[問題] 3n+1 problem

[sunnyboy1030 (No.000)]

The 3n + 1 problem

Background

Problems in Computer Science are often classified as belonging to a certain
class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will
be analyzing a property of an algorithm whose classification is not known for
all possible inputs.

The Problem

Consider the following algorithm:


                1.               input n

                2.               print n


                3.               if n = 1 then STOP


                4.                               if n is odd then


                5.                               else


                6.               GOTO 2



Given the input 22, the following sequence of numbers will be printed 22 11
34 17 52 26 13 40 20 10 5 16 8 4 2 1

It is conjectured that the algorithm above will terminate (when a 1 is
printed) for any integral input value. Despite the simplicity of the
algorithm, it is unknown whether this conjecture is true. It has been
verified, however, for all integers n such that 0 < n < 1,000,000 (and, in
fact, for many more numbers than this.)

Given an input n, it is possible to determine the number of numbers printed
(including the 1). For a given n this is called the cycle-length of n. In the
example above, the cycle length of 22 is 16.

For any two numbers i and j you are to determine the maximum cycle length
over all numbers between i and j.


The Input

The input will consist of a series of pairs of integers i and j, one pair of
integers per line. All integers will be less than 1,000,000 and greater than
0.

You should process all pairs of integers and for each pair determine the
maximum cycle length over all integers between and including i and j.

You can assume that no operation overflows a 32-bit integer.

The Output

For each pair of input integers i and j you should output i, j, and the
maximum cycle length for integers between and including i and j. These three
numbers should be separated by at least one space with all three numbers on
one line and with one line of output for each line of input. The integers i
and j must appear in the output in the same order in which they appeared in
the input and should be followed by the maximum cycle length (on the same
line).

Sample Input

1 10
100 200
201 210
900 1000
Sample Output

1 10 20


900 1000 174



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→ SansWord:題目不完整吧？
→ SansWord:這題好眼熟....
→ stopcrying:太眼熟了，可是這是這板的範疇嗎？
→ suhorng:所以原PO的問題是對任意正整數n,這個計算會不會終止嗎@@
→ suhorng:有 Prob Solve 板
→ godfat:走錯路了