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
28 12 100 200
Sample Output
3171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251
公式为:f[x]=f[x-1]+2*f[x-2];
至于为什么f[0]为1,我也不知道。。。我是根据公式以及给出的案例反推的f[0].
#include <stdio.h>
#include <string.h>
char s[260][200];
int main()
{
int n, i, a, j, x, b;
memset(s,'0',sizeof(s));
s[0][0]='1';
s[1][0]='1';
s[2][0]='3';
for(i=3;i<=250;i++)
{
for(j=0;j<100;j++)
{
a=(2*(s[i-2][j]-'0')+s[i-1][j]-'0'+s[i][j]-'0');
s[i][j]=a%10+'0';
s[i][j+1]=a/10+'0';
}
}
while(scanf("%d",&n)!=EOF)
{
x=0;
for(i=100;i>=0;i--)
{
if(s[n][i]!='0')
{
x=i;
break;
}
}
for(i=x;i>=0;i--)
{
printf("%c",s[n][i]);
}
printf("\n");
}
return 0;
}