sorting list of lists that contain both sorted and unsorted lists

Question

There are k lists, which contain m unsorted lists (0 <=m < k). How can the lists be merged into a single large list which should also be sorted, No information provided about the lists that are sorted.

You title talks of "both sorted and unsorted lists", but the description says "k lists, all sorted". Which is it? What do you mean by "instead of l(say 2)"? — Tony Delroy, Aug 20 '12 at 23:11
in practice just combining the lists and performing a [general sort can be faster (for small total number of items < 1e6) then a specialized algorithm (merge sort)](http://stackoverflow.com/a/482848/4279) despite worse asymptotic time complexity — jfs, Aug 21 '12 at 00:28

score 1 · Answer 1 · answered Aug 21 '12 at 08:49

Suppose n the number of the total elements in all lists.

Assuming this number of elements is distributed equally between all the lists, you can do the follows:

Sort every unsorted list
Merge all elements from all lists

Run-time analyze:

The number of elements in each list equals to n/k.

So sorting every unsorted list takes O((n/k)log(n/k) => run-time for sorting all m lists equals to O(m(n/k)*log(n/k)).

The merging part takes O(n).

Thus, we get overall run-time = O(n + m*(n/k)*log(n/k)).

score 0 · Answer 2 · answered Aug 21 '12 at 00:37

you can use insertion sort which would be an easy answer. worst it would run O(n**2) per se.

Otherwise sort (merge, or quicksort) unsorted lists and merge them. based on your m and k you can do some micro optimziation. Here your complexity would be O(nlogn) based on n. you can figure out what it corresponds with k and m.

score 0 · Answer 3 · answered Aug 22 '12 at 06:19

0

Sort the unsorted list using randomized quick sort and then merge all the sorted lists using merge sort .

answered Aug 22 '12 at 06:19

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sorting list of lists that contain both sorted and unsorted lists

3 Answers3