In this problem, we review binomial heap operations for heaps of the figure below. In case of merging trees in the following operations, in case there were three binomial trees of the same order, merge the two older trees (keep the new tree which is the product of previous merge).

a) Consider the heap H1. Indicate which nodes are probed in get-Max() operation on H1.

b) Apply the operation merge on heaps H1 and H2. Show intermediate steps.

c) Apply operation extract-max on heap H3. Show intermediate steps.

d) Apply operation insert on heap H4. Assume you insert value x = 30 to the heap. Show intermediate steps.

2310 68 154 15 (43 4 13 40 20 30 12 17 H1 40 10 20 20 15 30 27 0 19 18 15 H4 25 H3