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- Write a recursive function for Euclid's algorithm to find the greatest common divisor (gcd) of two positive integers. gcd is the largest integer that divides evenly into both of them. For example, the gcd(102, 68) = 34. You may recall learning about the greatest common divisor when you learned to reduce fractions. For example, we can simplify 68/102 to 2/3 by dividing both numerator and denominator by 34, their gcd. Finding the gcd of huge numbers is an important problem that arises in many commercial applications. We can efficiently compute the gcd using the following property, which holds for positive integers p and q: If p > q, the gcd of p and q is the same as the gcd of q and p % q.Write a recursive fibonacci (n) function with an expression body. The function should return an Int; it will be too slow to deal with inputs whose fibonacci numbers are too large anyway. You do *not* need to use memoization. Note that: fibonacci(0) = 0 fibonacci(1) = 1 fibonacci(n, where n is greater than 1) = fibonacci(n-2) + fibonacci(n - 1)Write a recursive function called that takes a string of single names separated by spaces and prints out all possible combinations (permutations), each combination on a new line. When the input is: Alice Bob Charlie then the output is: Alice Bob Charlie Alice Charlie Bob Bob Alice Charlie Bob Charlie Alice Charlie Alice Bob Charlie Bob Alice Here is the original code in Python: def all_permutations(permList, nameList): # TODO: Implement method to create and output all permutations of the list of names. pass if __name__ == "__main__": nameList = input().split(' ') permList = [] all_permutations(permList, nameList)
- Ackermann’s function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s function. Use the following logic in your function: If m = 0 then return n + 1 If n = 0 then return A(m-1, 1) Otherwise, return A(m-1, A(m, n-1)) Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)java C++ Ackermann’s FunctionAckermann’s Function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s Function. Use the following logic in your function:If m = 0 then return n + 1If n = 0 then return A(m−1, 1) Otherwise, return A(m−1, A(m, n−1))Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2) SAMPLE RUN #0: ./AckermannRF Hide Invisibles Highlight: Show Highlighted Only The·value·of·A(0,·0)=·1↵ The·value·of·A(0,·1)=·2↵ The·value·of·A(1,·1)=·3↵ The·value·of·A(1,·2)=·4↵ The·value·of·A(1,·3)=·5↵ The·value·of·A(2,·2)=·7↵ The·value·of·A(3,·2)=·29↵Compute f(6) for the recursive function below. def f(n): if n == 0: return 1 if n == 1: return 2 else: return f(n-1)+n*f(n-2)-n
- For function addOdd(n) write the missing recursive call. This function should return the sum of all postive odd numbers less than or equal to n. Examples: addOdd(1) -> 1addOdd(2) -> 1addOdd(3) -> 4addOdd(7) -> 16 public int addOdd(int n) { if (n <= 0) { return 0; } if (n % 2 != 0) { // Odd value return <<Missing a Recursive call>> } else { // Even value return addOdd(n - 1); }}RECURSIVE PYTHON The Fibonacci sequence begins with 0 and then 1 follows. All subsequent values are the sum of the previous two, for example: 0, 1, 1, 2, 3, 5, 8, 13. Complete the fibonacci() function, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1. Ex: If the input is: 7 the output is: fibonacci(7) is 13 Note: Use recursion and DO NOT use any loops. # TODO: Write recursive fibonacci() functiondef fibonacci(): if __name__ == "__main__": start_num = int(input()) print('fibonacci({}) is {}'.format(start_num, fibonacci(start_num)))By using a recursive function to find s value: S= 2/x – 4/x + 6/x – 8/x .. 2n/x
- Using C Write a recursive function find_sum that calculates the sum of successive integers starting at 1 andending at n (i.e., find_sum(n) = (1 + 2 +. . . + ( n − 1) +n ).You have to use recursive function to solve this problem.Write a recursive function to generate nth fibonacci term in C programming. How to generate nth fibonacci term in C programming using recursion. Logic to find nth Fibonacci term using recursion in C programming. Fibonacci series is a series of numbers where the current number is the sum of previous two terms. For Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, ... , (n-1th + n-2th) Example: Input: Input any number: 10 Output 10th Fibonacci term: 55 please use C languageWrite a recursive function called that takes a string of single names separated by spaces and prints out all possible combinations (permutations), each combination on a new line. When the input is: Alice Bob Charlie then the output is: Alice Bob Charlie Alice Charlie Bob Bob Alice Charlie Bob Charlie Alice Charlie Alice Bob Charlie Bob Alice Here is my original code that needs to be fixed: def all_permutations(permList, nameList): # TODO: Implement method to create and output all permutations of the list of names. if nameList == len(permList) - 1: return nameList else: for x in range(permList, len(nameList)): permList[nameList], permList[x] = permList[x], permList[name_List] return all_permutations(permList, nameList + 1) permList[nameList], permList[x] = permList[x], permList[name_List] if __name__ == "main": nameList = input().split(' ') permList = [] all_permutations(permList, nameList)