a100

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 integersn 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 givenn this is called thecycle-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 betweeni andj.

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 includingi andj.

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 includingi andj.  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 integersi andj 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 10100 200201 210900 1000

Sample Output

1 10 20100 200 125201 210 89900 1000 174

此题注意The integersi 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).（即输出顺序与输入顺序须相同）

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
package one;

import java.io.BufferedInputStream;
import java.util.Arrays;
import java.util.Scanner;

/**
 *
 * @author Administrator
 */
public class a100 {

    public static void main(String str[]) {
        Scanner in = new Scanner(new BufferedInputStream(System.in));
        while (in.hasNext()) {
            int n2 = in.nextInt();
            int n3 = in.nextInt();
            int n = 0, n1 = 0;
            if (n2 <= n3) {
                n = n2;
                n1 = n3;
            } else {
                n1 = n2;
                n = n3;
            }
            int sum[] = new int[n1 + 1];
            for (int i = n; i <= n1; i++) {
                int t = i;
                sum[i] = 1;
                while (t != 1) {
                    if (t % 2 == 0) {
                        t = t / 2;
                        sum[i]++;
                    } else {
                        t = t * 3 + 1;
                        sum[i]++;
                    }
                }
            }
            Arrays.sort(sum);
            System.out.println(n2 + " " + n3 + " " + sum[n1]);
        }
    }
}