Prove that the solution of the recurrence T(n) = T(n/2) +6(logk n) with T(1-6(1), for any integer...
1 =1 ifn -HS).lft! 6. For the recurrence T(n)-n = 37 1 +1 ifn>1 show that T(n) e Θ(n) . (Make sure that you prove two facts. T(n) O(n) and T(nje Ω(n)). Consider only n 3. Hint: use the idea of subtracting the lower-power term (see p.85).
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...
1. Solve the recurrence relation T(n) = 2T(n/2) + n, T(1) = 1 and prove your result is correct by induction. What is the order of growth? 2. I will give you a shortcut for solving recurrence relations like the previous problem called the Master Theorem. Suppose T(n) = aT(n/b) + f(n) where f(n) = Θ(n d ) with d≥0. Then T(n) is: • Θ(n d ) if a < bd • Θ(n d lg n) if a = b...
6. Consider the recurrence relation T(n) = 2T(n-1) + 5 for integers n 1 and T(O) = 0. Find a closed-form solution Using induction, prove your solution correct for all integers n 20.
Consider the recurrence T (n) = 3 · T (n/2) + n. • Use the recursion tree method to guess an asymptotic upper bound for T(n). Show your work. • Prove the correctness of your guess by induction. Assume that values of n are powers of 2.
Solve the recurrence relation T(n) = 2T(n / 2) + 3n where T(1) = 1 and k n = 2 for a nonnegative integer k. Your answer should be a precise function of n in closed form. An asymptotic answer is not acceptable. Justify your solution.
4. Suppose T (n) satisfies the recurrence equations T(n) = 2 * T( n/2 ) + 6 * n, n 2 We want to prove that T (n)-o(n * log(n)) T(1) = 3 (log (n) is log2 (n) here and throughout ). a. compute values in this table for T (n) and n*log (n) (see problem #7) T(n) | C | n * log(n) 2 4 6 b. based on the values in (a) find suitable "order constants" C and...
Solve the recurrence relation T(n)=T(n1/2)+1 and give a Θ bound. Assume that T (n) is constant for sufficiently small n. Can you show a verification of the recurrence relation? I've not been able to solve the verification part so far note: n1/2 is square root(n)
What is the solution to the following recurrence? T(n) = 16T(3/4)+ n T(1) = 1 T(n) = 0n) T(n) = 0 (n1/2) T(n) = O(na) T(n) = O(n log(n)) the four other possible answers are incorrect
Derive a good upper bound for recurrence T(n) = 5T(n/3)+ n, with base case T(n) = c when n ≤ 3, for some constant c > 0.