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

  • Thread starter Thread starter evinda
  • Start date Start date
  • Tags Tags
    Algorithm
AI Thread Summary
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
Gold Member
MHB
Messages
3,741
Reaction score
0
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:
 
Last edited:
Technology news on Phys.org
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)
 
Thread 'Is this public key encryption?'
I've tried to intuit public key encryption but never quite managed. But this seems to wrap it up in a bow. This seems to be a very elegant way of transmitting a message publicly that only the sender and receiver can decipher. Is this how PKE works? No, it cant be. In the above case, the requester knows the target's "secret" key - because they have his ID, and therefore knows his birthdate.
I tried a web search "the loss of programming ", and found an article saying that all aspects of writing, developing, and testing software programs will one day all be handled through artificial intelligence. One must wonder then, who is responsible. WHO is responsible for any problems, bugs, deficiencies, or whatever malfunctions which the programs make their users endure? Things may work wrong however the "wrong" happens. AI needs to fix the problems for the users. Any way to...

Similar threads

Back
Top