Question

What is the behavior of finding the k smallest items in a collection of size n using the quicksort option?

A) O(n)
B) O(kn)
C) O(k log n)
D) O(nk log n)
E) O(n log n)

Answer 1

The behavior of finding the k smallest items in a collection of size n using the quicksort algorithm can be represented by the time complexity of O(n).

Step-by-step explanation:

The behavior of finding the k smallest items in a collection of size n using the quicksort algorithm is represented by the time complexity of the algorithm. In this case, the time complexity is O(n). This means that the algorithm takes linear time, or grows proportionally to the size of the collection.

Quicksort works by partitioning the collection into two parts based on a chosen pivot element. By recursively applying the partitioning process, the algorithm progressively sorts the collection. In the case of finding the k smallest items, the algorithm can stop partitioning once the first k elements have been identified.

Therefore, the overall time complexity is O(n), as it only depends on the size of the collection and not on the value of k.