Chapter 3, Problem 5P

(a)

Program Plan Intro

To show that for any two function that are asymptotically nonnegative, either $f(n)=O(g(n))$ or $f(n)={\Omega }^{\infty }(g(n))$ .

(b)

Program Plan Intro

To describe the potential advantages and disadvantages of using ${\Omega }^{\infty }$ instead $\Omega$ of to characterize the running time of the program.

(c)

Program Plan Intro

To describe theeffect of using “if and only if” in theorem 3.1 as it substitute $O\text{'}$ for $O$ but still use $\Omega$ .

(d)

Program Plan Intro

To verify the corresponding analog of Theorem 3.1.