Chapter 17, Problem 4P

(a)

Program Plan Intro

To describe a legal red-black tree with n-nodes such that calling RB-INSERT to add the $(n+1)$ node causes $\Omega (\lg n)$

(b)

Program Plan Intro

To explain which fixed-up of RB tree algorithm is terminating and which are not.

(c)

Program Plan Intro

To argue the statement $\Phi (T\text{'})=\Phi (T)-1$ is obtained by applying RB-INSERT-FIXUP to T .

(d)

Program Plan Intro

To explain the structural modifications and potential changes resulting from RB-INSERT from nonterminating cases of RB-INSERT-FIXED.

(e)

Program Plan Intro

To argue that the amortized number of structural modifications performed by any call of RB-INSERT is $O(1)$ .

(f)

Program Plan Intro

To showthat the statement follow $\Phi (T\text{'})\le \Phi (T)-1$ for all nonterminating cases of RB-INSERT-FIXUP.

(g)

Program Plan Intro

To argue that the amortized number of modifications performed by any call of RB-DELETE-FIXUP is $O(1)$ .

(h)

Program Plan Intro

To show that any sequence of m RB-INSERT and RB-DELETE operations performed $O(m)$ structural modifications.