The 3n + 1 problem

The 3n + 1 problem
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  100 200 125  201 210 89  900 1000 174

public static void main(String[] args) throws Exception {

    Scanner in = new Scanner(System.in);

    PrintWriter out = new PrintWriter(System.out, true);

 

    // while there is some input to read

    while (in.hasNextInt()) {

        int i = in.nextInt(),

            j = in.nextInt(),

            from = Math.min(i, j),

            to = Math.max(i, j),

            max = 0;

 

        // loop through all the numbers

        // and find the biggest cycle

        for (int n = from; n <= to; n++) {

            max = Math.max(max, cycleLength(n));

        }

 

        out.printf("%d %d %d\n", i, j, max);

    }

}

// cache for already computed cycle lengths

public static int[] cache = new int[1000000];

 

public static int cycleLength(long n) {

    // our base case

    // 1 has a cycle length of 1

    if (n == 1)

        return 1;

 

    // check if we've already cached the

    // cycle length of the current number

    if (n < 1000000 && cache[(int)n] != 0)

        return cache[(int)n];

 

    // the cycle length of the current number is 1 greater

    // than the cycle length of the next number

    int length = 1 + cycleLength(next(n));

 

    // we cache the result if the

    // current number is not too big

    if (n < 1000000)

        cache[(int)n] = length;

 

    return length;

}

// a function that returns the

// next number in the sequence

public static long next(long n) {

    if (n % 2 == 0)

        return n / 2;       // if n is even

    else

        return 3 * n + 1;   // if n is odd

}

http://blog.adilakhter.com/2013/02/21/1729/
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