timus 1225 flags 基础DP 简单递推

 

　　　　　　　　　　　　　　　　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

input	output
3	4

 

 

 

 

 

1代表白色

2.蓝色

3.红色

 

dp[1][j]表示选到第i个条纹，第i个为j这种颜色的

 

然后递推

 

注意：

1.要用 long long

2.蓝色不能放在最后面和最前面，只能在中间

 

#include<iostream>
#include<cstring>

using namespace std;

const int maxn=48;

long long dp[maxn][4];

int main()
{
    dp[0][1]=dp[0][2]=dp[0][3]=0;
    dp[1][1]=dp[1][3]=1;
    dp[1][2]=0;

    for(int i=2;i<=45;i++)
    {
        dp[i][1]=dp[i-1][3]+dp[i-2][3];
        dp[i][2]=dp[i-1][1]+dp[i-1][3];
        dp[i][3]=dp[i-1][1]+dp[i-2][1];
    }

    int n;

    while(cin>>n)
    {
        long long  sum=dp[n][1]+dp[n][3];

        cout<<sum<<endl;
    }
    return 0;
}