## 思路&题解

PC/UVA 110101/100

//author: CHC
//First Edit Time:	2014-01-10 18:30
//Last Edit Time:	2014-01-10 18:30
//Filename:1.cpp
#include <iostream>
#include <cstdio>
#include <string.h>
#include <queue>
#include <algorithm>
using namespace std;
long long cs[1000001]={ 0 };
int main()
{
for(int j=1;j<1000001;j++)
{
int i=1;
long long n=j;
while(n!=1)
{
if(n%2)n=n*3+1;
else n/=2;
if(n<j)
{
cs[j]=cs[n]+i;
break;
}
++i;
}
if(!cs[j]) cs[j]=i;
}
int a,b,c,d;
while(~scanf("%d%d",&c,&d))
{
a=c,b=d;
if(a>b)a^=b^=a^=b;
int maxn=cs[a],maxi=a;
for(int i=a+1;i<=b;i++)
if(cs[i]>maxn)
{
maxn=cs[i];
maxi=i;
}
printf("%d %d %d\n",c,d,maxn);
}
return 0;
}


## The 3n + 1 problem

Consider the following algorithm to generate a sequence of numbers. Start with an integer n. If n is
even, divide by 2. If n is odd, multiply by 3 and add 1. Repeat this process with the new value of n,
terminating when n = 1. For example, the following sequence of numbers will be generated for n = 22:
22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
It is conjectured (but not yet proven) that this algorithm will terminate at n = 1 for every integer n.
Still, the conjecture holds for all integers up to at least 1, 000, 000.
For an input n, the cycle-length of n is the number of numbers generated
up to and including the 1. In the example above, the cycle length of 22 is 16. Given any two numbers i and j,
you are to determine the maximum cycle length over all numbers between i and j, including both
endpoints.

### 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.

### Output

For each pair of input integers i and j,
output i, j in
the same order in which they appeared in the input and then the maximum cycle length for integers between and including i and j.
These three numbers should be separated by one space, with all three numbers on one line and with one line of output for each line of input.

### Sample Input

1 10
100 200
201 210
900 1000


### Sample Output

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