【POJ 2663】Tri Tiling（dp|递推）

Tri Tiling Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 9912   Accepted: 5072 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 Source Waterloo local 2005.09.24

  当突出两块时：突出的两块时上侧两个：发现往后拼只有一种方法。突出的两块在下侧时同样一个，于是用这种突出的方法拼出f
有两种（就是以三个一组，两组并在一起时，将中间的两个竖放的改为横着的）。即f
+=2*(f[n-4]+f[n-6]+..+f[0]).
】

【于是f
=3*f[n-2]+2*(f[n-4]+..+f[0])，求通项得：f
=4*f[n-2]-f[n-4].】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int f[40];
int main()
{
int i,j;
f[0]=1; f[2]=3;
for (i=4;i<=30;i+=2)
f[i]=4*f[i-2]-f[i-4];
while (scanf("%d",&j)==1&&j!=-1)
printf("%d\n",f[j]);
return 0;
}