1. a. Show that N inserts into an initially empty binomial queue take O(N) time in the worst case.
b. Give an algorithm to build a binomial queue of N elements, using at most N - 1 comparisons between elements.
c. Propose an algorithm to insert M nodes into a binomial queue of N elements in O(M + log N) worst-case time. Prove your bound.
2. Write an ef?cient routine to perform insert using binomial queues. Do not call merge.
3. For the binomial queue
a. Modify the merge routine to terminate merging if there are no trees left in H2 and the carry tree is nullptr.
b. Modify the merge so that the smaller tree is always merged into the larger.