URAL 1225. Flags （dp）

1225. Flags

Time limit: 1.0 second

Memory limit: 64 MB

On the Day of the Flag of Russia a shop-owner decided to decorate the show-window of his shop with textile stripes of white, blue and red colors. He wants to satisfy the following conditions:

1. Stripes of the same color cannot be placed next to each other.
2. A blue stripe must always be placed between a white and a red or between a red and a white one.

Determine the number of the ways to fulfill his wish.

Example. For N = 3 result is following:

Input

N, the number of the stripes, 1 ≤ N ≤ 45.

Output

M, the number of the ways to decorate the shop-window.

Sample

3

4

题意：涂色问题。相邻颜色不能一样，蓝色只能在红白或白红之间出现。

解析：递推。

考虑第i个位置的颜色：若是红或白色，则只需要在i-1的后面加上一个白或红色即可；若是蓝色，则i-1必是红或白，则只需要在i-2的后面加上红或白即可。

必须用long long，否则会WA on Test 12.

AC代码：

#include <cstdio>

long long f[50];

int main(){
    f[1] = f[2] = 2;
    for(int i=3; i<=50; i++) f[i] = f[i-1] + f[i-2];
    int n;
    while(scanf("%d", &n)==1){
        printf("%lld\n", f[n]);
    }
    return 0;
}