Consider a recursive function, called f, that computes powers of 3 using only the + operator. Assume n > = 0. int f(int n) { if (n == 0) return 1; return f(n-1) + f(n-1) + f(n-1); } Give an optimized version of f, called g, where we save the result of the recursive call to a temporary variable t, then return t+t+t. i got int g(int n) { if (n == 0) return 1; int t = g(n - 1); return t+t+t; } so now Write a recurrence relation for T(n), the number addition operations performed by g(n) in terms of n.
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- Consider the following recursive function: if b = 0, if 6 > a > 0, a f(b, a) f (b, 2.(a mod b)) otherwise. f(a, b) = Estimate the number of recursive applications required to compute f(a, b).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: **** *** ** * ** *** ****Consider the following recursive function:int Func(int num){if (num == 0)return 0;elsereturn num+Func(num+1);}1. Is there a constraint on the values that can be passed as a parameter for this function to passthe smaller-caller question?2. Is Func(7) a good call? If so, what is returned from the function?3. Is Func(0) a good call? If so, what is returned from the function?4. Is Func(-5) a good call? If so, what is returned from the function?
- 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, the pattern generated is as follows: **** *** ** * * ** *** **** 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 preceding pattern.•rewrite calculateSum function as a recursive function. m(i) = m(i-1) + i/(i+1), where i >=1Write a recursive function myfactorial (n) for computing the factorial of a non-negative integer. (Hint: think about adapting the examples myfunction and anotherfunction in Chapter 1.) If an input other than a non-negative integer is entered into your function myfactorial, the process will never halt. Create a new function safefactorial which behaves identically to myfactorial on non-negative integers, but raises a ValueError when other values are entered. Use safefactorial to write a function mybinom (n,r) that re- turns the binomial coefficient ("). Use mybinom (n,r) to write a function hockeystick (n,r) that n H(n,r) = [ (c.). i=r computes H(n,r)
- Write an iterative function that determines the number of even elements in an array a of integers of size n. The function should return the number of elements that are even in array a of size n. Propose an appropriate prototype for your function and then write its code. Write a recursive function to solve the above problem. Propose an appropriate prototype for your function and then write its code.Write a recursive function called draw_triangle() that outputs lines of '*' to form a right side up isosceles triangle. Function draw_triangle() has one parameter, an integer representing the base length of the triangle. Assume the base length is always odd and less than 20. Output 9 spaces before the first '*' on the first line for correct formatting. Hint: The number of '*' increases by 2 for every line drawn. Ex: If the input of the program is: 3 the function draw_triangle() outputs: * *** Ex: If the input of the program is: 19 the function draw_triangle() outputs: * *** ***** ******* ********* *********** ************* *************** ***************** ******************* Note: No space is output before the first '*' on the last line when the base length is 19. if __name__ == '__main__': base_length = int(input()) draw_triangle(base_length)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)
- Implement a recursive function called evens that returns an integer with only theeven numbers. Note this function is returning an integer, not printing. There shouldbe no use of cout within your function. The function declaration should look asfollows:int evens(int n);(ex. evens(234567); returns 246)(ex. cout << evens(56032); prints 602)Write a recursive function (no auxiliary functions, for/while loops, STL containers or functions, static/global variables) bool mirrorMirrorOnTheWall(string n); Given a string, recursively determine if the string is the same forwards and backwards. mirrorMirrorOnTheWall(""); mirrorMirrorOnTheWall("a"); mirrorMirrorOnTheWall("mirror"); // returns false mirrorMirrorOnTheWall("racecar"); // returns true // returns true // returns true Edit View Insert Format Tools Table 12pt v Paragraph v BIU ...Write a function decimal_to_binary(decimal_number) that takes in a non-negative integer and returns it in binary as an integer representation. Solve this problem using recursion. Use a helper function (with extra parameters) to handle the recursion. Examples decimal_to_binary(7) should return 111 decimal_to_binary(128) should return 10000000 decimal_to_binary(5) should return 101 Make sure your function signature matches the given function decimal_to_binary(decimal_number) because I will be using unit tests to evaluate your code. Return an integer representing the binary number from the function, not a string representation. Python