版权声明:欢迎转载博客(转载时请附上原文链接^_^) https://blog.csdn.net/OneLine_/article/details/88831397
这是一道找规律的题目……
Tiling
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 11380 | Accepted: 5258 |
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
一看这个数据就不简单……(就想到要用java做)
先把前四个数列出来
分别是 1 3 5 11
可以推出 a[i] = a[i-1] + a[i-2]*2
(其实是有思考过程的啦 但是脑子快废了 改天再补~~
放一下代码
import java.math.*;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
//@SuppressWarnings(value = { "all" })
public class Main {
public static void main(String[] args) {
Scanner cin = new Scanner(System.in);
// BigInteger zero = BigInteger.valueOf(0);
BigInteger sum, n, ans;
while (cin.hasNextBigInteger()) {
BigInteger a = BigInteger.valueOf(1);
BigInteger b = BigInteger.valueOf(3);
BigInteger two = BigInteger.valueOf(2);
n = cin.nextBigInteger();
int N = n.intValue();
for (int i = 1; i < N ; i++) {
BigInteger c = a.multiply(two);
c = c.add(b);
a = b;
b = c;
}
System.out.println(a);
}
}
}