We define the following recursive Python function: def cool(n): if n==0: return 2 if n==1: return 1 return cool(n-1)+2*cool(n-2) where n is assumed to be a natural number. Change the cool function into a dyna programming one: def coolDP (n) using memoisation. Note that you can use Python dictionaries for this function.
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- Problem: Recursive Power Method Design a python function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised, and the exponent. Assume the exponent is a nonnegative integer. Write the main() function to input the required parameters as shown in thesample input/output. Sample Output:Average number of words per line: 26.0Enter a number: 2Enter a positive whole number between 1 and 100: 102.0 raised to the power of 10 is 1,024.00In C programing Write a recursive function that returns the product of the digits of its integer input parameter, n. You may assume that n is non-negative. For example, productDigits(243) should return 24, since 2 x 4 x 3 = 24.int productDigits (int n) {Please solve this in C programming language as early as possible. .Write a recursive function that can use to add all the numbers from 5 to n, where n>5. n will be given by the user. Prototype: int add_num(int n);
- Q6 In Python implement a recursive function named test() that accepts an integer parameter. If the parameter value is even then the test function should divide the parameter value by 2 and return this value. If the parameter value is odd, then the function should return 3 times the parameter value + 1. Then request a user to enter an integer number and recursively call converge() on that number until the function returns the value 1.Q6 Python code In Python implement a recursive function named test() that accepts an integer parameter. If the parameter value is even then the test function should divide the parameter value by 2 and return this value. If the parameter value is odd, then the function should return 3 times the parameter value + 1. Then request a user to enter an integer number and recursively call converge() on that number until the function returns the value 1.A recursive function is a function defined in terms of itself via self-referential expressions. This means that the function will continue to call itself and repeat its behavior until some condition is met to return a result. a- Write a python recursive function prod that takes x as an argument, and returns the result where, result=1*1/2*1/3*….*1/n b- Include a screenshot that shows a python program that uses the above function and prints the rounded result to three decimal places after prompting the user to enter a number, x. Use x=3. N.B: The code should be included in your answer.
- Write factorial1 function in python 3.8 follow the directions provided below, don't need anything else as long as it meets all the requirements below. Function: factorial1 The function implements an iterative factorial. It takes an integer n as argument and returns n! The method needs to be computed interactively (not recursivelylanguage: Python Problem: Write a recursive function power(x, n), where n is 0 or a postive integer. For example, power(2, 10) will return 1024. Write a suitable base case, and for the general case use the idea that xn = x * x 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 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)
- Write the definition of a recursive function int simpleSqrt(int n) The function returns the integer square root of n, meaning the biggest integer whose square is less than or equal to n. You may assume that the function is always called with a nonnegative value for n. Use the following algorithm: If n is 0 then return 0. Otherwise, call the function recursively with n-1 as the argument to get a number t. Check whether or not t+1 squared is strictly greater than n. Based on that test, return the correct result. For example, a call to simpleSqrt(8) would recursively call simpleSqrt(7) and get back 2 as the answer. Then we would square (2+1) = 3 to get 9. Since 9 is bigger than 8, we know that 3 is too big, so return 2 in this case. On the other hand a call to simpleSqrt(9) would recursively call simpleSqrt(8) and get back 2 as the answer. Again we would square (2+1) = 3 to get back 9. So 3 is the correct return value in this case.In C++ 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: 123 the output is: 12 9 6 3 0 3 6 9 12 #include <iostream> 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 a recursive function (Java) called Fac which takes one positive integer argument (n) and returns n! You may not use a built-in factorial method or function.