POJ 2506：Tiling

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Tiling

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 7452 Accepted: 3639

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

2812100200

Sample Output

317127318451004001521529343311354702511071292029505993517027974728227441735014801995855195223534251

题目大意就是有2×1和2×2两种规格的地板，现要拼2×n的形状，共有多少种情况。

递推思想：

假设我们已经铺好了2×（n-1）的情形，则要铺到2×n则只能用2×1的地板

假设我们已经铺好了2×（n-2）的情形，则要铺到2×n则可以选择1个2×2或两个2×1，故可能有下列三种铺法

其中要注意到第三个会与铺好2×（n-1）的情况重复，故不可取，故可以得到递推式

a[i]=2*a[i-2]+a[i-1];

而且是大数问题。。前面用JAVA水过特别爽。。所以这题也是用JAVA写的。

import java.math.BigInteger;import java.util.Scanner;public class Main{public static void main(String[] args) {Scanner cin=new Scanner(System.in);    int n;    BigInteger[] a = new BigInteger[300];a[0]=BigInteger.ONE;a[1]=BigInteger.ONE;a[2]=BigInteger.valueOf(3);for(int i=2;i<a.length;i++){a[i]=a[i-1].add(a[i-2].multiply(BigInteger.valueOf(2)));}while (cin.hasNext()){n=cin.nextInt();System.out.println(a[n]);}}}

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