# The 3n + 1 problem

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.

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.

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.

``````1 10
100 200
201 210
900 1000
``````

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

``````#include <stdio.h>
int F(int i);
int main()
{
int a,b,i,temp=0,temp1,temp2,a1,a2;
while(scanf("%d %d",&a,&b)==2)
{
a1=a;
a2=b;
if(a>b)
{
temp2=a;
a=b;
b=temp2;
}
for(i=a;i<=b;i++)
{
temp1=F(i);
//printf("%d\n",temp1);
if(temp<temp1)
temp=temp1;
}
printf("%d %d %d\n",a1,a2,temp);
temp=0;
}
}

int F(int i)
{
int temp=i,j=1;
while(1)
{
if(temp==1)
return j;
if(temp%2==0)
{
temp=temp/2;
}
else
{
temp=temp*3+1;
}
j++;
}
}``````

``````#include"stdio.h"
int a;
char s;
int main()
{
int m,n,i,j,c=0;
while(scanf("%d %d",&n,&m)==2&&(n||m))
{
getchar();
for(i=0;i<=n;i++)
for(j=0;j<=n;j++)
a[i][j]=0;
c++;
for(i=1;i<=n;i++)
{
for(j=1;j<=m;j++)
{
scanf("%c",&s[i][j]);
if(s[i][j]=='*')
{
a[i][j]=-1;
if(a[i-1][j-1]!=-1)a[i-1][j-1]++;
if(a[i][j-1]!=-1)a[i][j-1]++;
if(a[i-1][j]!=-1)a[i-1][j]++;
if(a[i+1][j+1]!=-1)a[i+1][j+1]++;
if(a[i-1][j+1]!=-1)a[i-1][j+1]++;
if(a[i+1][j-1]!=-1)a[i+1][j-1]++;
if(a[i][j+1]!=-1)a[i][j+1]++;
if(a[i+1][j]!=-1)a[i+1][j]++;
}
}
getchar();
}
printf("Field #%d:\n",c);
for(i=1;i<=n;i++)
{
for(j=1;j<=m;j++)
{
if(a[i][j]==-1)printf("*");
else printf("%d",a[i][j]);
}
printf("\n");
}
printf("\n");
}
return 0;
}
``````