The 3n + 1 problem 分类： POJ 2015-06-12 17:50 11人阅读 评论(0) 收藏

The 3n + 1 problem

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 53927		Accepted: 17142

Description

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.

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 before the 1 is printed. 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.

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 10,000 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.

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

#include <cstdio>
#include <string.h>
#include <cmath>
#include <iostream>
#define WW freopen("output.txt","w",stdout)
using namespace std;
const int Max=11000;
int Arr[Max];
int main()
{
    memset(Arr,0,sizeof(Arr));
    Arr[1]=1;
    Arr[2]=2;
    for(int i=3; i<Max; i++)
    {
        int ans=i;
        int sum=1;
        while(ans!=1)
        {
            if(ans<i)
            {
                break;
            }
            if(ans%2)
            {
                ans=ans*3+1;
            }
            else
            {
                ans/=2;
            }
            ++sum;
        }
        Arr[i]=Arr[ans]+sum-1;
    }
    int Star,End;
    int vis;
    while(~scanf("%d %d",&Star,&End))
    {
        vis=0;
        if(Star>End)//可能输入的开始比结束大，所以要交换
        {
            swap(Star,End);
            vis=1;
        }
        int MAX=0;
        int flag=0;
        for(int i=Star; i<=End; i++)
        {
            if(MAX<Arr[i])
            {
                MAX=Arr[i];
                flag=i;
            }
        }
        if(!vis)//输出时要按照输入的顺序
            printf("%d %d %d\n",Star,End,Arr[flag]);
        else
        {
            printf("%d %d %d\n",End,Star,Arr[flag]);
        }
    }
    return 0;
}

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