First, let us expound certain basic concepts relating to Collatz conjecture. Next, list the mathematical induction that proves the conjecture. Then again, prepare several judging criteria, which are solely used to determine whether each such operational result fits the conjecture. After that, we sort positive integers successively and prove directly one of certain sorts after each sorting, until the last two sorts are proved bidirectionally. The bidirectional proofs mean that for these two sorts of integers, on the one hand, start with several proven kinds of integers to expand successively the scope of proven kinds of integers, up to all kinds of integers. On the other, each unproven kind of integers is operated by the operational rule to find an integer expression that is less than the unproven kind of integers, from this, it meets a judging criterion, such that the unproven kind of integers is proved to fit the conjecture.