The following is a implementation of the Ackermann function: public static long Ackermann(int m, int n){ if (m == 0) return n + 1; else if (n == 0) return Ackermann(m - 1, 1); else return Ackermann(m - 1, Ackermann(m, n - 1)); }
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- Given two integers x snf y, the following recurrsive definition determined the greatest common divisor of x and y, Write gcd(xy). Write a recursive function, gcd, that takes two integers as parameters and returns the greatest commmon divisorof numbers.Also write a program to test your function. Write a recursive function,reverseDigits, that takes an integer as a parameter snd returns the number with the digits reversed. Also write a program to test your application.Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, the pattern generated is as follows: **** *** ** * * ** *** **** Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the preceding pattern.Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is:********************Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern.
- Using a source-level debugger, determine for what values of argumentsthe function Mystery returns a zero.#include <stdio.h>int Mystery(int a, int b, int c);int main(void){int sum = 0; // running sum of Mysteryfor (int i = 100; i > 0; i--) {for (int j = 1; j < i; j++) {for (int k = j; k < 100; k++)sum = sum + Mystery(i, j, k);}}}int Mystery(int a, int b, int c){int out;out = 3*a*a + 7*a - 5*b*b + 4*b + 5*c ;return out;}Write a recursive function, reverseDigits, that takes an integer as a parameter and returns the number with the digits reversed. Also, write a program to test your function.In Kotlin, Write and test a recursive function called harm with an expression body that takes an Int argument n and calculates the sum of 1/1 ... 1/n. For example, harm(3) should return about 1.833333333. You do not need to worry about integer division.
- In C programming Mathematically, given a function f, we recursively define fk(n) as follows: if k = 1, f1(n) = f(n). Otherwise, for k > 1, fk(n) = f(fk-1(n)). Assume that there is an existing function f, which takes in a single integer and returns an integer. Write a recursive function fcomp, which takes in both n and k (k > 0), and returns fk(n). int f(int n);int fcomp(int n, int k){Write a recursive function that returns true if the digits of a positive integer are in increasing order; otherwise, the function returns false. Also, write a program to test your function.Write a recursive function that returns a value of 1 if its string argument is apalindrome and zero otherwise.* Note that for the function parameters, you need to accommodate for the shrinkingstring, so that the string shrinks both from beginning and end after each recursive call.** Think about the simple cases or base cases. The 2 base cases have conditions thatwould return 0 and return 1 independently.For the palindrome, create a driver program. First ask the user to enter anystring through the keyboard. Then remove all the spaces and punctuations from thestring. Also, remove any letter capitalization from the string. Finally, pass the string tothe palindrome function through a function call.
- Write a recursive function, sumDigits, that takes an integer as a parameter and returns the sum of the digits of the integer. Also, write a program to test your function.Write a recursive function definition for the following function: int squares(int n); //Precondition: n >= 1 //Returns the sum of the squares of numbers 1 through n. For example, squares(3) returns 14 because 12 + 22 + 32 is 14.Write a function that takes in an integer n and computes n!. Do this without recursion. In [ ]: deffactorial_iter(n):"""Takes in an integer n>0 and returns the product of all integers from 1 to n."""# YOUR CODE HEREraiseNotImplementedError() In [ ]: In [ ]: assert factorial_iter(6) == 720 assert factorial_iter(7) == 5040 assert factorial_iter(10) == 3628800