hdu1041 Computer Transformation 大数找规律

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();}}