1. Implement Gale-Shapley Algorithm for computing Stable Marriage Assignment in any language, such as Python, Java, C++ or MATLAB, using the approach and data structures described in the first two Chapters of the Kleinberg and Tardos text. The input file should include number of subjects, n, preference list for men and women one line for each. n m1: w11, w12, , w1n mn: wn1, wn2, , wnn w1: m11, m12, , m1n wn: mn1, mn2, , mnn a) Write the output, explicitly checking to see that it is a stable match (It requires a separate function to check). Turn in sample inputs and corresponding outputs in separate files. b) Write a function to create preference lists for men and women. Function should take number of men (women), say n, create preferences and output them. c) Run the algorithm on several instances of the problem for n = 10 with different input files and plot the variation in the running time. d) Run the algorithm on several instances of the problem for n = 10 with the same input file and plot the variation in the running time. e) Run the algorithm on problem instances with n = 10, 15, 20, 50, 100, and plot the average running time as a function of the problem input size (n). (20 pts) 2. Run Gale-Shapley Algorithm using the preference lists tables below. Are there any unstable pairs in the final match? (15pts) 3. Do Problem 3 in Chapter 2 on page 67 of the Kleinberg and Tardos text. Provide a clear explanation in each case. (15 pts) 4. Do Problem 1 in Chapter 3 on page 107 of the Kleinberg and Tardos text. Look at solved exercise 1 on page 104 as an example. You can write your answers for the questions 2 to 4 on paper, scan and create a pdf file for each question. Name each file using Question-#.pdf format. TURNIN: Bundle your source code, sample inputs/results, timing plots and answers of each question as a single zip archive, name it using lastnamefirstname format, and submit to Isidore by the deadline.