POJ 2663 Tri Tiling

Description

In how many ways can you tile a 3xn rectangle with 2x1 dominoes? 
Here is a sample tiling of a 3x12 rectangle. 

Input

Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer 0 <= n <= 30.

Output

For each test case, output one integer number giving the number of possible tilings.

Sample Input

2812-1

Sample Output

3153

分析：这是一道思维训练的好题。分两种情况考虑

1.在此处放一单位的积木。等于 3 * DP[i-1];
      2.与前面相连接。连接的方案有 2 * (DP[i-2] + DP[i-3] +......+ DP[0]);
      因此有：DP[i] = 3 * DP[i-1] + 2 * (DP[i-2] + DP[i-3] +......+ DP[0]);

      理解到这里应该就差不多了，当然也可以再化简为 DP[i] = 4 * DP[i-1] - DP[i-2];

#include <iostream>using namespace std;int main(){    long long a[32];    int n;    a[0] = 1; a[2]= 3;a[1] = 0;    for(long long i =3 ;i<31;i++)    {        if(i&1)            a[i] = 0;        else        {            a[i] = 4*a[i-2] - a[i-4];        }        //cout << i<< "  "<< a[i] <<endl;    }    while(cin>>n)    {        if(n == -1)            break;        cout << a[n] <<endl;    }    return 0;}