UVA11310 Delivery Debacle铺砖问题

Posted 2021-05-24 海岛Blog

Wolfgang Puck has two very peculiar habits:
• I. He only makes two shapes of cakes. One is square and has an area of one unit. The other is L-shaped and has an area of three units.
• II. He will only deliver cakes packed in very specific box sizes. The boxes are always 2 units wide and are of varying length.
    One day Wolfgang wondered in how many different ways he can pack his cakes into certain sized boxes. Can you help him?

The precise sizes of the cakes Wolfgang makes and one way to pack them in a box of length 6.

The five ways to pack a box of length 2.
Input
The input begins with t, the number of different box lengths. The following t lines contain an integer n (1 ≤ n ≤ 40).
Output
For each n output on a separate line the number of different ways to pack a 2-by-n box with cakes described above. Output is guaranteed to be less than 10¹⁸.
Sample Input
2
1
2
Sample Output
1
5

问题链接：UVA11310 Delivery Debacle
问题简述：（略）
问题分析：铺砖问题，关键是找到递推式，不解释。
程序说明：（略）
参考链接：（略）
题记：（略）

AC的C++语言程序如下：

/* UVA11310 Delivery Debacle */

#include <bits/stdc++.h>

using namespace std;

const int N = 40;
long long f[N + 1];

int main()
{
    f[0] = 1;
    f[1] = 1;
    f[2] = 5;
    for (int i = 3; i <= N; i++)
        f[i] = 2 * f[i - 3] + 4 * f[i - 2] + f[i - 1];

    int t, n;
    scanf("%d", &t);
    while (t--) {
        scanf("%d", &n);
        printf("%lld\\n", f[n]);
    }

    return 0;
}