QUESTION 13 Trace the following algorithm for the input: x = 7 and n = 4 1. input: positive integer x and n 2. for i = 1 to n 2.1. if x is odd then 2.1.1. x+ (3 x x) + 1 %3! else 2.1.2. x+x+ 2 3. output x

Modify the previous program. Show the user a list of the names (with integers before each name). Allow the user to select which friend is his/her best friend.

Below is C code and Python code for an algorithm.C code:1: void foo( int n, int A, int B, int C ) {2: if( n==1 ) {3: printf("%d to %d\n",A,B);4: return;5: }6: foo( n-1, A, C, B );7: printf("%d to %d\n",A,B);8: foo( n-1, B, C, A );9: }Python code:1: def foo(n , A, B, C):2: if n==1:3: print(A, "to", B)4: return5:6: foo(n-1, A, C, B)7: print(A, "to", B)8: foo(n-1, B, C, A)Let Hn be the number of times the printing function is executed. Assume n ≥ 1. Give a recurrence equation and an initial value for Hn and solve it. Note, you do not need to know what thecode is doing to answer this question.

II. Determine the big-O measure for each of the functions in the lower table. Choose from the various big-O measures in the upper table. A. O(1) G. O(Y) M. O(Y¹6) S. O(N log N) Y. O(W!) EE. O(X³Y) B. O(X) H. O(log Y) N. O(Z) T. O(N²) Z. O(67W) C. O(log X) I. O(Y log Y) O. 0(Z²) U. O(N²log N) AA. O(V) D. O(X log X) J. O(Y²) P. O(Z³) V. O(W³) BB. O(VV) E. O(X²) K. O(Y³) Q. O(log N) W. O(W⁹) CC. O(25¹) F. O(X³) L. O(Y¹5) R. O(N) X. O(9W) DD. O(XY)

The following code implements Newton's algorithm for finding the square root of a number using repetition: n = 17                # we want the square root of 17 for exampleg = 4                 # our guess is 4 initiallyerror = 0.0000000001  # we want to stop when we are this closewhile abs(n - (g**2)) > error:  g = g - ((g**2 - n)/(2 * g))# g holds the square root of n at this point   Implement this algorithm in a function sqRoot(n), that returns the square root using recursion. Assume that the function will be called with positive numbers only. Note: Your initial guess cannot be zero!