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最新推荐文章于 2016-07-22 10:01:31 发布

原创最新推荐文章于 2016-07-22 10:01:31 发布 · 1.3k 阅读

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本文介绍了一个计算2xN矩形使用2x1或2x2瓷砖铺砌的方法，通过递推公式实现高效求解，并给出了具体示例输入输出及完整的Java实现代码。

Tiling

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 5487		Accepted: 2676

Description

In how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles?
Here is a sample tiling of a 2x17 rectangle.

Input

Input is a sequence of lines, each line containing an integer number 0 <= n <= 250.

Output

For each line of input, output one integer number in a separate line giving the number of possible tilings of a 2xn rectangle.

Sample Input

Sample Output

3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251

Source

The UofA Local 2000.10.14

import java.util.*; import java.math.*; public class Main { /** * @param args the command line arguments */ public static void main(String[] args) { BigInteger[] f; BigInteger t; f=new BigInteger[255]; f[0]=BigInteger.valueOf(1); f[1]=BigInteger.valueOf(1); for(int n=2; n<=250; n++) { t=f[n-2].multiply(BigInteger.valueOf(2)); t=t.add(f[n-1]); f[n]=t; } Scanner cin=new Scanner(System.in); Integer n=0; String s; while(cin.hasNext()) { n=cin.nextInt(); s=f[n].toString(); System.out.println(s); } // TODO code application logic here } }