Flag(Ural_1225)

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:

Stripes of the same color cannot be placed next to each other.
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:
Problem illustration

Input

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

Output

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

Sample input output

3

4

Problem Source

2002-2003 ACM Central Region of Russia Quarterfinal Programming Contest, Rybinsk, October 2002

Ural动规专题第一道小题，一直不懂是怎么推出来的，直到又把动规学了一遍加上看了别人的题解才豁然开朗。

用dp[i]代表n = i时的方法数，那么我们怎样可以得到它呢？根据题意，每种方法最后的颜色必定是红色或白色（因为蓝色只能放在它们俩中间），所以，我们可以把n = i - 1时的每种方法最后加上红色或白色来得到n = i的一部分方法数，即dp[i]有一部分是dp[i-1]。除了可以红白搭和白红搭，还有一种就是把蓝色放在红白或白红的中间，这种也很简单，我们可以在n = i - 2状态的最后添加两种颜色，蓝色+红/白色，而n = i - 2状态下的方法数就是dp[i - 2]，所以总结起来dp[i]就等于dp[i-1] + dp[i-2];（弱语言障碍只能解释成这样了= =下面上代码）

代码

#include <iostream>#include <cstdio>#include <cstring>#define LL long longusing namespace std;int main(){    LL ans[50] = {0, 2, 2};    for(int i = 3; i < 46; i++)        ans[i] = ans[i - 1] + ans[i - 2];    int n;    scanf("%d", &n);    printf("%lld\n", ans[n]);    return 0;}