hdu3519Lucky Coins Sequence

Lucky Coins Sequence

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 912    Accepted Submission(s): 481


Problem Description

As we all know,every coin has two sides,with one side facing up and another side facing down.Now,We consider two coins's state is same if they both facing up or down.If we have N coins and put them in a line,all of us know that it will be 2^N different ways.We
call a "N coins sequence" as a Lucky Coins Sequence only if there exists more than two continuous coins's state are same.How many different Lucky Coins Sequences exist?

 

Input

There will be sevaral test cases.For each test case,the first line is only a positive integer n,which means n coins put in a line.Also,n not exceed 10^9.

 

Output

You should output the ways of lucky coins sequences exist with n coins ,but the answer will be very large,so you just output the answer module 10007.

 

Sample Input

3
4

 

Sample Output

2
6

 

Source

2010 ACM-ICPC Multi-University
Training Contest（9）——Host by HNU

 

Recommend

zhengfeng

构造矩阵，运用矩阵快速幂即可。

构造矩阵是关键点，可先推导出递推式：设a
为长度为n的满足要求的方案数目，b
为长度为n的末尾最后两位不同的方案数字，c
为长度为n的末位相同的方案数。

那么有a
=c[n-1]+2a[n-1];b
=c[n-1]+b[n-1];c
b[n-1];

可知

[2,0,1]   [a(n-1)]     [a(n)][0,1,1]  * [b(n-1)]  =  [b(n)][0,1,0]   [C(n-1)]     [C(n)]