CSCI 305, Homework # 3 (Solution)

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• Find Θ(T(n)) for each case.
• For problem 1, find the solution three ways:
– The master theorem
– The substitution method
– Iterate, cancel, and solve the summation to find an exact solution.
• For all other problems, use just the master theorem.
• When using the master theorem, be explicit about nlogba, and about which case of the master theorem applies, about making sure the special condition applies in case 3 of the master theorem, and about proving f’s correct asymptotic relationship to nlogba.
1. Solve this one three different ways: master theorem, substitution method, and the iterate/cancel/summation method.
T(n) = 2T(n/2) + n4 2. Solve this one using the master theorem.
T(n) = 16T(n/4) + n2
3. Solve this one using the master theorem.
√ T(n) = 2T(n/4) + n
4. Solve this one using the master theorem.
T(n) = 4T(n/3) + nlgn
5. Solve this one using the master theorem.
2√
T(n) = 4T(n/2) + n n
1

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