1- Solve the following recursive relationship using the Master Theorem T(n) = 3T(n/2) + n^2 2- Solve the following recursive relationship T(n) = 3 T(n-1) + 1; T(2) = 0 3- Prove that n^2 is in Theta(n^2 + 20 n) 4- Prove that n log n is in Omega (100 n) 5- Prove that n^2 is in O(0.01 n^3)
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In this case, a = 3 and b = 2. Since log_b(a) = log_2(3) is approximately 1.585, we can see that f(n) = n^2 is larger than g(n) = n^(log_2(3)) for large values of n. Therefore, according to the Master Theorem, the solution to the recursive relationship is T(n) = Show more…
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