周赛 大数找规律

Problem A

Time Limit : 2000/1000ms (Java/Other) Memory Limit : 131072/65536K (Java/Other)
Total Submission(s) : 71 Accepted Submission(s) : 11
[align=left]Problem Description[/align]
In how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles?

Here is a sample tiling of a 2x17 rectangle.



[align=left]Input[/align]
Input is a sequence of lines, each line containing an integer number 0 <= n <= 250.

[align=left]Output[/align]
For each line of input, output one integer number in a separate line giving the number of possible tilings of a 2xn rectangle.

[align=left]Sample Input[/align]

2
8
12
100
200

[align=left]Sample Output[/align]

3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251

//找规律的题，就是一块一块的加，每一次在前面的基础上加，也就相当于加一个2*1的矩形，它既可以放在前面，也可以放在后面，所以是2*a[n-1];但是加入的那一个可以和前面也可以构成一种情况，a[n-2]种情况，剩下就是大树的问题了，代码如下：

#include<stdio.h>
#include<string.h>
int aa[1000][100];
void sum()
{
aa[0][0]=1;
aa[1][0]=1;
aa[2][0]=3;
int cnt,i,j;
cnt=0;
for(i=3;i<=1000;i++)
for(j=0;j<100;j++)
{
cnt+=(aa[i-2][j])*2+aa[i-1][j];
aa[i][j]=cnt%10;
cnt/=10;
}

}
int main()
{   sum();
int n;
while(scanf("%d",&n)!=EOF)
{
int i;
for(i=99;i>=0;i--)
if( aa
[i]!=0)
break;
for(;i>=0;i--)
printf("%d",aa
[i]);
printf("\n");
}
}