B - Tri Tiling
HDU - 1143
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
題意：瓷磚問題，3 x n的區(qū)域用3 x 1的瓷磚鋪一共有多少種方案。
解法：dp算法，遞推，有三種基礎(chǔ)排法，所以f(n)=3f(n-2)，但還要考慮與前面相連的情況，所以f(n)=3f(n-2)+2f(n-4)+2f(n-6)+······+2f(2)，所以得到f(n)=4*f(n-2)-f(n-4)
代碼：
#include<iostream>
using namespace std;
int main()
{
int a[31]={0,};
a[0]=1,a[2]=3;
for(int i=4;i<=30;i+=2)
a[i]=4*a[i-2]-a[i-4];
int n;
while(cin>>n&&n!=-1)
cout<<a[n]<<endl;
return 0;
}
