> The problem is to find a circuit that goes through each city once and that ends where it starts. This in itself isn't diffcult. This is the Hamiltonian circ

> The problem is to find a circuit that goes through each city once and that ends where it starts. This in itself isn't diffcult. This is the Hamiltonian circuit problem, and is NP-complete. And the OP doesn't know what a decision problem is. Not the best person to be correcting other people's confusion.