The time complexity of quicksort is ……..a.O(n)b.O(logn)c.O(n2)d.O(n logn)

The time complexity of quicksort is d.O(n logn).

Here's why:

1. Quicksort is a divide and conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot.

2. The sub-arrays are then recursively sorted. This means that the array is divided in each step, which gives us a logn component.

3. However, for each division, we perform n operations (comparing each element with the pivot). This gives us the n component.

4. Therefore, the average time complexity of quicksort is O(n logn).

However, in the worst-case scenario, when the smallest or largest element is always chosen as the pivot, the time complexity of quicksort can be O(n^2). But this scenario is not common if we choose the pivot randomly.