**Keywords:**Traveling Salesman Problem | TSP | P=NP | P vs NP

Solving the TSP:

-----NP-hard version-----

*Get a matrix with the values;

*Sum the numbers of the matrix lines, generating one sum per line (The line has the distance from

one city to others);

*Find the cities that have the 3 biggest sums and connect the cities with it other. (E.g. A-B-C-A);

*The previous step will generate rows (E.g. AB; AC; BC);

*For every next city (that will be the biggest remaining sum, coming from the sums made in the

second step):

-for all the already generated rows:

--sum the distance from the actual city to both of the row cities and subtract the row size (Generating a cost).

-get the row with the smallest cost delete this row and add 2 new ones, from the actual city

to the cities that were forming the deleted row.

-----NP-complete version-----

*Just do the steps from the NP-hard version and at the end sum the the path to see if it is smaller

than the given number.