Suppose, for now, that n is a power of 2. An easy way of doing so is theexpansion method, which simply expands f (n) all the way down:f (n) ≤ c2 + f (n/2)≤ c2 + c2 + f (n/22)≤ c2 + c2 + c2 + f (n/23)≤ c2 + ... + c2| {z }log2 n of them+f (1)= c2 · log2 n + c1 = O(log n).Yufei Tao Recursion

Which of the given options provides the increasing order of complexity of functions f1, f2, f3 and f4:f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)

What is the time complexity of the recursive implementation used to find the nth fibonacci term?  O(1)  O(n2) O(n!) Exponential

Practice the Substitution method, recursive tree method, and master theorem on the following:i) F(n)=n∗F(n−1)ii) T(n) = 1, when n=1=1+T(n-1) when n>1iii) Fn=Fn−1+Fn−2.iv) T(n)=4T(n/2)+n^2v) T(n)=2T(n/2)+n

Cho biết độ phức tạp của đoạn mã giả sau dùng ký hiệu big-O.int F(int n)if (n <= 2)return 1elsereturn F(n − 2) * F(n − 2)a.O(2^(n/2))b.O(2^n)c.O(n^2)d.O( n )

What is the time complexity of this function / algorithm?int Fibonacci(int number){ if (number <= 1) return number; return Fibonacci(number - 2) + Fibonacci(number - 1);}O(n)O(1)O(log(n))O(nlog(n))O(2^n)O(n!)O(n^2)