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### For this programming assignment, you will implement a Graph using an adjacency list representation and then perform Dijkstra’s shortest path algorithm on the graph

INSTRUCTIONS TO CANDIDATES

Graphs

Description:

For this programming assignment, you will implement a Graph using an adjacency list representation and then perform Dijkstra’s shortest path algorithm on the graph.

Your program will read a graph from an input .txt file that describes graph connectivity.  The file is a text file where the first line contains two numbers.  The first is the number of vertices n and the second is the number of edges m.  After this line, there will be m lines with three numbers.  The first two numbers represent the source and destination vertex for the undirected edge.  The third number is the weight for that edge.  The final line of the file contains two numbers representing the index of two numbers (start and end vertices in the shortest path calculation)

Your program should construct the graph and run Dijkstra’s shortest path algorithm.

An example input file:

4 5

0 2 1

1 2 5

2 3 3

1 3 2

0 3 10

0 3

This file represents a graph with 4 vertices, 5 edges, and has edges (0,2) with weight 1, (1,2) with weight 5, (2,3) with weight 3, (1,3) with weight 2, and (0,3) with weight 10.  Your program should output the shortest path between vertex 0 and vertex 3 as a sequence of vertex labels 0, 2, 3 (in this example).

NOTE: The weight does NOT have to be an integer.  In general the weight will be a floating point number.  An example graph and its solution is provided as a reference for you to test your code.

To implement the graph please start with the included implementation Graph.h filling in the specified functions. Your program should read the graph in the input txt file, and output the solution in the format from the example above.  Your shortest path algorithm will also need a Heap using locators (included with this assignment).  As you insert items into the heap, you will need to store the locator for each vertex in the vertex itself.

Coding Portion (100 Points):

• Start with the following template: h and fill in the entire member functions or implement your own version of the graph.

• You should implement the adjacency list data structure for the graph.

• Be sure to test the correctness of your algorithms and implementations.

• Your code will be graded based on whether or not it compiles, runs, produces the expected output, produces correct output, and your coding style (does the code follow proper indentation/style and comments).

• Please be sure to turn in the cover page.

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