11.What is the order of growth of the recurrence relation A(n)-8A(n/8)+n? * A(n) € 8(n**3) A(n) € 8(n**2) OA(n) e e(n log n) A(n) € 8(n)

Solve this recurrence relations together with the initialconditions given. a_{n+2} = −4a_{n+1} + 5a_n for n ≥ 0, a_0 = 2, a_1 = 8

Asymtotic Analysis : Prove the following claims

The runtime complexity, T(n), of the three following recurrence relation solved by Master's Theorem) are T(n) = 6T(n/3) + n² logn T(n) = 64T(n/8)- n² log n T(n) = 4T(n/2) + n/logn (The solution for the three relations are respectively given by) A: (nlogn), 9(n²), (n² logn) B: 9(n²), (n² logn), (n log n) C: (n²logn), Master's Theorem does not apply, 9(n²) D: 0(n²), Master's Theorem does not apply, 9(n² log n) E: 0(n² logn), 9(n²), Master's Theorem does not apply F: 9(n²), (n² logn), Master's Theorem does not apply

25 f(n) = f(n/2) + 2 is a recurrence relation for the binary search problem true?

Find the order of growth for solutions of the following recurrences using master theorem. 1. T(n) = 4T(n/2) + n, T(1) = 1 2. T(n) = 4T(n/2) + n^2, T(1) = 1 3. T(n) = 4T(n/2) + n^3, T(1) = 1

Simplify n∧(¬q∨q) to n

Determine the strongest asymptotic relation between the functions f(n)= 2log and g(n)-(logn), i.e., whether f(n) = o(g(n)), f(n) = O(g(n)), f(n) = (g(n)), f(n) = w(g(n)), or f(n) = (g(n)).

Apply Master Theorem to bound each one of the following recurrence relations using Big-O notation. Please show work in depth. In all cases T(n)=1.