What is the time complexity of the following functions? a) f(n) = 5log(n) + 10 b) h(n) = 3n³+ 2n
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- Question 4: The function T(n) is recursively defined as follows: 1 if n = 1, 고 +. T(n -1) if n> 2. Prove that T(n) = 0(n log n).Produce the recursive version of the following iterative code. Also find T (n) and S (n). for (int x-0;x*Find a non-recursive formula for f (n) : f (0) = 7, f (n) = 4f (n − 1)/9 for n ≥ 1 *Define the sequence: an = 1+ (n+3)2 for n = 1,2,3, ... recursively.r Examples: Find the tight bound of the following recursive functions, T(n). T(n)=9T(n/3) +n T(n)= T(2n/3) +1 ● T(n)=3T(n/4)+nlogn ● T(n) = 2T (n/2)+nlogn T(n)=2T(n/2) + O(n) • T(n)=8T(n/2) +0(n²) ● T(n) = 7T(n/2) + O(n²)Solve the recursion by substitution: T(n) = 3T(n/2)+ 5n where T(1)=1Find the space complexity of the following code fib(int n) { if (n <= 1) return n; return fib(n-1) + fib(n-2); }Using the recursion three method find the upper and lower bounds for the following recur- rence (if they are the same, find the tight bound). T(n) = T(n/2) + 2T(n/3) + n.8. Give a recursive definition of the sequence {an}, n =1, 2, 3, ... ifa) an = 4n − 2. b) an = 1 + (−1)n.c) an = n(n + 1). d) an = n2.Given the recursive function definition:s(n) = 5 + n * s(n-1) + s(n-2) s(0) = 1 s(1) = 3Question: Evaluate: s(3)Derive the tight-bound notation of the function given below using recursion method с, n 1Determine the running time for each recursive functions 1. T(n) = T([n/2]) + 1 2. T(n) = T(n-1) + n 3. T(n) = 2T([n/2] + √n 4. T(n) = 16T([n/4]) + n2Q3) Fibonacci sequence is computed as follows Fib(0) = 0, Fib(1) = 1, Fib(n) = Fib(n-1) + Fib(n-2) n>=2 a) Implement a recursive function that receives n and returns Fib(n)SEE MORE QUESTIONS