Computer Transformation
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 8161 Accepted Submission(s): 3069
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?
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
题目大意就是，屏幕上开始是1，以后，1会变成01,0会变成10，最后问每次有多少对0,（两个连续的0算一对），最后可得递推公式f(n)=f(n-1)+2*f(n-2);由于数据过大，需要进行大数处理，故可采用java
import java.util.Scanner;
import java.math.*;
public class Main {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
BigInteger[] a = new BigInteger[1005];
a[0]=BigInteger.valueOf(0);
a[1]=BigInteger.valueOf(0);
a[2]=BigInteger.valueOf(1);
for(int i=3;i<1005;i++){
a[i] = a[i-1].add(a[i-2]).add(a[i-2]);
}
int n;
while(in.hasNext()){
n = in.nextInt();
System.out.println(a[n]);
}
in.close();
}
}
