Euler's totient function, also known as phi-function ϕ(n), counts the number of integers between 1 and n inclusive, which are coprime to n. (Two numbers are coprime if their greatest common divisor (GCD) equals 1). """ def euler_totient(n):     """Euler's totient function or Phi function.     Time Complexity: O(sqrt(n))."""     result = n     for i in range(2, int(n ** 0.5) + 1):         if n % i == 0:             while n % i == 0:                 n //= i.

Exercise 1: (Design of algorithm to find greatest common divisor) In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. Why? Divisors of 8 are 1, 2, 4, 8. Divisors of 12 are 1, 2, 4, 6, 12 Thus, the common divisors of 8 and 12 are 1, 2, 4. Out of these common divisors, the greatest one is 4. Therefore, the greatest common divisor (gcd) of 8 and 12 is 4. Write a programming code for a function FindGCD(m,n) that find the greatest common divisor. You can use any language of Java/C++/Python/Octave. Find GCD Algorithm: Step 1 Make an array to store common divisors of two integers m, n. Step 2 Check all the integers from 1 to minimun(m,n) whether they divide both m, n. If yes, add it to the array. Step 3 Return the maximum number in the array.

Python question Application: Big-O Notation (Q8-11)  For each of the time complexities in this segment give the tightest bound in terms of a simple polylogarithmic function using big-O notation. Note: use the ‘^’ symbol to indicate exponents, i.e., write O(n^2) for O(n2).   Question 8 (Big-O Notation 1) T(n) =  n2+ log n + n   Question 9 (Big-O Notation 2) T(n) = n/3 + 4 log n + 2n log(n)   Question 10 (Big-O Notation 3) T(n) = 7n5 + 2n   Question 11 (Big-O Notation 4) T(n) = (n%5) + 12,000

% says recursive functions take how much memory and CPU.

Develop python program of function randomArray(m, n) that takes two integers as argument and returns a 2D m-by-n array with random elements in it. Develop python program of function adder(a1, a2) that reads two 2D arrays of the same size and returns an array that is the summation of a1 and a2. To add the two arrays, you need to add their elements, correspondingly. Develop a  python program of function inverseArray(a) that takes a 2D-array as argument and inverses the array. You will need to inverse the rows, first and then inverse the columns, next. For instance, if the array = [[2, 3, 4], [5, 6, 7]], the inverse will be = [[7, 6, 5], [4, 3, 2]]

Complete this code using Python   m1 = [] #Matrix 1m2 = [] #Matrix 2#Write a function that will return the addition of Matrix A and B.#Create a new matrix C that will hold the addtion result of Matrix A and B (A+B).#Return the resultant matrix Cdef addMatrix(A,B):#Write your code here#Write a function that will return the subtraction of Matrix B from A.#Create a new matrix C that will hold the substraction result of Matrix B from A (A-B).#Return the resultant matrix Cdef subsMatrix(A,B):#Write your code here#Write a function that will return the multiplication of Matrix A and B.#Create a new matrix C that will hold the multiplication result of Matrix A and B (A*B).#Keep in mind,in order to perform matrix multiplication, the number of columns in Matrix A must be equal to the number of columns in Matrix B. #Return the resultant matrix Cdef multipyMatrix(A,B):#Write your code here#Write a function that will transform matrix A to the transpose of matrix A.#The transpose of a matrix means…

explain the use of each line

% says recursive functions take how much memory and CPU.

In c language please