2013
11-11

# Tiling

In how many ways can you tile a 2xn rectangle by 2×1 or 2×2 tiles?

Here is a sample tiling of a 2×17 rectangle.

Input is a sequence of lines, each line containing an integer number 0 <= n <= 250.

For each line of input, output one integer number in a separate line giving the number of possible tilings of a 2xn rectangle.

2
8
12
100
200

3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251

import java.util.*;
import java.math.*;
public class Main{
static BigInteger[] ans;
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
ans=new BigInteger[251];
ans[0]=BigInteger.valueOf(1);
ans[1]=BigInteger.valueOf(1);
ans[2]=BigInteger.valueOf(3);
for(int i=3;i<=250;i++)
while(sc.hasNextInt()){
int n=sc.nextInt();
System.out.println(ans[n]);
}
}
}

1. #include <cstdio>
#include <algorithm>

struct LWPair{
int l,w;
};

int main() {
//freopen("input.txt","r",stdin);
const int MAXSIZE=5000, MAXVAL=10000;
LWPair sticks[MAXSIZE];
int store[MAXSIZE];
int ncase, nstick, length,width, tmp, time, i,j;
if(scanf("%d",&ncase)!=1) return -1;
while(ncase– && scanf("%d",&nstick)==1) {
for(i=0;i<nstick;++i) scanf("%d%d",&sticks .l,&sticks .w);
std::sort(sticks,sticks+nstick,[](const LWPair &lhs, const LWPair &rhs) { return lhs.l>rhs.l || lhs.l==rhs.l && lhs.w>rhs.w; });
for(time=-1,i=0;i<nstick;++i) {
tmp=sticks .w;
for(j=time;j>=0 && store >=tmp;–j) ; // search from right to left
if(j==time) { store[++time]=tmp; }
else { store[j+1]=tmp; }
}
printf("%dn",time+1);
}
return 0;
}