Homework problem K on Binomial Heaps

1. (5 points) Rewrite Binomial_Heap_Insert( H, k ) so that it's worst case run time, T_Ins(n), is Θ(1+lssb(n))^[1], where lssb(n) is the number of consecutive least significant set bits in the binary representation of n, the number of keys in the heap at the time of insertion. Put another way, lssb(n) is the largest k such that 2^k divides n + 1. For example, lssb(n) is 0 if n is even, and lssb(23=10111₂) is 3.

   You may start from the Binomial_Heap_Insert() in binomialHeap.h in the course directory. Your code is not required to be runnable C++ code, as long as it is sufficiently clear pseudocode. The testing code at the bottom of the file may be of help on part b.

2. (5 points) Let S(n) = max{T_Ins(k): 1 ≤ k ≤ n)}. Show that S(n) is Θ(lg(n)).

footnote:
[1]. corrected from Θ(lssb(n)), Oct 25.