In Java, There are two algorithms that perform a particular task. Algorithm 1 has a complexity function f(n) =2n + 248. Algorithm 2 has a complexity function g(n) = n^2 + 16. Which algorithm is more efficient when n = 5? Which is more efficient when n = 20?

Algorithm Prime2 (n: integer):{T,F};           prime = F; d=2; while d < n/2 and prime = F do    if n mod d = 0 then prime = T                           else d = d+1 return prime; How many times is the operation "n mod d" performed, when the input for Algorithm Prime 2 is n=123? Group of answer choices 1 4 3 2 None of these.

Find the Time Complexity and The Space Complexity

n-1 Geometric (n) = i=1 i=1 1 1 * n-1 П %3D Harmonic (n) = i=1 n Let's look at examples. If we use n = 4, the geometric progression would be 1 * 2 * 3 * 4 = 24, and the harmonic 1.1.1 1 progression would be 1* -= 0.04166. 2 3 4 24 Task #1 Tracing Recursive Methods 1. Copy the file Recursion.java (see Code Listing 16.1) from the Student Files or as directed by your instructor. 2. Run the program to confirm that the generated answer is correct. Modify the factorial method in the following ways: a. Add these lines above the first if statement: int temp; System.out.println ("Method call -- " + "calculating " "Factorial of: " + n); + Copyright © 2019 Pearson Education, Inc., Hoboken NJ b. Remove this line in the recursive section at the end of the method: return (factorial (n - 1) * n); c. Add these lines in the recursive section: temp = factorial (n - 1); System.out.println ("Factorial of: " (n - 1) + " is " temp); return (temp * n); 3. Rerun the program and note how the recursive calls…

Using recursion, write a Java program that takes an input ‘n’ (a number) from a user to calculate and print out the Fibonacci using the following modified definition:   F(N) = 1                                                    if n = 1 or n = 2         = F((n+1)/2)2 + F((n-1/2)2           if n is odd         = F(n/2 + 1)2 – F(n/2 – 1)2         if n is even                                     Your solution must implement recursion to receive points for this question.

Use Master Therom to determine the complexity of the following:

Suppose an algorithm requires 2n steps to complete a task for an input of size n. If the size of the input is doubled, what happens to the number of steps?     The number of steps for the larger input is equal to the number of steps for the original input.     The number of steps for the larger input is twice the number of steps for the original input.     The number of steps for the larger input is four times the number of steps for the original input.     The number of steps for the larger input is the square of the number of steps for the original input.     The number of steps for the larger input is more than the number of steps for the original input, but is none of the above.

1. A certain computer algorithm executes four times as many operations when it is run with an input of size n as when it is run with an input of size n – 1. Here, n > 1 is an integer. When the algorithm is run with an input of size 1, it executes 12 operations. How many operations does the algorithm execute when it is run with an input of size 5? How many operations does the algorithm execute when it is run with an input of size n?