Abstract: In order to find all Hamiltonian cycles in a digraph, to begin with, it presented an encoding method for the power set, which converts the problem of Hamilton circuits into the computation of hierarchical matrix Secondly, it estimated the complexity of algorithm with the proof of Xiaerci guess.Finally, it gave the exact algorithm for CTSP.

Key words: Hamiltonian cycle, CTSP, Combination optimization, Interface path, Infinity paradox