When writing a recursive method, O you do not need to know ahead of time exactly how many levels of recursion will occur. you must keep count of how many recursion call levels you have traversed. O you must make sure the method does not take any input parameters.
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- JAVA Question 2: For two integers m and n, their GCD (Greatest Common Divisor) can be computed by a recursive method. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Method body: If m is 0, the method returns n. If n is 0, the method returns m. If neither is 0, the method can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n (or m % n). The recursive method cannot have loops. Note: although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. main method: Prompt and read in two numbers to find the greatest common divisor. Call the gcd method with the two numbers as its argument. Print the result to the monitor. Example program run: Enter m: 12 Enter n: 28 GCD(12,28) = 4 And here is what I have so far, package CSCI1302;import java.util.*;public class RecursionDemo { public static void…Java Program: Recursive Method There are n people in a room where n is an integer greater then or equal to 2. Each person shakes hands once with every other person. What is the total number of handshakes in the room? Write a recursive method to solve this problem with the following header:public static int handshake(int n)where handshake(n) returns the total number of handshakes for n people in the room. To get you started if there are only one or two people in the room, then:handshake(1)=0handshake(2)=1Which of the following is/are true regarding the characteristics of recursion? a.Every recursive call reduces the original problem, bringing it increasingly closer to a base case until it becomes that case. b.Recursive method requires less memory than an iterative method. c. It is possible to convert every recursive method to an iterative method. d.The method is implemented using an if-else or a switch statement that leads to different cases. e.One or more base cases are used to stop recursion.
- Write factorial1 function in python 3.8 follow the directions provided below, don't need anything else as long as it meets all the requirements below. Function: factorial1 The function implements an iterative factorial. It takes an integer n as argument and returns n! The method needs to be computed interactively (not recursivelyGiven the sequence, S2 = 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, … Write a RECURSIVE method called “sequence2” that takes a single int parameter (n) and returns the int value of the nth element of the sequence S2. You will need to determine any base cases and a recursive case that describes the listed sequence. Use the following code to test your answers to questions 3 and 4the output should print the two sequences given (S & S2): public class TestSequences { public static void main(String[] args) { for(int i = 0; i < 10; i++) { System.out.print(sequence(i) + " "); // 2, 4, 6, 12, 22, 40, 74, 136, 250, 460 } System.out.println(); for(int i = 0; i < 10; i++) { System.out.print(sequence2(i) + " "); // 1, 2, 4, 5, 7, 8, 10, 11, 13, 14 } } // *** Your method for sequence here *** // *** Your method for sequences2 here *** } // end of TestSequences class1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…
- JAVA Remember to look at the examples input and output at the bottom! Implement the recursive function such that creates an unfilled triangle with the base of the number inputted by the user as shown at the link at the bottom. Notice that the spaces in between the stars start on the 3rd row asterix and the bottom row is always filled with the number the user inputs. You may pass in any parameters you want into the function. There is no test cases. Requirements A) Parameters picked such that enables the recursive functionality B) Uses the user input to do recursion with the number the user enters as the base of the triangle (see below) C) Has a base case that stops the recursion D) Prints out the correct shape user input 2 * ** user input 3 * ** *** user input 4 * ** * * **** user input 5 * ** * * * * ***** user input 6 * ** * * * * * * ******- use Eclipse or Netbeans to create a project. - In the new created project, create a recursive method to implement the following formula : a1 = 3 an = 4 an−1 +1, for n ≥ 2 - Use the main method to test the recursive method for various values of n like : for n=1, n=2, n=3, n= 10; - write the same method but in sequential form (not Recursive). And compare between results for the same values of n. using java (data structure )Create a class Recursion. It will have two static methods: removeX and countSubstring and write each function recursively. Recursion class removeX The removeX function will take a String as a parameter. It will return a new String that is the same as the original String, but with all “x” characters removed. This method will be case insensitive. countSubstring The countSubstring function will take two strings as parameters and will return an integer that is the count of how many times the substring (the second parameter) appears in the first string without overlapping with itself. This method will be case insensitive. For example: countSubstring(“catwoman loves cats”, “cat”) would return 2 countSubstring(“aaa nice”, “aa”) would return 1 because “aa” only appears once without overlapping itself. Create a Main class to test and run your Recursion class.
- C# Write a recursive method called Power(base, exponent) that, when called, returns base exponent . For example, Power ( 3, 4 ) = 3 * 3 * 3 * 3. Assume that exponent is an integer greater than or equal to 1. The recursion step should use the relationship: base exponent = base * base exponent – 1 The terminating condition occurs when exponent is equal to 1 because base 1 = base Incorporate this method into an application that enables the user to enter the base and exponent. Requirements: In the Main() method, declare three arrays of long data types: baseNumbers, exponents, and results. Each array should be created to hold exactly 5 members. Using a FOR loop, populate the baseNumbers array with random integers between 1 and 50 and populate the exponents array with random integers between 1 and 10. Use a random number generator to create these random numbers. Using another FOR loop, call the Power method, passing it a member of the baseNumbers array and a member of the exponents…Exercise 4 (class Ackermann) The Ackermann recursive function is defined as follows: n +1 А(т - 1,1) A(m – 1, A(m, n – 1)) if m> 0 and n > 0. if m %3D А(т, п) — if m > 0 and n = 0 Its arguments are never negative and it always terminates. Write a Java method which returns the value of A(m,n). Write the following code fragment inside the main method to test Ackermann function and report what will happen. for (m = 0; m <= 4; m++) for (n = 0; n < 6 - m; n++) System.out.printf("A(%d, %d) = %d\n", m, n, ackermann(m, n));Determine whether a string is a palindromeA palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces.The specifications for this assignment are: •Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution: Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes StackVector and QueueVector respectively. You already have access to the relevant exception classes and interfaces for the above ADTs. •All of your belong to a Java…