Given the recursive function definition: t(n) = n+ 3 * t(n-1) + t(n-2) t(0) = 2 t(1) = 1 a. Evaluate: t(3) b. Write the source code to implement this function
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Given the recursive function definition:
t(n) = n+ 3 * t(n-1) + t(n-2) t(0) = 2 t(1) = 1
a. Evaluate: t(3)
b. Write the source code to implement this function
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- 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 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 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: **** *** ** * ** *** ****
- For function addOdd(n) write the missing recursive call. This function should return the sum of all postive odd numbers less than or equal to n. Examples: addOdd(1) -> 1addOdd(2) -> 1addOdd(3) -> 4addOdd(7) -> 16 public int addOdd(int n) { if (n <= 0) { return 0; } if (n % 2 != 0) { // Odd value return <<Missing a Recursive call>> } else { // Even value return addOdd(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 the original code in Python: def all_permutations(permList, nameList): # TODO: Implement method to create and output all permutations of the list of names. pass if __name__ == "__main__": nameList = input().split(' ') permList = [] all_permutations(permList, nameList)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.
- 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.•rewrite calculateSum function as a recursive function. m(i) = m(i-1) + i/(i+1), where i >=1Write 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.
- 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)1. Below, enter code to complete implementation of a recursive function sum allintegers(), which takes an input n and adds all integers preceding it, up to n: add all integers(n):In Lisp Programming (Please show that it does work) Write a simple recursive function to compute the f(n) for the following sequence: f(n) = f(n-1) + f(n-3) f(0) = 0 f(1) = f(2) = 1 Optimize this function using dynamic programming. You can assume that the number n in the function call for testing will be less than 20.