## 23. Merge k Sorted Lists

Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity.

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## Solution

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#### Approach #1 Brute Force [Accepted]

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Intuition & Algorithm

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• Traverse all the linked lists and collect the values of the nodes into an array.
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• Sort and iterate over this array to get the proper value of nodes.
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• Create a new sorted linked list and extend it with the new nodes.
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As for sorting, you can refer here for more about sorting algorithms.

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Complexity Analysis

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Time complexity : where is the total number of nodes.

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• Collecting all the values costs time.
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• A stable sorting algorithm costs time.
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• Iterating for creating the linked list costs time.
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Space complexity : .

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• Sorting cost space (depends on the algorithm you choose).
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• Creating a new linked list costs space.
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#### Approach #2 Compare one by one [Accepted]

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Algorithm

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• Compare every nodes (head of every linked list) and get the node with the smallest value.
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• Extend the final sorted linked list with the selected nodes.
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Complexity Analysis

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Time complexity : where is the number of linked lists.

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• Almost every selection of node in final linked costs ( times comparison).
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• There are nodes in the final linked list.
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Space complexity :

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• \n Creating a new linked list costs space.
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• \n It\'s not hard to apply in-place method - connect selected nodes instead of creating new nodes to fill the new linked list.
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#### Approach #3 Optimize Approach 2 by Priority Queue [Accepted]

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Algorithm

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Almost the same as the one above but optimize the comparison process by priority queue. You can refer here for more information about it.

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Complexity Analysis

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Time complexity : where is the number of linked lists.

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• The comparison cost will be reduced to for every pop and insertion to priority queue. But finding the node with the smallest value just costs time.
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• There are nodes in the final linked list.
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Space complexity :

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• \n Creating a new linked list costs space.
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• \n The code above present applies in-place method which cost space. And the priority queue (often implemented with heaps) costs space (it\'s far less than in most situations).
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#### Approach #4 Merge lists one by one [Accepted]

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Algorithm

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Convert merge lists problem to merge 2 lists () times. Here is the merge 2 lists problem page.

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Complexity Analysis

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Time complexity : where is the number of linked lists.

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• We can merge two sorted linked list in time where is the total number of nodes in two lists.
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• Sum up the merge process and we can get: .
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Space complexity : \n

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• We can merge two sorted linked list in space.
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#### Approach #5 Merge with Divide And Conquer [Accepted]

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Intuition & Algorithm

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This approach walks alongside the one above but is improved a lot. We don\'t need to traverse most nodes many times repeatedly

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Pair up lists and merge each pair.

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After the first pairing, lists are merged into lists with average length, then , and so on.

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Repeat this procedure until we get the final sorted linked list.

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Thus, we\'ll traverse almost nodes per pairing and merging, and repeat this procedure about times.

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Complexity Analysis

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Time complexity : where is the number of linked lists.

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• We can merge two sorted linked list in time where is the total number of nodes in two lists.
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• Sum up the merge process and we can get: \n
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Space complexity : \n

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• We can merge two sorted linked lists in space.
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Analysis written by: @Hermann0

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