大二第二次月赛--The number of maximum subset

                                                         The number of maximum subset

1000 ms  |  内存限制： 65535

1

You are given a set with n distinct numbers of 1 to n, and your task is to calculate the number of maximum subsets with the following properties:

1：no two elements in the subset should be adjacent

2：it shouldn't be possible to add numbers to the subset without violating the first condition

For example, if n = 5, the number of maximum subsets which fulfill the above conditions is 4. The subsets are {1,3,5},{2,4},{2,5},{1,4}. 

The input will consist of a sequence of numbers n,1 ≤ n ≤ 76. Each number will be on a separate line. The input will be terminated by EOF. 输出 Output the number of maximum subsets as described above on a single line. The number of all subsets will be less than 2^31. 样例输入

1
2
3
4
5
30

样例输出

1
2
2
3
4
4410

题意：给定一组n个不同的数字1到N，你的任务是计算具有以下属性的最大数目的子集：

1：没有两个元素应相邻子集。

2：不可以添加编号的子集在不违反第一条件。

例如，如果n = 5，最大的子集，满足上述条件的号码是4。的子集{ } { } 1，2，5，{ }，{ 1,4 }。

规律题，方程：dp[i]=dp[i-2]+dp[i-3];

#include<cstdio>
int main()
{
    int n, dp[80];
    dp[0] = dp[1] = 1;
    dp[2] = 2;
    for(int i = 3; i <= 76; i++)
        dp[i] = dp[i-2] + dp[i-3];
    while(~scanf("%d", &n))
    {
        printf("%d\n", dp[n]);
    }
    return 0;
}