杭电 1143 Tri Tiling

Tri Tiling

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1898    Accepted Submission(s): 1080

Problem Description

In how many ways can you tile a 3xn rectangle with 2x1 dominoes? Here is a sample tiling of a 3x12 rectangle.

 

Input

Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer 0 ≤ n ≤ 30.

 

Output

For each test case, output one integer number giving the number of possible tilings.

 

Sample Input

  
  

   
   2
8
12
-1
  
  

 

Sample Output

  
  

   
   3
153
2131
  
  

通过递推不难得到a[i]=3*a[i-2]+2*a[i-4]+...........+2*a[2]+2*a[0]，其中a[0]=1意义不大，用于递推。

AC代码如下：

#include<iostream>
#include<cstring>
using namespace std;
int main ()
{
	int a[31],n,i;
	memset(a,0,sizeof(a));
	a[0]=1;a[2]=3;
	for(i=4;i<=30;i+=2)
		a[i]=4*a[i-2]-a[i-4];
	while(cin>>n,n!=-1)
	{
		cout<<a[n]<<endl;
	}
	return 0;
}