I. Compute for the running time for each algorithm/code and give its complexity 1. for i = 1 to n do Statement B 2. for(j=1; js n*n*n;j++) for (k=1; ksn) Statement f; for(m=1;m
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- Calculate the time complexity and represent by using asymptotic notation for the following code: int p=3, r=2; int f=1; for(int i=0; iWrite a recursive function to compute the following series: m(i) = 1/2 + 2/ 3 + . . . + i/i + 1 Write a test program that prompts the user to enter an integer for i and displays m(i).a) You are given two different codes for finding the n-th Fibonacci number. Find the time complexity of both implementations and compare the two. Implementation 1 def fibonacci_1 (n) : if n < 0: print ("Invalid input!") elif n <= 1: return n else: return fibonacci_1 (n-1) +fibonacci_1 (n-2) n = int (input ("Enter a number: ")) nth_fib= fibonacci_1 (n) print("The {}th fibonacci number is {}.". format (n, nth_fib)) Implementation 2 def fibonacci_2 (n) : if n<0: return "Invalid Input" if n<=1: return n fib [0] (n+1) fib[0] = 0 fib[1] = 1 for i in range (2, n+1): fib[i] = fib[i-1]+ fib[i-2] return fib[n] n = int(input ("Enter a number: ")) nth_fib = fibonacci_2 (n) print("The {} th fibonacci number is {}.". format (n, nth_fib))1. Consider the following recursive function: def foo(n): if (n == 0): return 0 return n + foo(n - 1)a. What is foo(5) b. What is foo(10) c. Suppose that n + foo(n - 1) is changed to n * foo(n - 1). What is foo(5) now? d. What happens if foo(-1) is called?Write a recursive algorithm with the following prototype: int divide (int x, int y); that returns x/y (integer division). You need not test for divide by 0. THE FUNCTION MUST BE RECURSIVE. (hint: base case should be when xSuppose the runtime efficiency of an algorithm is presented by the function f(n) = 10n + 10². Which of the following statements are true? Indicate every statement that is true. A. The algorithm is O(n log n) B. The algorithm is O(n) and O(log n). C. The algorithm is O(log n) and 80(n). D. The algorithm is (n) and (log n). E. All the options above are false.calculate number of operations in this algorithm void my_dgemv(int n, double* A, double* x, double* y) { double alpha=1.0, beta=1.0; int lda=n, incx=1, incy=1; cblas_dgemv(CblasRowMajor, CblasNoTrans, n, n, alpha, A, lda, x, incx, beta, y, incy); }Question 8 Consider the following code where n and m can be any number of more than 20. Select the correct time complexity. int iter_count = 0; for (int i = 0; i < n; i *= 2) { for (int j = 0; j < m; j++){ iter_count += 1; } for (int i = }) 0; iThe time complexity of the following code is O(n^2). In C++, write a code to confirm the time complexity of the following pseudocode: int j = 2 while (j<n) { int k = j while (k<n) { sum += a[k]=b[k] k += n^1/3 log n } j = j*sqrt(5) }In program C Write a recursive function find_sum(n)that calculates the sum of successive integers starting at 1and ending at n(i. e., find_sum( n) = 1 + 2 . . .+( n -1) + n.language: Python Problem: Write a recursive function power(x, n), where n is 0 or a postive integer. For example, power(2, 10) will return 1024. Write a suitable base case, and for the general case use the idea that xn = x * x n-1.1. A certain computer algorithm executes four times as many operations when it is run with an input of size n as when it is run with an input of size n – 1. Here, n > 1 is an integer. When the algorithm is run with an input of size 1, it executes 12 operations. How many operations does the algorithm execute when it is run with an input of size 5? How many operations does the algorithm execute when it is run with an input of size n?Recommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education