Given the following recursive algorithm to calculate the summation of the square of the first nnn positive integers.

procedure square_sum( n )

1    if (n==1)

2        s = 1

3    else

4        s = (n*n) + square_sum(n-1)

5    end of if

6    return s

Let b∈R+b∈R+b \in R^+ and n∈Nn \in N. Determine the sequence of codes in an efficient recursive algorithm to return bnb^n

procedure power_bin(b, n)

What is the Big-O notation that can best describe the power_bin(b,n) algorithm?

What is the Big-O notation that can best describe the power(b,n) algorithm?

What is the Big-O notation that can best describe the merge sort algorithm when the input is a list of nnn elements?

Let b∈R+b∈R+b \in R^+ and n∈Nn∈Nn \in N. Determine the sequence of codes in an efficient recursive algorithm to return bnbnb^n

procedure power_bin(b, n)

Let b∈R+b∈R+b \in R^+ and n∈Nn∈Nn \in N. Determine the sequence of codes in a recursive algorithm to return bnbnb^n

procedure power(b, n)

A set is defined recursively as follows:

1. Basis step: (1∈S)∧(3.5∈S)(1∈S)∧(3.5∈S)(1 \in S) \wedge (3.5 \in S)

2. Recursive step: if x∈Sx∈Sx \in S, then (x+1)∈S(x+1) \in S.

Which of the following is the best statement that describes SS?

Suppose a function f:N→Zf:N→Zf: N \to Z is defined as:

1. Basis step: f(0)f(0)f(0) = 8

2. Recursive step: f(i)=2×f(i−1)+4f(i)=2×f(i−1)+4f(i) = 2 \times f(i-1) + 4 for all i≥1i≥1i \geq 1

What is f(2)?

A set is defined recursively as follows:

1. Basis step: 2∈S2∈S2 \in S

2. Recursive step: if x∈Sx∈Sx \in S, then (x+1)∈S(x+1)∈S(x+1) \in S.

Which of the following is the best statement that describes SSS?