Consider the following two binomial queues:

Q1: 0101

Q2: 1001

a. How many elements are there in each of Q1 and Q2?

b. What is the binary representation of the binomial queue obtained after merging Q1 and Q2?

c. Note that a binomial tree of height h is formed by merging two binomial trees of height h-1. Let C(h,d) be the number of nodes at a depth d in a tree of height h. i. (1 point) How much are C(h,0) and C(h,h)? ii. (3 points) Write down an recurrence for C(h,d) in terms for the C values for trees of smaller heights.

d. What is the time complexity of inserting an element in a binomial queue in which the height of the tallest binomial tree is h?