i just noticed:-
in case we have :-
distance{a,b} > distance{a,c} + distance{c,b}
then in our case P!=NP
hence good tours cannot be found in polynomial time. i.e we will require infinite time => cannot be solved.
=> we must have :-
distance{a,b} <= distance{a,c} + distance{c,b}
for all a,b and c such that
a,c,b belong to list of towns
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