UVA100 The 3n + 1 problem

3n+1问题求解与分析

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本文探讨了一个在计算机科学中未被普遍分类的问题，即3n+1问题。通过给出一个简单的算法实现，文章详细解释了如何确定输入整数n的循环长度，并进一步分析了两个整数之间的最大循环长度。文章提供了代码示例，演示了如何验证算法正确性和计算给定范围内的最大循环长度。

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 nthis 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

Sample Output

1 10 20
100 200 125
201 210 89
900 1000 174

注意：（1）i和j的大小关系

     （2）3*n+1的值可能会超过int

参考代码：

#include <stdio.h>
typedef long long ll;
int main(){
	ll i,j;
	while (~scanf("%lld%lld",&i,&j)){
		ll ii=i,jj=j;
		int max=0;
		if (i>j){
			ll temp=j;
			j=i;
			i=temp;
		}
		for (ll y=i;y<=j;y++){
			ll x=y;
			int count=1;
		//	printf("%lld ",x);
			while (x!=1){
				count++;
				if (x%2!=0)
					x=3*x+1;
				else
					x=x/2;
			//	printf("%lld ",x);
			}
		//	printf("\n");
			if (max<count)
				max=count;
		}
		printf("%lld %lld %d\n",ii,jj,max);
	}
	return 0;
}

The 3n + 1 problem

Background