists in 'queue'``        ``for` `(``int` `i = ``0``; i < K; i++) {``            ``if` `(arr[i] != ``null``) {``                ``queue.add(arr[i]);``            ``}``        ``}``        ``// Handles the case when k = 0``        ``// or lists have no elements in them``        ``if` `(queue.isEmpty())``            ``return` `null``;``        ``// Loop till 'queue' is not empty``        ``while` `(!queue.isEmpty()) {``            ``// Get the top element of 'queue'``            ``Node curr = queue.poll();` `            ``// Add the top element of 'queue'``            ``// to the resultant merged list``            ``last.next = curr;``            ``last = last.next;``            ``// Check if there is a node``            ``// next to the 'top' node``            ``// in the list of which 'top'``            ``// node is a member``            ``if` `(curr.next != ``null``) {``                ``// Push the next node of top node``                ``// in 'queue'``                ``queue.add(curr.next);``            ``}``        ``}``        ``// Address of head node of the required``        ``// merged list``        ``return` `head.next;``    ``}``    ``// Print linked list``    ``public` `static` `void` `printList(Node node)``    ``{``        ``while` `(node != ``null``) {``            ``System.out.print(node.data + ``" "``);``            ``node = node.next;``        ``}``    ``}` `    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `N = ``4``;``        ``// array to store head of linkedlist``        ``Node[] a = ``new` `Node[N];``        ``// Linkedlist1``        ``Node head1 = ``new` `Node(``1``);``        ``a[``0``] = head1;``        ``head1.next = ``new` `Node(``2``);``        ``head1.next.next = ``new` `Node(``3``);``        ``// Limkedlist2``        ``Node head2 = ``new` `Node(``4``);``        ``a[``1``] = head2;``        ``head2.next = ``new` `Node(``5``);``        ``// Linkedlist3``        ``Node head3 = ``new` `Node(``5``);``        ``a[``2``] = head3;``        ``head3.next = ``new` `Node(``6``);``        ``// Linkedlist4``        ``Node head4 = ``new` `Node(``7``);``        ``a[``3``] = head4;``        ``head4.next = ``new` `Node(``8``);` `        ``Node res = mergeKList(a, N);` `        ``if` `(res != ``null``)``            ``printList(res);``        ``System.out.println();``    ``}``}`

Output:

`0 1 2 3 4 5 6 7 8 9 10 11 `

Complexity Analysis:

• Time Complexity: O(N * log k) or O(n * k * log k), where, ‘N’ is the total number of elements among all the linked lists, ‘k’ is the total number of lists, and ‘n’ is the size of each linked list.
Insertion and deletion operation will be performed in min-heap for all N nodes.
Insertion and deletion in a min-heap require log k time.
• Auxiliary Space: O(k).
The priority queue will have atmost ‘k’ number of elements at any point of time, hence the additional space required for our algorithm is O(k).

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.