GATE | GATE MOCK 2017 | Question 40

Consider n elements that are equally distributed in k stacks. In each stack, elements of it are arranged in ascending order (min is at the top in each of the stack and then increasing downwards).

Given a queue of size n in which we have to put all n elements in increasing order. What will be the time complexity of the best known algorithm?
(A) O(n logk)
(B) O(nk)
(C) O(n2)
(D) O(k2)


Answer: (A)

Explanation:

In nlogk it can be done by creating a min heap of size k and adding all the top – elements of all the stacks. After extracting the min , add the next element from the stack from which we have got our 1st minimum.
Time Complexity = O(k) (For Creating Heap of size k) + (n-k)log k (Insertions into the heap).

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