Describe a Turing machine that solves the specified decision problem. Use Example 11.1.2 as a model for defining the actions of a computation of the machine. You need not explicitly construct the transition function.
A tour in a directed graph is a path $p_0, p_1, \ldots, p_n$ in which
i) $p_0=p_n$.
ii) For $0<i, j \leq n, i \neq j$ implies $p_i \neq p_j$.
iii) Every node in the graph occurs in the path.
Design a Turing machine that decides whether a directed graph contains a tour. Use the representation of a directed graph given in Example 11.1.2.