poj 2506 Tiling

最新推荐文章于 2021-11-23 17:35:59 发布

hpuhjl

最新推荐文章于 2021-11-23 17:35:59 发布

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CC 4.0 BY-SA版权

本文链接：https://blog.youkuaiyun.com/hpuhjl/article/details/80956089

本文介绍了一种计算2xn矩形使用2x1或2x2瓷砖铺砌的方法数目的算法，并提供了一个Java实现示例。该算法通过递推公式进行高效计算，能够处理最大宽度为250的矩形。

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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

2
8
12
100
200

Sample Output

3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251

import java.math.*;
import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        BigInteger a[] = new BigInteger[300];
        a[0] = a[1] = BigInteger.ONE;
        for(int i = 2; i < 300 ; i++)
            a[i] = a[i-1].add(a[i-2].multiply(BigInteger.valueOf(2)));
        int n;
        while(in.hasNext()){
            n = in.nextInt();
            System.out.println(a[n]);
        }
    }
}