MHB Merging $k$ Sorted Lists with a Thin Heap: A $\mathcal{O}(n \lg k)$ Algorithm

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The discussion revolves around creating an efficient algorithm to merge k sorted lists into one sorted list with a time complexity of O(n log k), where n is the total number of elements across all lists. The key suggestion is to utilize a thin heap for a k-way merge. A thin heap is likely a specialized data structure that optimizes space and time for this specific merging task. The merging process involves initializing a min-heap with the first elements from each of the k lists, performing a heapify operation, and then repeatedly extracting the minimum element (the root of the heap) to build the final sorted list. After extracting the minimum, the next element from the list that provided the minimum is added to the heap, followed by another heapify operation, continuing this process until all elements are merged. This method ensures efficient merging while maintaining the required time complexity.
evinda
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Hello! (Wave)

I am asked to write a $Ο (n \lg k)$ - time algorithm that merges $k$ sorted lists into one sorted list, where $n$ is the the total number of elements in all the input lists.
Hint: Use a thin heap for a $k$ -way merging.

Do you have an idea what could be meant with [m] thin heap [/m] ? (Worried)

Also, how could we merge $k$ sorted lists into one using a heap? :confused:
 
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Finally, a min heap is meant...
So do we have to have a heap with $k$ positions, put the elements of the first positions of the $k$ lists in the heap, heapify and delete the root, which will be the smallest element, and put it into the new list, then place at the root the second element from the list from which the minimum was, then heapify and continue the same procedure? (Thinking)
 

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