Xadd_to LogisticRegression def fit(self, X, Y, epochs=1000, print_loss=True): This function implements the Gradient Descent Algorithm Arguments: x -- training data matrix: each column is a training example. The number of columns is equal to the number of training examples Y -- true "label" vector: shape (1, m) epochs -- Return: params -- dictionary containing weights losses -- loss values of every 100 epochs grads dictionary containing dw and dw_e -- losses = [1] for i in range(epochs): # Get the number of training examples m = x. shape[1] ### START YOUR CODE HERE ### # Calculate the hypothesis outputs A (* 2 lines of code) Z = A = # Calculate loss (* 1 line of code) loss = # calculate the gredients for W and w_e dw = dw_e = # weight updates self.W = self.w_e = ### YOUR CODE ENDS ###

15. Code to Recurrence Relation What is the recurrence relation of the runtime of the following algorithm: T(n) represents the time it takes to complete func called with the parameter n value n. def func(n): if n == 0: return print(n) func(n//2) func(n//3) Pick ONE option T(n) = T(n-1) + T(n-2) + C; T(1) = C T(n) = T(n-2) + T(n-3) + C; T(1) = C T(n) = T(n/2) + T(n/3) + C; T(1) = C T(n) = T(n-5) + C; T(1) = C Clear Selection 81

Design data structures: present five data structures including B-tree for big data (you find data), for sorting algorithms. In this project, you will implement and analyze the following. Median finding, Order Statistics, and Quick Sort: In this project, you will implement the median-finding algorithms. The user should be able to select the "k”, i.e., the rank of the number desired as output (k = n/2 is the median). You should also be able to select groups of 3, 5, 7, etc. in the linear-time median finding algorithm and be able to compare the performance of each. Also, implement the randomized median finding algorithm and compare it against the linear-time one. Implement quick sorting using both algorithms and compare the performances of these different versions.

MATLAB: Create a vector named n which starts at -10 and steps by 1 to end at +10 by using the start:step:stop syntax. Next, generate a vector x1 so that x1 satisfies the mathematical relationship ?ଵ[?]=(0.60). Since n is a vector, one will need to utilize 0.60.^n (i.e., .^ is used in place of ^) to define x1. Redo the work just completed, but for a vector x2 where x2 satisfies the mathematical relationship ?ଶ[?]=(0.85). Repeat the work just completed, but for a vector x3 where x3 satisfies the mathematical relationship ?ଷ[?]=(1.10).  In one figure window, plot x1 as a function of n using the stem command. The stem plot must show BLACK (versus the default blue) lines that have filled circles and a line width of 2; refer to the lecture example script file. Further, the horizontal axis label (xlabel) must be n, the title (title) must include your name and the vertical axis label (ylabel) must show ?ଵ[?]=(0.60)(note the subscript and superscript). In addition, turn on the grid (doc grid),…