The 3n+1 Problem
Public  09/25/09  6xp  Programming  63.6% 
Consider the following algorithm:
1. input n
2. print n
3. if n = 1 then STOP
4. if n is odd then n < 3n + 1
5. else n < n/2
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 cyclelength 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.(inclusive)
What is the answer if i=1 j=1000000 ?
Source:http://fdemesmay.dyndns.org/cs/acm/v1/100.html
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