The travelling salesperson problem (TSP) is as follows; "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city". The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. Even though the problem is computationally difficult, a large number of heuristics and algorithms are known, so that some instances with tens of thousands of cities can be solved completely and even problems with millions of cities can be approximated within a small fraction of 1% optimal distance. This question has 3 parts:

a) loadTSP(filename) (4 marks). This p5.js function will read a TSP problem from a .tsp file. For this assignment, we will only consider Euclidean distance problems. The information you need to load in includes the problem name, total number of cities, the id of each city, and the co-ordinates of those cities. You could store the city information as 3 parallel arrays (ids, xcords, ycoords) or an array of objects with an id, x and y value. You can find the TSPLIB documentation and the dataset with Euclidean only problems on the course website. Your function should take the name of a .tsp file to load. Hint: Reading the TSPLIB.pdf file can be a little daunting. Have a look at some of the actual .tsp files (berlin52.tsp, a280.tsp). It should make the problem seem a lot easier.

b) showLoadedTSP() (4 marks). This function that will visualise a loaded problem. You will need to find a way to scale the loaded problem to fit correctly on the canvas. You may choose what shapes/colours to use to visualise the problem. You should make sure you display the problem name and number of cities somewhere on the canvas.

c) showSolution(solutionFile) (4 marks). This function that will visualise a solution to a loaded problem from a file. You may assume that this function will only be used AFTER showLoadedTSP() has already been run. The first line of a .sol file contains the problem file name (you should check this matches the loaded TSP). The second line contains the tour length, and the rest of the file contains a list of ID's (one on each line) that represents the order that the cities should be connected to form the shortest tour. You should display the solution tour distance on the canvas. Some sample .sol files have been provided on the course website.