Tri Tiling
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 Sample Output Source Waterloo local 2005.09.24 |
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[题意][用1×2的小矩阵填充3×n,一共有多少种方法]
【题解】【递推】
【明明是dp,却硬生生的写成了递推 】
【完整的2*3矩形有3种拼法,所以f[n]+=3*f[n-2]。
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[n]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[n]+=2*(f[n-4]+f[n-6]+..+f[0]). 】
【于是f[n]=3*f[n-2]+2*(f[n-4]+..+f[0]),求通项得:f[n]=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;
}