Practice-Exam-Final

3 e) Complete the missing lines in the code for the class Vertex that represents a vertex in a finite state machine. (6 points) class Vertex: def __init__ ( self , n): self . number = n self . edgeList = [] self .isAcceptingState = … def setAcceptingState ( self ): … def addEdge ( self , e): … def followEdge ( self , c): … … … return … Question 2: Fast Fourier Transform (FFT) We have learned that the FFT is an essential algorithm for Shazam (an App that identifies a song by playing a recording to a smartphone). a) The Fast Fourier Transform makes use of a divide and conquer algorithm to simplify the number of operations, breaking a big FFT into smaller FFTs, which are easier to solve).

6 Figure 3 c) Given the linear program below, determine the maximum values for x 3 , for which the constraints for x 1 , x 4 , x 5 are still valid . z = 27 + 𝑥 2 4 + 𝑥 3 2 − 3𝑥 6 4 𝑥 1 = 9 − 𝑥 2 4 − 𝑥 3 2 − 𝑥 6 4 𝑥 4 = 21 − 3𝑥 2 4 − 5𝑥 3 2 + 𝑥 6 4 𝑥 5 = 6 − 3𝑥 2 4 − 4𝑥 3 + 𝑥 6 2 d) One major component of the simplex algorithm is pivoting. In this problem you are tasked to perform pivoting for the linear program shown below and x 1 = 9. Start by solving the 3 rd constraint for x 1 and substitute it in the remaining equations z = 3𝑥 1 + 𝑥 2 + 2𝑥 3 𝑥 4 = 30 − 𝑥 1 − 𝑥 2 − 3𝑥 3

9 Figure 5 c) Assume you are given a dataset that contains the information shown below. Your goal is to develop a Machine Learning approach that predicts class of an Iris flower. Based on the given information in the table below, which columns identify potential features, which identify labels? Sepal length Sepal width Petal length Petal width Class 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12