# Python Program To Merge K Sorted Linked Lists – Set 1

• Last Updated : 28 Feb, 2022

Given K sorted linked lists of size N each, merge them and print the sorted 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.```

Method 1 (Simple):

Approach:
A Simple Solution is to initialize the result as the first list. Now traverse all lists starting from the second list. Insert every node of the currently traversed list into result in a sorted way.

## Python3

 `# Python3 program to merge k  ` `# sorted arrays of size n each ` ` `  `# A Linked List node ` `class` `Node:   ` `    ``def` `__init__(``self``, x):       ` `        ``self``.data ``=` `x ` `        ``self``.``next` `=` `None` ` `  `# Function to print nodes in a given  ` `# linked list  ` `def` `printList(node): ` `   `  `    ``while` `(node !``=` `None``): ` `        ``print``(node.data,  ` `              ``end ``=` `" "``) ` `        ``node ``=` `node.``next` ` `  `# The main function that takes an  ` `# array of lists arr[0..last] and  ` `# generates the sorted output ` `def` `mergeKLists(arr, last): ` ` `  `    ``# Traverse form second  ` `    ``# list to last ` `    ``for` `i ``in` `range``(``1``, last ``+` `1``): ` `        ``while` `(``True``): ` `            ``# head of both the lists, ` `            ``# 0 and ith list. ` `            ``head_0 ``=` `arr[``0``] ` `            ``head_i ``=` `arr[i] ` ` `  `            ``# Break if list ended ` `            ``if` `(head_i ``=``=` `None``): ` `                ``break` ` `  `            ``# Smaller than first  ` `            ``# element ` `            ``if` `(head_0.data >``=`  `                ``head_i.data): ` `                ``arr[i] ``=` `head_i.``next` `                ``head_i.``next` `=` `head_0 ` `                ``arr[``0``] ``=` `head_i ` `            ``else``: ` `                ``# Traverse the first list ` `                ``while` `(head_0.``next` `!``=` `None``): ` `                    ``# Smaller than next  ` `                    ``# element ` `                    ``if` `(head_0.``next``.data >``=`  `                        ``head_i.data): ` `                        ``arr[i] ``=` `head_i.``next` `                        ``head_i.``next` `=` `head_0.``next` `                        ``head_0.``next` `=` `head_i ` `                        ``break` `                    ``# go to next node ` `                    ``head_0 ``=` `head_0.``next` `                    ``# if last node ` `                    ``if` `(head_0.``next` `=``=` `None``): ` `                        ``arr[i] ``=` `head_i.``next` `                        ``head_i.``next` `=` `None` `                        ``head_0.``next` `=` `head_i ` `                        ``head_0.``next``.``next` `=` `None` `                        ``break` `    ``return` `arr[``0``] ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `   `  `    ``# Number of linked  ` `    ``# lists ` `    ``k ``=` `3` `     `  `    ``# Number of elements ` `    ``# in each list ` `    ``n ``=` `4` ` `  `    ``# an array of pointers  ` `    ``# storing the head nodes  ` `    ``# of the linked lists ` `    ``arr ``=` `[``None` `for` `i ``in` `range``(k)] ` ` `  `    ``arr[``0``] ``=` `Node(``1``) ` `    ``arr[``0``].``next` `=` `Node(``3``) ` `    ``arr[``0``].``next``.``next` `=` `Node(``5``) ` `    ``arr[``0``].``next``.``next``.``next` `=` `Node(``7``) ` ` `  `    ``arr[``1``] ``=` `Node(``2``) ` `    ``arr[``1``].``next` `=` `Node(``4``) ` `    ``arr[``1``].``next``.``next` `=` `Node(``6``) ` `    ``arr[``1``].``next``.``next``.``next` `=` `Node(``8``) ` ` `  `    ``arr[``2``] ``=` `Node(``0``) ` `    ``arr[``2``].``next` `=` `Node(``9``) ` `    ``arr[``2``].``next``.``next` `=` `Node(``10``) ` `    ``arr[``2``].``next``.``next``.``next` `=` `Node(``11``) ` ` `  `    ``# Merge all lists ` `    ``head ``=` `mergeKLists(arr, k ``-` `1``) ` ` `  `    ``printList(head) ` `# This code is contributed by Mohit Kumar 29`

Output:

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

Complexity Analysis:

• Time complexity: O(nk2)
• Auxiliary Space: O(1).
As no extra space is required.

Method 2: Min Heap
A Better solution is to use Min Heap-based solution which is discussed here for arrays. The time complexity of this solution would be O(nk Log k)
Method 3: Divide and Conquer
In this post, Divide and Conquer approach is discussed. This approach doesn’t require extra space for heap and works in O(nk Log k)
It is known that merging of two linked lists can be done in O(n) time and O(n) space.

1. The idea is to pair up K lists and merge each pair in linear time using O(n) space.
2. After the first cycle, K/2 lists are left each of size 2*N. After the second cycle, K/4 lists are left each of size 4*N and so on.
3. Repeat the procedure until we have only one list left.

Below is the implementation of the above idea.

## Python3

 `# Python3 program to merge k sorted ` `# arrays of size n each ` `  `  `# A Linked List node ` `class` `Node:     ` `    ``def` `__init__(``self``): ` `         `  `        ``self``.data ``=` `0` `        ``self``.``next` `=` `None` ` `  `# Function to print nodes in a ` `# given linked list ` `def` `printList(node): ` `    ``while` `(node !``=` `None``): ` `        ``print``(node.data, end ``=` `' '``) ` `        ``node ``=` `node.``next` `     `  `# Takes two lists sorted in increasing order,  ` `# and merge their nodes together to make one  ` `# big sorted list. Below function takes  ` `# O(Log n) extra space for recursive calls, ` `# but it can be easily modified to work with ` `# same time and O(1) extra space  ` `def` `SortedMerge(a, b): ` `    ``result ``=` `None` `  `  `    ``# Base cases  ` `    ``if` `(a ``=``=` `None``): ` `        ``return``(b) ` `    ``elif` `(b ``=``=` `None``): ` `        ``return``(a) ` `  `  `    ``# Pick either a or b, and recur  ` `    ``if` `(a.data <``=` `b.data): ` `        ``result ``=` `a ` `        ``result.``next` `=`  `               ``SortedMerge(a.``next``, b) ` `    ``else``: ` `        ``result ``=` `b ` `        ``result.``next` `=`  `               ``SortedMerge(a, b.``next``) ` `     `  `    ``return` `result ` ` `  `# The main function that takes an array  ` `# of lists arr[0..last] and generates  ` `# the sorted output ` `def` `mergeKLists(arr, last): ` ` `  `    ``# Repeat until only one list is left ` `    ``while` `(last !``=` `0``): ` `        ``i ``=` `0` `        ``j ``=` `last ` `  `  `        ``# (i, j) forms a pair ` `        ``while` `(i < j): ` `             `  `            ``# Merge List i with List j and store ` `            ``# merged list in List i ` `            ``arr[i] ``=` `SortedMerge(arr[i], arr[j]) ` `  `  `            ``# Consider next pair ` `            ``i ``+``=` `1` `            ``j ``-``=` `1` `             `  `            ``# If all pairs are merged, update last ` `            ``if` `(i >``=` `j): ` `                ``last ``=` `j ` `  `  `    ``return` `arr[``0``] ` ` `  `# Utility function to create a new node. ` `def` `newNode(data): ` ` `  `    ``temp ``=` `Node() ` `    ``temp.data ``=` `data ` `    ``temp.``next` `=` `None` `    ``return` `temp ` ` `  `# Driver code ` `if` `__name__``=``=``'__main__'``: ` `     `  `    ``# Number of linked lists ` `    ``k ``=` `3` `     `  `    ``# Number of elements in each list ` `    ``n ``=` `4`  `  `  `    ``# An array of pointers storing the  ` `    ``# head nodes of the linked lists ` `    ``arr ``=` `[``0` `for` `i ``in` `range``(k)] ` `  `  `    ``arr[``0``] ``=` `newNode(``1``) ` `    ``arr[``0``].``next` `=` `newNode(``3``) ` `    ``arr[``0``].``next``.``next` `=` `newNode(``5``) ` `    ``arr[``0``].``next``.``next``.``next` `=` `newNode(``7``) ` `  `  `    ``arr[``1``] ``=` `newNode(``2``) ` `    ``arr[``1``].``next` `=` `newNode(``4``) ` `    ``arr[``1``].``next``.``next` `=` `newNode(``6``) ` `    ``arr[``1``].``next``.``next``.``next` `=` `newNode(``8``) ` `  `  `    ``arr[``2``] ``=` `newNode(``0``) ` `    ``arr[``2``].``next` `=` `newNode(``9``) ` `    ``arr[``2``].``next``.``next` `=` `newNode(``10``) ` `    ``arr[``2``].``next``.``next``.``next` `=` `newNode(``11``) ` `  `  `    ``# Merge all lists ` `    ``head ``=` `mergeKLists(arr, k ``-` `1``) ` `  `  `    ``printList(head) ` ` `  `# This code is contributed by rutvik_56`

Output:

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

Complexity Analysis:

Assuming N(n*k) is the total number of nodes, n is the size of each linked list, and k is the total number of linked lists.

• Time Complexity: O(N*log k) or O(n*k*log k)
As outer while loop in function mergeKLists() runs log k times and every time it processes n*k elements.
• Auxiliary Space: O(N) or O(n*k)
Because recursion is used in SortedMerge() and to merge the final 2 linked lists of size N/2, N recursive calls will be made.

Please refer complete article on Merge K sorted linked lists | Set 1 for more details!

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