uva 100 The 3n+1 problem

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-lengthof 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 iand 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

这道题目注意一点，输入的i，j大小不确定，要判断一下，并且输出的时候要按照原来的顺序输出，我的办法是输入了i和j后，立刻就输出，然后在调换它们的大小，这样就避免了输出的问题。另外，还有一个问题，就是每一次循环中，该更新的变量要更新或者该初始化的变量一定要初始化，比如下面的程序中的max，其实这不是一个小问题，要重视，写程序的时候认真一点，用变量之前一定要想一下它初始化了没有。

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>

using namespace std;

int get(int n)
{
    int cnt = 1;
    
    while (n != 1)
    {
        if (n % 2)
            n = 3 * n + 1;
        else
            n /= 2;
        cnt++;
    }
    return cnt;
}

int main(void)
{
    int a, b, i, max = 0;

    while (cin >> a >> b)
    {
        max = 0;
        cout << a << ' ' << b << ' ';
        int x = a <= b ? a : b;
        int y = a + b - x;
        for (i = x; i <= y; i++)
        {
            if (max < get(i))
            {
                max = get(i);
            }
        }
        cout << max << endl;
    }
    
    return 0;
}