poj 2506Tiling 大数

最新推荐文章于 2024-09-05 23:19:08 发布

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本文介绍了一种计算2xN矩形使用2x1或2x2瓷砖进行铺砌的方法数量的算法。通过递推公式解决该问题，并提供了一个Java实现示例。

Tiling

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 9971		Accepted: 4681

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.io.*;  
import java.math.BigInteger;  
import java.util.*;  
  
public class Main  
{  
    public static void main(String args[])  
    {  
        Scanner cin = new Scanner(System.in); 
        int n;
        BigInteger a[] = new BigInteger[255];  
        while(cin.hasNext())  
        {  
        	a[0] = BigInteger.valueOf(1);
            a[1] = BigInteger.valueOf(1);
            a[2] = BigInteger.valueOf(3);
            n = cin.nextInt();
            for(int i = 3; i <= n; ++i)  
                a[i] = a[i - 1].add(a[i - 2]).add(a[i - 2]);  
            System.out.println(a[n]);  
        }  
    }  
}