17: recursion.cpp) Write two recursive integer functions. The first function should calculate factorials using the definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too large it should be able to detect integer overflow before it happens. The next function should calculate the greatest common factor (gcf) of two numbers. If the second number is zero, then the gcf is the other number. Otherwise, the gcf of a and b is the same as the gcf of b and a mod b.

17: recursion.cpp) Write two recursive integer functions. The first function should calculate factorials using the definition 0! = 1 and n! = (n-1)! x n. In addition, if n is too large it should be able to detect integer overflow before it happens. The next function should calculate the greatest common factor (gcf) of two numbers. If the second number is zero, then the gcf is the other number. Otherwise, the gcf of a and b is the same as the gcf of b and a mod b.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 12PE

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4.10 LAB: All permutations of names Write a program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names, then use a recursive function to create and output all possible orderings of those names separated by a comma, one ordering per line. When the input is: Julia Lucas Mia then the output is (must match the below ordering): Julia, Lucas, Mia Julia, Mia, Lucas Lucas, Julia, Mia Lucas, Mia, Julia Mia, Julia, Lucas Mia, Lucas, Julia def print_all_permutations(permList, nameList): # TODO: Implement method to create and output all permutations of the list of names. if __name__ == "__main__": nameList = input().split(' ') permList = [] print_all_permutations(permList, nameList)
Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1
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.
C++ (a) Use iteration (b) Use recursion (c) Convert the function that you wrote in part (b) into a template function. The template function should work for arrays of any type.
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…
Modify the recursive Fibonacci function to employ the memoization technique discussed in this chapter. The function creates a dictionary and then defines a nested recursive helper function named memoizedFib. You will need to create a dictionary to cache the sum of the fib function. The base case of the fib function is the same as before. However, before making any recursive calls, the helper function looks up the value for the function’s current argument in the dictionary (use the method get, with None as the default value). If the value exists, the function returns it and skips any recursive calls. Otherwise, after the helper function adds the results of its two recursive calls, it saves the sum in the dictionary with the current argument of the function as the key. Note: The program should output in the following format: n fib(n) 2 1 4 3 8 21 16 987 32 2178309 ---------------------------------------------------------------------------------- def…
Recursive Copy Function Given a string str and number n, write a program that recursively appends a copy of string str n times and returns the resulting string. Please complete the following function. n is the number of copies to add to str: function RecursiveCopy(str, n) {// your code here} The problem must satisfy the following: You must use recursion. You should end up with n+1 copies of the str total in the output because you are appending additional str copies. Use string literal formatting for the output.
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)))
11.11 LAB: Number pattern Write a recursive function called PrintNumPattern() to output the following number pattern. Given a positive integer as input (Ex: 12), subtract another positive integer (Ex: 3) continually until 0 or a negative value is reached, and then continually add the second integer until the first integer is again reached. For this lab, do not end output with a newline. Ex. If the input is: 12 3 the output is: 12 9 6 3 0 3 6 9 12 main.cpp: #include using namespace std; // TODO: Write recursive PrintNumPattern() function int main(int argc, char* argv[]) { int num1; int num2; cin >> num1; cin >> num2; PrintNumPattern(num1, num2); return 0; }
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('{}^{} = {}'.format(user_base, user_exponent,raise_to_power(user_base, user_exponent)))
11.10 LAB: All permutations of names Write a program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names (until -1), and use a recursive method to create and output all possible orderings of those names, one ordering per line. When the input is: Julia Lucas Mia -1 then the output is (must match the below ordering): Julia Lucas Mia Julia Mia Lucas Lucas Julia Mia Lucas Mia Julia Mia Julia Lucas Mia Lucas Julia #include #include #include main.cpp: using namespace std; // TODO: Write method to create and output all permutations of the list of names. void AllPermutations(const vector &permList, const vector &nameList) { } int main(int argc, char* argv[]) { vector nameList; vector permList; string name; // TODO: Read in a list of names; stop when -1 is read. Then call recursive method. return 0; }