Week 9 Programming Assignments (8 points)

Your task is to create a class Graph in python which stores a weighted directed or undirected graph structure. The initializer method takes a \(V \times V\) weighted adjacency matrix as an input value (\(V\) sized list of \(V\) sized lists). The class must have following methods:

Feel free to store the graph structure to your class as you wish as long as the given functions above work as intended. You can use the adjacency matrix or create a adjacency list to keep track of neighbors of each vertex (or even both).

Note: This graph class will be used in following assignments related to graphs so it is recommended to complete this assignment before moving to others.

class Graph:
    # TODO


if __name__ == "__main__":

    matrix = [
    #    0  1  2  3  4  5
        [0, 0, 7, 0, 9, 0], # 0
        [0, 0, 0, 0, 0, 0], # 1
        [0, 5, 0, 1, 0, 2], # 2
        [6, 0, 0, 0, 0, 2], # 3
        [0, 0, 0, 0, 0, 1], # 4
        [0, 6, 0, 0, 0, 0]  # 5   
    ]
    
    graph = Graph(matrix)

    graph.df_print(0)           # 0 2 1 3 5 4 
    graph.bf_print(0)           # 0 2 4 1 3 5 
    print(graph.weight(0, 2))   # 7
    print(graph.weight(3, 4))   # -1

With Dijkstra's algorithm we not only get the shortest paths from the start vertex to other vertices but we can build a new graph with only the arcs that constructs those paths.

Create a function dijkstragraph(graph: Graph, start: int) that takes a Graph object and the start vertex as an input value. The function returns a new Graph object that has only the arcs that constructs the shortest paths computed by Dijkstra's algorithm. The new graph will be directed despite whether the original graph was directed or undirected.

For example the on the left we have the original directed graph and on the right we have a graph that the function produces, starting from vertex \(0\).

from graph import Graph


def dijkstragraph(graph, start):
    # TODO


if __name__ == "__main__":

    matrix = [
        [0, 25,  6,  0,  0,  0,  0,  0,  0,  0],
        [0,  0,  0, 10,  3,  0,  0,  0,  0,  0],
        [0,  0,  0,  7,  0, 25,  0,  0,  0,  0],
        [0,  0,  0,  0, 12, 15,  4, 15, 20,  0],
        [0,  0,  0,  0,  0,  0,  0,  2,  0,  0],
        [0,  0,  0,  0,  0,  0,  0,  0,  2,  0],
        [0,  0,  0,  0,  0,  0,  0,  8, 13, 15],
        [0,  0,  0,  0,  0,  0,  0,  0,  0,  5],
        [0,  0,  0,  0,  0,  0,  0,  0,  0,  1],
        [0,  0,  0,  0,  0,  0,  0,  0,  0,  0]
        ]

    graph = Graph(matrix)

    new_graph = dijkstragraph(graph, 0)
    new_graph.df_print(0)           # 0 1 2 3 4 5 6 7 9 8 
    new_graph.bf_print(0)           # 0 1 2 3 4 5 6 7 8 9
    print(new_graph.weight(3, 6))   # 4
    print(new_graph.weight(5, 8))   # -1

Hint: try to do the Dijkstra's algorithm and new graph construction separately. What other information can we get while running Dijkstra's algorithm?

Assignment 9.1: Creating a Graph (4 points)

Assignment 9.2: Dijkstra's Algoritmh (4 points)