Let's analyze the Heap enqueue/dequeue operations with different assumptions. Imagine that the elements already in the queue were put into a sequence with the head element at the front at the lowest priority elements toward the end. Then assume that any new element to be enqueued is equally likely to be placed anywhere into that sequence. You can assume that the heap contains n = 2k-1 elements for simplicity.

a) Find the average complexity of an enqueue operation.

b) Find the average complexity of the dequeue (remove) operation.