An introduction to some of the key ideas in computer graphics is given. Modeling, 2D and 3D viewing,
transformations and related ideas from linear algebra are presented.
Write a program to decide if a graph has a cycle or not. The given graph can be a directed or undirected graph, which is indicated at the time of reading the input (0 for directed graph and 1 for undirected graphs). The input is given as an adjacency list.
Shortest Paths with Multiplicative Cost. In a given undirected graph, the path cost is measured as a product of all the edges in the path. The weights are rational numbers (e.g., 0.25, 0.75, 3.75 etc) or integers (2, 3). There are no negative edges. given such a graph as input, you are to output the shortest path between any two given vertices. Input is the adjacency matrix and the two vertices. You must output the path.
In some graphs, the shortest path is given by optimizing two different metrics: the sum of weights of the edges and the number of edges. For example: if two paths with equal cost exist then, the path with the least number of edges is chosen as the shortest path. given this metric, you have find out the shortest path between a given pair of vertices in the input graph. The output should be the number of edges on the path, the cost of the shortest path, and the path itself. Input is the adjacency matrix and the two vertices.
Edge Disjoint Cycles. You are given an input graph that is either directed or undirected. Write a program that reads in a vertex number and lists the number of edge disjoint cycles that start and end at this vertex. The output should also list the edges in each of the cycle discovered. Input will be the adjacency matrix preceded by a 0 or 1 representing Directed or Undirected graphs respectively.
You will recieve a Standard Grade for completion of this
Extra credit will be given for a more creative approach to the problem, either minimum amount
of code, an additional display of seating beyond just the boarding pass, etc
