Using the substitution method, Prove that the running time of the following recursive relation is O(N) T(n) = T(n / 2) + T(7n / 10) + O(n)

Problem 3. Consider the following recurrence. T(n) = {(n) = 37(n T(n) = 3T(n/2) + n2 if n=1 otherwise. (a) Solve this recurrence exactly by the method of substitution. You may assume n is a power of 2. (b) Solve it using the recursion tree method.

Please Help ASAP!!!!

Solving Recurrences Using Back-Substitution.step by stepFunction Fun(n){if (n >1)return (Fun(n/2))}

Use a recursion tree to determine a good asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. Use the substitution method to prove your answer.

Solving recurrences using the Substitution method. Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Solve using the substitution method. Assume that T(n) is constant n ≤ 2. Make your bounds as tight as possible and justify your answers. Hint: You may use the recursion trees or Master method to make an initial guess and prove it through induction a. T(n) = 2T(n-1) + 1 b. T(n) = 8T(n/2) + n^3

Solve using the recursion tree T(n) = 4T(n-1) + c, where c is a positive constant, and T(0)=0.

data structure and algorithm

Explain the complete work !

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=4T(n/2+2)+n. Use the substitution method to verify your answer.

Use the recursion tree method to solve the following recurrence T(n) by finding the tightest function f(n) such that T(n) = O(f(n)). T(n) ≤ 4.T(n/3) +0(n3)