Recommended Problems

B level

1. Problem 2 only
2. Problem 1
3. Problem 1a
4. Problem 4

A level

1. Suppose the optimal (and possibly unknown) solution to problem P has order of growth F(N). Suppose that the best known solution has runtime that is Θ(B(N)). Finally, suppose that there is a clever proof that no solution can possibly have order of growth that is less than L(N). Which of the following can you surmise?

• F(N) = O(B(N))
• B(N) = O(F(N))
• The limit of F(N)/B(N) as N goes to infinity cannot be infinity.
• F(N) = Ω(L(N))
• L(N) = Ω(F(N))
• B(N) > F(N) for sufficiently large N.