Tiling
Time limit:1000 ms |
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Memory limit:65536 K |
Total submissions:7437 |
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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
2812100200
Sample output
317127318451004001521529343311354702511071292029505993517027974728227441735014801995855195223534251
Pay special attention to input 0 and output 1 !!!!!!!
Recursive formula is not difficult, AI = Ai-1 + 2 * Ai-2, it is easy to think clearly
The AC code is as follows:
#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;}