a recursive function called print_num_pattern() 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. Ex. If the input is: 12 3 the output is: 12 9 6 3 0 3 6 9 12   # TODO: Write recursive print_num_pattern() function if __name__ == "__main__":     num1 = int(input())     num2 = int(input())     print_num_pattern(num1, num2)

Write a program that generates random numbers between -25 and 25 by using the randint function. The program will add up the numbers and terminate when the sum of the values becomes zero. The program should contain the following functions: add()    : add up the values main(): the function where the program execution should begin and end.  randomgen(): a function that returns a number between -25 and 25 A global variable subsetsum that keeps track of the sum The program should output the count of the number of values generated before exiting saying that the subset sum was zero.

Write a recursive function that accepts a number and returns its factorial. b. Write a recursive function that accepts an array, its size and the index of the initial element as arguments. The function fills the array with the elements of the following sequence: n1 = 3, nk+1 = nk+35 c. Write an iterative and a recursive versions of the binary search. In C++ coding

Consider a network of streets laid out in a rectangular grid, In a northeast path from one point in the grid to another, one may walk only to the north (up) and to the east (right). Write a program that must use a recursive function to count the number of northeast paths from one point to another in a rectangular grid. Your program should prompt the user to input the numbers of points to the north and to east respectively, and then output the total number of paths. Notes: 1. Here is a file (timer.h  download and timer.cpp download) which should be included in your program to measure time in Window or Unix (includes Mac OS and Linux) systems (use start() for the beginning of the algorithm, stop() for the ending, and show() for printing). 2. The computing times of this algorithm is very high, and the number of paths may be overflow, don't try input numbers even over 16. 3.  Name your recursive function prototype as calcPath(int north,  int east) to ease grading. 4. Paste your output

Using recursion, write a function sum that takes a single argument n and computes the sum of all integers between 0 and n inclusive. Do not write this function using a while or for loop. Assume n is non-negative. def sum(n): """Using recursion, computes the sum of all integers between 1 and n, inclusive. Assume n is positive. >>> sum(1) 1 >>> sum(5) # 1 + 2 + 3+ 4+ 5 15 "*** YOUR CODE HERE ***"

Convert Newton's method for approximating square roots in Project 1 to a recursive function named newton . (Hint: The estimate of the square root should be passed as a second argument to the function.) An example of the program input and output is shown below: Enter a positive number or enter/return to quit: 2 The program's estimate is 1.4142135623746899 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit

Write a statement that calls the recursive function backwards_alphabet() with input starting_letter. Sample output with input: 'f f e d b a 344614.2214230.qx3zgy7 1 def backwards_alphabet (curr letter): if curr_letter print(curr_letter) 2 'a': == 3 4 else: print (curr_letter) prev_letter backwards_alphabet (prev_letter) 5 chr (ord(curr_letter) 1) 7 9 starting_letter = input () 10 Your solution goes here ... 11 12