6. What is the run-time complexity of locating (but not removing) the maximum element in a max-heap of N elements?

(a) O(1) (b) O(log N) (c) O(N) (d) O(N log N) (e) O(N2 )

7. What is the run-time complexity of inserting a new element into a max-heap of N elements and ensuring the heap property is maintained?

(a) O(1) (b) O(log N) (c) O(N) (d) O(N log N) (e) O(N2 )

8. A student has proposed the following method as a faster way of counting the number of elements in a doubly-linked list with a sentinel head node.

def fast_count(self):

n = 0

h = self.head.next

while h is not self.head:

if h.next is not self.head:

n, h = n+2, h.next.next

else: n, h = n+1, h.next

return n

What is the time complexity of fast_count when run on a list with N elements?

(a) O(1) (b) O(log N) (c) O(N) (d) O(N log N) (e) O(N2 )