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- (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.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…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 Function
- Question 2: Implementing a Recursive Function .Write recursive function, recursionprob(n), which takes a positive number as its argument and returns the output as shown below. The solution should clearly write the steps as shown in an example in slide number 59 and slide number 60 in lecture slides. After writing the steps, trace the function for “recursiveprob(5)” as shown in an example slide number 61. Function Output: >> recursionprob(1) 1 >> recursionprob(2) 1 4 >> recursionprob(3) 1 4 9 >>recrusionprob(4) 1 4 9 161. 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…
- 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.Computer scientists and mathematicians often use numbering systems other than base 10. Write a program that allows a user to enter a number and a base and then prints out the digits of the number in the new base. Use a recursive function baseConversion (num, base) to print the digits. Hint: Consider base 10. To get the rightmost digit of a base 10 number, simply look at the remainder after dividing by 10. For example, 153 % 10 is 3. To get the remaining digits, you repeat the process on 15, which is just 153 // 10. This same process works for any base. The only problem is that we get the digits in reverse order (right to left). The base case for the recursion occurs when num is less than base and the output is simply num. In the general case, the function (recursively) prints the digits of num // base and then prints num % base. You should put a space between successive outputs, since bases greater than 10 will print out with multi-character "digits." For example, baseConversion(1234,…