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?

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≤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 arguments lists are respectively

Consider a binary max-heap implemented using an array. What is the content of the array {25, 14, 16, 13, 10, 8, 12} after two delete operations?

Consider a binary max-heap implemented using an array. Which one of the following array represents a binary max-heap?