The Traveling Salesman Problem Given a collection of cities, along with pairwise

The Traveling Salesman Problem
Given a collection of cities, along with pairwise distances between the cities, what is the
shortest route that visits each city exactly once and returns the the starting city? This
question is commonly referred to as the traveling salesman problem (TSP). The traveling
salesman problem can be reformulated as finding a Hamiltonian cycle of least cost in a
weighted graph — a Hamiltonian cycle is a cycle that includes every vertex in the graph.
This assignment will focus on a brute-force solution to the traveling salesman problem.
Program Specifications
You will write a C++ program to implement a brute-force, permutation-based solution for
the traveling salesman problem. Your program will take in a single command line input
specifying a file to read. The input file will contain one or more lines, each of which specifies
a directed edge the form “src dst wt” where src and dst are non-negative integers indicating
the source and destination vertices of the edge, and wt is the weight of the edge. I will
provide you with sample input files for testing, but it is your responsibility make sure that
your program behaves correctly on any valid input file. Your program will output the cost
of the minimum Hamiltonian cycle. See the end of this handout for example output.
You will need to implement your own adjacency matrix or adjacency list structure to store the
graph. Take care not to over engineer your data structure — you do not need to write a full
class to implement your graph data structure. I suggest that you rely on standard template
library containers for your implementation (see https://cplusplus.com/reference/stl/). For
instance
• std::vector > adj matrix;
• std::vector > adj list;
Regardless of the data structure you choose, do not hard-code limits on your data structure
size. Also, please note that variable-length arrays (VLAs) are not part of the C++ standard
and should not be used. For your solution, you make use the std::next permutation
function.
Submission and Grading
You must use skeleton3.cpp (see iLearn) as a starting point for your program, and complete
the TSP function; feel free to create any additional helper functions or include any additional
standard libraries that you need, but do not modify any other existing functions. Your
source code should be contained in a single file and should be named after your TTU email
address excluding the “@tntech.edu” (e.g., jagraves21.cpp). All submissions will be made
on iLearn — please do not zip or compress your files. Make sure to follow best coding
practices (proper naming conventions, useful comments, etc.). Your program should compile
without errors or warnings. Programs will be compiled using the following command:
g++ -Wall -pedantic -std=c++11 [source file]
Sample Output
The following lines contain sample input and expected output to your programs. Please note
that these examples are not exhaustive, and you should verify your programs with additional
test cases.
$ ./a.out graph1.txt
18
$ ./a.out graph2.txt
14
$ ./a.out graph3.txt
No Hamiltonian cycle exists.