You want to plan your course schedule to graduate. You are interested in the following ten courses: CS 115, CS 116, CS 122, CS 131, CS 132, CS 126, CS 127, CS 141, CS 169, and CS 170. The course prerequisites are: CS 115 Prerequisites: none CS 116 Prerequisites: CS 115 CS 122 Prerequisites: none CS 126 Prerequisites: CS 122, CS 132 CS 127 Prerequisites: CS 116 CS 131Prerequisites: CS 115 CS 132 Prerequisites: CS 116, CS 131 . CS 141 Prerequisites: CS 122, CS 116 .CS 169 Prerequisites: CS 132 CS 170 Prerequisites: CS 132 What you need to do: Draw a directed graph that represents the courses and their prerequisites. The arrow should point towards the prerequisite. For example 1. 115 116 Find the adjacency matrix of the graph (the columns should show the prerequisites) For example, column 116 has as prerequisite 115: 2. 115 0 0 116 115 116 0 3. 4. What are the in-degree and out-degree of CS 116? Assume you can only take two courses at a time every semester and you would like to know what possible combinations you have to complete all courses. Draw all possible states of two courses at a time, starting with CS 115 and CS 122 on the first semester. Make sure you do not consider cases where your choice is one class only and you complete all prerequisites (This is similar to the coin game presented on the slides.) How many different paths are possible