This part contributes to module outcomes $1$ and $2.$

The TSP will be implemented as follows: suppose there are n cities. You will create an n$-$by$-$n matrix M$,$ with one row and one column per city. M$($i$,$j$)$ gives the cost of going from city i to city j$.$ If there is a road from i to j then M$($i$,$j$)$ is a positive integer, otherwise it is $-1$ by convention. We assume all roads are bi$-$directional so M is symmetric. A tour is a path that starts at city $1,$ visits every other city once, and ends back at city $1.$ A minimal tour is one with minimum cost $($where the cost of a tour is the sum of the costs of the roads that constitute it$).$ Note there may be more than one minimal tour.

The TSP asks that we find a minimal tour.

d$)$ Given a tour generated from matrix M$,$ how do you compute its cost? $($If this question feels easy, it is$)$

e$)$ Just in case your algorithm gets a matrix M that does not contain any tours $($e$.$g$.,$ it is not possible to come back to the starting city $1),$ it's a good idea to be able to detect that and output some message like "This matrix does not contain any tours" before you attempt to find non$-$existent tours. How do you detect that?