Flags-Ural1225簡單遞推

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:
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
3
output
4

Problem Source:

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

簡單的遞推，三種顏色的布，相鄰的顏色不能相同，藍色在紅色與白色之間，則用1表示紅色，2表示白色，Dp[i][j]表示第i個條紋的顏色爲j是的狀態數目，當j=1時，若是i-1的顏色爲白色，則Dp[i][1]+=Dp[i-1][2],若是爲藍色，則取決於i-2的顏色爲白色狀態，因此Dp[i][1]=Dp[i-1][2]+Dp[i-2][2],則Dp[i][2]=Dp[i-1][1]+Dp[i-2][1].

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <string>
#include <queue>
#include <vector>
#include <deque>
#include <iostream>
#include <algorithm>

using namespace std;

long long Dp[50][3];

int main()
{
    memset(Dp,0,sizeof(Dp));

    Dp[1][1]=Dp[1][2]=1;

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

        Dp[i][2] = Dp[i-1][1]+Dp[i-2][1];
    }

    int n;

    while(~scanf("%d",&n))
    {
        cout<<Dp[n][1]+Dp[n][2]<<endl;
    }

    return 0;
}