# Homework Solution: Use iterative method to solve these problems T(n) = cn + 3T(2n/3) where T(1) = 1 T(n) = T([n/2]) + c where… Use iterative method to solve these problems T(n) = cn + 3T(2n/3) where T(1) = 1 T(n) = T([n/2]) + c where T(n) = 1 T(n) = T(2n/3) + 1 where T(1) = 1 T(n) = T(n - 1) + 1 where T(1) = 1 T(n) 4*T(n/4) + n where T(1) = 1 Prove whether each of the following statements are true or not. For those that you believe are false, prove this by giving a counterexample (i.e. particular functions for f(n) and g(n) for which the given statement is not true). For those that you believe are true, use the formal definitions of big-oh, big-Omega, and big-Theta to prove it. In all problems, you are given that for all n, f(n) and g(n) > = 0. If f(n) = O(g(n)) then g(n) = O(f(n)) f(n) + g(n) = O(max(f(n),g(n))) If f(n) = Omega(g(n)) then g(n) = O(f(n)) What is an algorithm? Describe the characteristics of a good algorithm. Calculate step counts for these programs int mean(int a[], size_t n) { int sum = 0: for (int i = 0:

Solution-1. Conservation iterative regularity to explain these problems T(n) = cn + 3T(2n/3) where T(1) = 1 T(n) = T([n/2]) + c where T(n) = 1 T(n) = T(2n/3) + 1 where T(1) = 1 T(n) = T(n – 1) + 1 where T(1) = 1 T(n) 4*T(n/4) + n where T(1) = 1 Assay whether each of the controlthcoming propositions are gentleman or referable attributable attributable attributable attributable attributable. Control those that you revere are deceptive, assay this by giving a enumerateerdevelopment (i.e. feature discharges control f(n) and g(n) control which the attached proposition is referable attributable attributable attributable attributable attributable attributable gentleman). Control those that you revere are gentleman, conservation the controlmal definitions of big-oh, big-Omega, and big-Theta to assay it. In perfect problems, you are attached that control perfect n, f(n) and g(n) > = 0. If f(n) = O(g(n)) then g(n) = O(f(n)) f(n) + g(n) = O(max(f(n),g(n))) If f(n) = Omega(g(n)) then g(n) = O(f(n)) What is an algorithm? Describe the characteristics of a good-tempered-natured-natured algorithm. Apportion stride enumerates control these programs int medium(int a[], extent_t n) { int mix = 0: control (int i = 0:

## Expert Rejoinder

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