We define the function foo on natural numbers as follows: foo(n) = n, if 0 < n < 10 (i.e. n > 0 and n < 10) • foo(n) = 1+2 · foo(n – 10), if n > 10 (where “"." is the product function) Write a Python function: def fooDPBU (n) that, on input n, returns foo(n). Your function should use dynamic programming
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- 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.Part (a) Write a python function that computes the binomial coefficient ("). The function should return the correct answer for any positive integer n and k where k=m pass Part (c) Suppose that the number of people in the trial is 100. Then: • Plot a curve that shows how the probability of type 1 error changes with the choice of m, for m = 1,...n assuming that the null hypothesis holds (in red), • On the same picture, plot the probability of type 2 error vs the value of m in the case in which the new drug is effective with proability 0.68 (in blue). You can plot the two curves using matplotlib.pyplot. You can select the color by passing color='r' or color='b' to the plt.plot() function. [4]: n - 100 # your code here def plot_curve (): pass [5]: plot_curve() Part (d) Based on the picture above, what value of m do you think would be suitable to keep both type 1 and type 2 error small at the same time? (You may assume that the company claims the new drug has 68% accuracy) [6]: # your…Write java overloaded function calculate() with following function definitions.void calculate(int x, int y ) – to calculate the sum of all even numbers from xtill y and print the sum .void calculate(char a,char n) – to print all vowels from variable a to n if anyvoid calculate(int x, int y, int z) – to print the middle number from x,y,z ifyou arrange them in ascending order.
- 1. Given the following function: int Fn (int N) { } if (N == 0) return 2; else return N + Fn (N/3); a) What type of function is this, Iterative or Recursive? Give justification. b) Given N = 17, what will be the output from this function? Show your work.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)STEP 1 : Write a python function that computes an interpolating polynomial through a set of points (xi , yi ) in R . The routine should output the coefficients of theinterpolating polynomial. below is the answer, but with missing data import numpy as npfrom scipy import linalgimport matplotlib.pyplot as plt %matplotlib inline def LPoly(x,y):# input x: array of x-values# y: array of y-values# output coef: array of coefficients for the polynomial interpolating (x,y)-points# < your code here >return coef
- Write a function sum_of_digits(a,b), that takes two arguments a and b, computes a to the power of b, then recursively finds the sum of digits until there is only one digit left. You must PRINT all steps of the process as shown in the below example. sum_of_digits(5,3) will PRINT on the screen the following: 5ˆ3 = 125 = 1 + 2 + 5 = 8 sum_of_digits(2,8) will PRINT on the screen the following: 2ˆ8 = 256 = 2 + 5 + 6 = 13 = 1 + 3 = 4Write a recursive Python function that matches the following docstring: '''Function -- sum_fivesSums all positive multiples of five between 0 and some integer, n, inclusive.Parameters:n -- an integer.Returns:The sum of all positive multiples of five up to and including n.''' Examples: sum_fives(1) returns 0 sum_fives(5) returns 5 sum_fives(10) returns 15Hi here Python3 function sqr(n) that returns the square of its numeric parameter n..
- What does the function return for any positive values of x and n ? The answer should be a general formula in terms of x and n. int what_do_I_do ( int x, int n ) { if ( n = = 1 ) return x; else return x + what_do_I_do ( x, n – 1 ); } C++ be quick pleaseWrite a python function that takes a positive integer n as an argument. This function will return the number of positive integers less than n that are co-prime to n. Co-prime Numbers: Two numbers are coprime to each other if they don't have any common divisor except 1. Sample Input 1: 1 Sample Output 1: Reason: Since 1 is the smallest positive integer, there exists no positive integer that is less than and coprime to 1. Sample Input 2: 2 Sample Output 2: 1 Reason: Only 1 doesn't share any common divisor (except 1 itself) with 2. Also, 1 < 2. Sample Input 3: Sample Output 3: Reason: Namely, the two coprime numbers to 6 are 1 and 5. Sample Input 4: 36 Sample Output 4: 12 Reason: The numbers coprime to 36 are 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31 and 35code in python (A) please Solve the so-called "Birthday Problem". Write a program that takes an integer ?N and uses the function np.random.randint (low = 0, high = N) from numpy to generate a random sequence of integers between 00 and ?−1N−1. Run experiments to validate the hypothesis that the number of integers generated until the first repeated value is approximately ?∗?2⎯⎯⎯⎯⎯⎯⎯√π∗N2. a) Write a function birthday(N) that returns the number of values generated until a value is repeated as a function of the range of possible values ?N (from 00 to ?−1N−1); b) Write a function birthday_sim(N) that repeats birthday(N) a total of n_sim = 20000 times and returns the average of all the numbers generated; c) Show on one plot that as ?N increases (with a doubling experiment), from ?=2N=2 to ?=1000N=1000, the value of birthday_sim(N) approaches ?∗?2⎯⎯⎯⎯⎯⎯⎯√π∗N2.