CLRS 17.1 Polymerization Analysis

17.1-1
No

17.1-2
Assuming that in addition to the highest bit is 1, the remaining bits are all 0, that is, the 2k−1=10...0 2^{k-1}=10...0, the sequence of operations is −1,+1,−1+1,...-1,+1,-1+1,..., at which time each operation is to be flipped, the runtime is Θ (NK) \theta ( NK).

17.1-3
∑i=1nci≤n+∑j=0lgn2j=n+ (2n−1) <3n \sum \limits_{i=1}^{n}c_i\le n+\sum \limits_{j=0}^{\lg n}2^j=n+ (2n-1). So the average cost is less than 3.
It is also the cost of O (1) O (1) to know the amortization through the aggregation analysis.