1) a) b) Consider the following recursive function. You can assume that it will be invoked with non-negative integers. int mystery (int n, { } = m) if (n == return n; int m) else if (n == 0) return m; else if (m == 0) return n; else return mystery(m, n % m); Trace the execution of the three function calls mystery(363, 55), mystery(126, 49), and mystery(81, 37). For each of these three cases, how many calls do each of them make until they return the answer? What are the values of the parameters in each of the calls? Which base case do they reach? What does the mystery function actually do? Can you connect it to a known algorithm for solving this problem?
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- 09. Question Write a recursive function printRev ( int a[ ], int s, int e) that receives an integer array a [ ], a start index s, and an end index e. The function should print the array elements in reverse order. void printRev ( int a[ ], int s, int e); Trace your function given the following array and function call. Draw your steps. int a[ ] = {4, 2, 3, 5};and printRev(a, 0, 3); language c++ .1. 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. 2. A palindrome is a string that reads the same both forward and backward. For example, the string "madam" is a palindrome. Write a program that uses a recursive function to check whether a string is a palindrome. Your program must contain a value-returning recursive function that returns true if the string is a palindrome and false otherwise. Do not use any global variables; use the appropriate parameter.1. Write a recursive function that takes a string as an input and returns the reverse of the string. 2.Write a recursive function rec_string that produces the output shown below for the corresponding function calls. Write a main function to test the function. Method call rec_string(‘abcde’), will produce the following output: *ede cde bcde abcde Method call rec_string(‘abc’), will produce the following output: *cbc abc 3. 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…
- 4.7.1: Writing a recursive math function. Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val):if exponent_val == 0:result_val = 1else:result_val = base_val * ''' Your solution goes here ''' return result_val user_base = int(input())user_exponent = int(input()) print('%d^%d = %d' % (user_base, user_exponent,raise_to_power(user_base, user_exponent))) need solution to result_val =base_val* ???????4.7.1: Writing a recursive math function. Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val):if exponent_val == 0:result_val = 1else:result_val = base_val * ''' Your solution goes here ''' return result_val user_base = int(input())user_exponent = int(input()) print('%d^%d = %d' % (user_base, user_exponent,raise_to_power(user_base, user_exponent))) need to be in pythonWrite code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val):if exponent_val == 0:result_val = 1else:result_val = base_val * ''' Your solution goes here ''' return result_val user_base = int(input())user_exponent = int(input()) print('{}^{} = {}'.format(user_base, user_exponent,raise_to_power(user_base, user_exponent)))
- Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val): if exponent_val == 0: result_val = 1 else: result_val = base_val * Your solution goes here return result_val user_base = int(input())user_exponent = int(input()) print('%d^%d = %d' % (user_base, user_exponent, raise_to_power(user_base, user_exponent)))1. Implement a recursive function called firstTwo that returns the sum of the firsttwo digits in a positive number. If there is only one digit, that digit is returned.Note this function is returning an integer, not printing. There should be no use ofcout within your function.Title line: int firstTwo(int n)ex. firstTwo(8325) returns 11ex. cout << firstTwo(428); // prints 62. Implement a function called findMinGap that will return the smallest gap betweenadjacent entries of an integer array. A gap between two numbers is the absolutevalue of their difference. For example, if an array contains the elements {10, 14,-5, -3, 0, 5, 7}, the minimum gap is 2 (between -5 and -3).Title line: int findMinGap(int array[], int length)3. Implement a function called findLargestIndex which returns the index of the rowwith the largest sum.ex. int array[3][6] = {{3, 6, 8, 2, 4, 1}, // sum = 24{2, 4, 5, 1, 3, 4}, // sum = 19{1, 0, 9, 0, 1, 0}}; // sum = 11If the findLargestIndex function was called…1. Implement a recursive function called firstTwo that returns the sum of the firsttwo digits in a positive number. If there is only one digit, that digit is returned.Note this function is returning an integer, not printing. There should be no use ofcout within your function.Title line: int firstTwo(int n)ex. firstTwo(8325) returns 11ex. cout << firstTwo(428); // prints 62. Implement a function called findMinGap that will return the smallest gap betweenadjacent entries of an integer array. A gap between two numbers is the absolutevalue of their difference. For example, if an array contains the elements {10, 14,-5, -3, 0, 5, 7}, the minimum gap is 2 (between -5 and -3).Title line: int findMinGap(int array[], int length)3. Implement a function called findLargestIndex which returns the index of the rowwith the largest sum.ex. int array[3][6] = {{3, 6, 8, 2, 4, 1}, // sum = 24{2, 4, 5, 1, 3, 4}, // sum = 19{1, 0, 9, 0, 1, 0}}; // sum = 11If the findLargestIndex function was called…
- Consider the following recursive function. What does it calculate in terms of x, y, and z? 01: Private Function CalcRecurse(ByVal x As Integer, ByVal y As Integer, ByVal z As Integer) As Integer 02: If x <= 1 Then 'Assume that CalcRecurse always starts with x > 1 03: Return y 04: Else 05: Return z + CalcRecurse(x - 1, y, z) 06: End If 07: End Function4.7.1: Writing a recursive math function. Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16Write code to complete raise_to_power(). Note: This example is for practicing recursion; a non-recursive function, or using the built-in function math.pow(), would be more common.Sample output with inputs: 4 24^2 = 16 def raise_to_power(base_val, exponent_val): if exponent_val == 0: result_val = 1 else: result_val = base_val * ''' Your solution goes here ''' return result_val user_base = int(input())user_exponent = int(input()) print('{}^{} = {}'.format(user_base, user_exponent, raise_to_power(user_base, user_exponent)))