Reference no: EM13945702
1. Suppose that an algorithm A runs in time fA(n) = 2n2 + 7n and that an algorithm B runs in time fB(n) = 45n + 4, for problems sizes of n. For what values of n is algorithm A faster than
B. That is, for what n is fA(n) < fB(n)?
2. Prove part 7 of Lemma 1.1 about logarithms. Use one of the earlier parts of Lemma 1.1 and consider taking the log of both sides.
3. How many different arrangements for a 52 card deck are there? How does this compare to the 1018 seconds that have passed since the Big Bang?
4. Show from definitions that P(S) = P(S | T)P(T) + P(S | not T)P(not T).
5. Prove equation 1.6 of your textbook.
6. Write an algorithm to find the second largest integer in a list of n integers. How many comparisons does your algorithm do in the worst case?
7. Prove Lemma 1.10 of your textbook.
8. Prove or disprove ∑ni=1 i2∈θ(n2).
9. Draw a decision tree for the binary search algorithm (Algorithm 1.4 on pages 55-56) for n = 17.
10. Add a row to Table showing the maximum input size that can be solved in one hour.
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