Sorting

Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting $n$ ($\geq 2$) numbers? In the recurrence equations given in the options below, $c$ is a constant.

Suppose you are provided with the following function declaration in the C programming language.

int partition(int a[], int n);

The function treats the first element of a[] as a pivot, and rearranges the array so that all elements less than or equal to the pivot is in the left part of the array, and all elements greater than the pivot is in the right part. In addition, it moves the pivot so that the pivot is the last element of the left part. The return value is the number of elements in the left part. The following partially given function in the C programming language is used to find the $k^{th}$ smallest element in an array a[] of size n using the partition function. We assume $k \leq n$.

int kth_smallest(int a[], int n, int k)
{
    int left_end = partition(a,n);

    if ( left_end+1 == k ){
        return a[left_end];
    }

    if ( left_end+1 > k ){
        return kth_smallest( ____________ );
    } else {
        return kth_smallest( ____________ );
    }
}

The missing argument lists are respectively

Assume that a mergesort algorithm in the worst case takes 30 seconds for an input of size 64. Which of the following most closely approximates the maximum input size of a problem that can be solved in 6 minutes?