Computer Transformation
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 8831 Accepted Submission(s): 3331
Problem Description
A sequence consisting of one digit, the number 1 is initially written into a computer. At each successive time step, the computer simultaneously tranforms each digit 0 into the sequence 1 0 and each digit 1 into the sequence 0 1. So, after the first time step, the sequence 0 1 is obtained; after the second, the sequence 1 0 0 1, after the third, the sequence 0 1 1 0 1 0 0 1 and so on.
How many pairs of consequitive zeroes will appear in the sequence after n steps?
How many pairs of consequitive zeroes will appear in the sequence after n steps?
Input
Every input line contains one natural number n (0 < n ≤1000).
Output
For each input n print the number of consecutive zeroes pairs that will appear in the sequence after n steps.
Sample Input
23
Sample Output
11
f[n]=2*f[n-2]+f[n-1]
import java.util.*;
import java.math.*;
public class Main
{
BigInteger []f=new BigInteger[1005];
public static void main(String args[])
{new Main().run();}
public void run()
{
Scanner cin=new Scanner(System.in);
while(cin.hasNextInt())
{
int n=cin.nextInt();
f[1]=BigInteger.valueOf(0);
f[2]=BigInteger.valueOf(1);
BigInteger b=BigInteger.valueOf(2);
for(int i=3;i<=1000;i++)
{
BigInteger a=f[i-2];
f[i]=a.multiply(b).add(f[i-1]);
}
System.out.println(f[n]);
}
}
}