> For the complete documentation index, see [llms.txt](https://bhabs.gitbook.io/prepbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://bhabs.gitbook.io/prepbook/coding/merge-k-sorted-arrays.md).

# Merge K sorted arrays

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

```
# Definition for singly-linked list.
# class ListNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.next = None
'''
heap[k] <= heap[2*k+1] and heap[k] <= heap[2*k+2] for all k, counting elements from zero. For the sake of comparison, non-existing elements are considered to be infinite. The interesting property of a heap is that its smallest element is always the root, heap[0].
'''
class Solution(object):
    def mergeKLists(self, lists):
        """
        :type lists: List[ListNode]
        :rtype: ListNode
        """
        # import heapq module
        import heapq

        h = [] # this list will define the heap using the heapq module in Python

        k = len(lists) # number of k sorted lists

        mergedList = [] # return this
        #================================================================================
        # base case
        #================================================================================
        if not k:
            return mergedList

        #================================================================================
        # Store the pointers to the next Node in an iterable list
        # This will help us to quickly come to the next Node in the correct kth list, after the smallest
        # element is popped from the heap.
        #================================================================================
        iterList = [None for i in xrange(k)]

        #================================================================================
        # Initially: Just buld a heap with the first elements from all k sorted lists
        #            Each heap element is a tuple of (element value, listIndex)
        #            The listIndex in the tuple will help us identify the which list number
        #            out of those k lists to go to after this tuple gets popped.
        #================================================================================
        for listIndex in xrange(k):
            list = lists[listIndex]
            if list:
                tup = tuple((list.val, listIndex))
                #print 'tup(start): ', tup
                heapq.heappush(h, tup)
                iterList[listIndex] = list.next # store the next pointer


        #================================================================================
        # Main task: 1. Pop the smallest tuple from the heap.
        #            2. Find the listIndex from that popped tuple
        #            3. Find the list Node from the pointer stored in the iterList for that listIndex
        #            4. Push that list node on to the heap
        #            5. The heapq will maintain the smallest element always at the top
        #================================================================================

        while h:
            elem = heapq.heappop(h)
            listIndex = elem[1]
            #print 'min elem: ', elem[0], ' listIndex = ', listIndex
            mergedList.append(elem[0])

            if iterList[listIndex] is not None:
                tup = tuple((iterList[listIndex].val, listIndex))
                #print 'tup: ', tup
                heapq.heappush(h, tup)
                iterList[listIndex] = iterList[listIndex].next

        #print 'merged List: ', mergedList
        return mergedList
```


---

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