Consider the following statements:

I. The smallest element in a max-heap is always at a leaf node
II. The second largest element in a max-heap is always a child of the root node
III. A max-heap can be constructed from a binary search tree in Θ(n) time
IV. A binary search tree can be constructed from a max-heap in Θ(n) time

Which of the above statements are TRUE?

The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is ________

Consider the following pseudo code. What is the total number of multiplications to be performed?

D = 2
for i = 1 to n do
   for j = i to n do
      for k = j + 1 to n do
           D = D * 3

Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter.

MultiDequeue(Q){
   m = k
   while (Q is not empty and m  > 0) {
      Dequeue(Q)
      m = m - 1
   }
}

What is the worst case time complexity of a sequence of n operations on an initially empty queue?