Tiling
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 7437 | Accepted: 3635 |
Description
In how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles?
Here is a sample tiling of a 2x17 rectangle.
Input
Input is a sequence of lines, each line containing an integer number 0 <= n <= 250.
Output
For each line of input, output one integer number in a separate line giving the number of possible tilings of a 2xn rectangle.
Sample Input
2
8
12
100
200
Sample Output
3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251
特别注意输入0。输出1！。！！
。！
！
递推公式不难，Ai=Ai-1+2*Ai-2。非常easy就想清楚了
AC代码例如以下：
#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std; int a[300][3005],b[3005];
int x,y,z; void work(int c)
{
int i;
memset(b,0,sizeof b);
for(i=0;i<=x;i++)
{
b[i]+=(a[c-2][i]*2);
if(b[i]>10)
{
b[i]=b[i]%10;
x++;
b[i+1]=1;
}
}
z=x+2;
for(i=0;i<=z+2;i++)
{
a[c][i]+=a[c-1][i]+b[i];
if(a[c][i]>=10&&i==z+1)
z++;
if(a[c][i]>=10)
{
a[c][i]=a[c][i]%10;
a[c][i+1]=1;
} }
x=y;y=z;
} int main()
{
int n;
int i;
while(cin>>n)
{
if(n==0)
{cout<<"1"<<endl;continue;}
int bj=0;
memset(a,0,sizeof a);
a[1][0]=1;a[2][0]=3;
x=0;y=0;
for(i=3;i<=251;i++)
work(i);
for(i=z-1;i>=0;i--)
{
if(bj==0&&a[n][i]==0)
continue;
if(a[n][i]!=0)
bj=1;
cout<<a[n][i];
}
cout<<endl;
}
return 0;
}