The 3x+1 problem is one of the most classical problems in computer science,
related to many fields. As it is thought by scientists a highly hard problem,
resolving it successfully not only can improve the research in many relating
fields, but also be meaningful to the method study. By deep analyzing the 3x+1
calculation process with the input positive integer becoming greater, we find a
useful way for solving this problem with high probability.
We present a polynomial time algorithm for finding a Hamilton Cycle(Path) in
an undirected graph and proves its correctness. A program is developed
according to this algorithm and it works very well. This paper declares the
algorithm, its proof, and the experiment data. Even only our experiment data is
a breakthrough.