I have two questions: Is my programs code the most effective way at finding recursion or is there a much better and cleaner way? Why is the program showing 0 when I implement a number that depth is greater than 100? Shouldn't it show the number 1? Source code: package recursiveModule; public class RecursiveMethod { public static long calculateFactorial(int n, int depth) { if (depth > 100 || n <= 1) { return 1; } return n * calculateFactorial(n - 1, depth + 1); } public static void main(String[] args) { System.out.println("Factorial of 1 is " + RecursiveMethod.calculateFactorial(1, 0)); System.out.println("Factorial of 8 is " + RecursiveMethod.calculateFactorial(8, 0)); System.out.println("Factorial of 101 is " + RecursiveMethod.calculateFactorial(101, 0)); } }

Write a RECURSIVE method called "sequence" that takes a single int parameter (n) and returns the int value of the nth element of the sequence S = 2, 4, 6, 12, 22, 40, 74, 136, 250, 460, ... Where S is defined by the recursive formula: For n >= 0S(0) = 2; // Base case 1S(1) = 4; // Base case 2S(2) = 6; // Base case 3S(N) = 2 * ( S(N-1)/2 + S(N-2)/2 + S(N-3)/2)

Please help me with this using java and recursion

write a code in java (using recursion)

Write a recursive method that returns the value of N! (N factorial) using the definition given in this chapter. Explain why you would not normally use recursion to solve this problem.

Write and test a Java/Python recursive method for finding the minimum element in an array, A, of n elements. What the running time? Hint: an array of size 1 would be the stop condition. The implementation is similar to linearSum method in lecture 5 examples. You can use the Math.min method for finding the minimum of two numbers.

Implement the logarithmBase22 method which, given a long integer number, returns the result of Logz2(number), rounded down to the nearest floor integer. Design and implement this as a recursive method. Read the test cases in the JUnit tester file for more detailed specification.

The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence:1, 1, 2, 3, 5, 8, 13, 21...Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence.Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.

Personal project Q5. This question is concerned with the design and analysis of recursive algorithms. You are given a problem statement as shown below. This problem is concerned with performing calculations on a sequence A of real numbers. Whilst this could be done using a conventional loop-based approach, your answer must be developed using a recursive algorithm. No marks will be given if your answer uses loops. FindAverageAndProduct(a1, ...., an) such that n > 1 Input: A sequence of real values A = (a1, ...., an) Output:, A 2-tuple (average, product) containing the average (average) of all the values and the product (product) of all the values of the elements in A. Your recursive algorithm should use a single recursive structure to find the average and product values, and should not use two separate instances of a recursive design. You should not employ any global variables. (a) Produce a pseudo code design for a recursive algorithm to solve this problem. (b) Draw a call-stack...

Implement the recursive function for the Fibonacci code programming language: java Need full code with explanation

Personal project Q5. This question is concerned with the design and analysis of recursive algorithms. You are given a problem statement as shown below. This problem is concerned with performing calculations on a sequence ? of real numbers. Whilst this could be done using a conventional loop-based approach, your answer must be developed using a recursive algorithm. No marks will be given if your answer uses loops. FindAverageAndProduct(a1, ...., an) such that n > 1 Input: A sequence of real values A = (a1, ..., an) Output:, A 2-tuple (average, product) containing the average (average) of all the values and the product (product) of all the values of the elements in A. Your recursive algorithm should use a single recursive structure to find the average and product values, and should not use two separate instances of a recursive design. You should not employ any global variables. (a) Produce a pseudo code design for a recursive algorithm to solve this problem. (b) Draw a call-stack...

Write a static recursive method in Java called mRecursion that displays all of the permutations of the charactersin a string passed to the method as its argument. For example, the character sequence abc has thefollowing permutations: acb, bac, bca, cab, cba. Then Write a static method called getInput that get aninput string from the user and passed it to the mRecursion method written above in a method call.Please does so using what I already had //Get input from in to call recursive method //to display those char permutations public static String getInput ( ) { Scanner in = new Scanner(System.in); String combination = in.nextLine(); System.out.println("Enter string:); return stringComb; //Method to show permutations of a desired string// This only return 3 string combination for some reason static void myRecursion(String aString) { //isEmpty check if ( aString.length() == 0){...

write a code in java (using recursion)