In lisp 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.
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In lisp
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
Step by step
Solved in 3 steps with 2 images
- (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.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.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.
- 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 dynamic programming one: def coolDP (n) using memoisation. Note that you can use Python dictionaries for this 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 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.
- 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.please code in python Write a recursive function to add a positive integer b to another number a, add(a, b), where only the unit 1 can be added, For example add(5, 9) will return 14. The pseudocode is: # Base case: if b is 1, you can just return a + 1 # General case: otherwise, return the sum of 1 and what is returned by adding a and b - 1.
- 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)Given two integers x snf y, the following recurrsive definition determined the greatest common divisor of x and y, Write gcd(xy). Write a recursive function, gcd, that takes two integers as parameters and returns the greatest commmon divisorof numbers.Also write a program to test your function. Write a recursive function,reverseDigits, that takes an integer as a parameter snd returns the number with the digits reversed. Also write a program to test your application.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).
