整数划分(允许相同)，时间复杂度O(n*sqrt(n))

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<iostream>
#include<queue>
#include<map>
#include<cmath>
#include<set>
#include<stack>
#define ll long long
#define max(x,y) (x)>(y)?(x):(y)
#define min(x,y) (x)>(y)?(y):(x)
#define cls(name,x) memset(name,x,sizeof(name))
using namespace std;
const int inf=1<<28;
const int maxn=50010;
const int maxm=110;
const int mod=1e9+7;
const double pi=acos(-1.0);
int dp[maxn];
int main()
{
    //freopen("in.txt","r",stdin);
    int n;
    while(~scanf("%d",&n))
    {
        cls(dp,0);
        dp[0]=1;
        for(int i=1;i<=n;i++)
        {
            for(int j=1;;j++)
            {
                if(i-j*(j*3-1)/2>=0)
                dp[i]=((dp[i]+((j+1)%2==0?1:-1)*dp[i-j*(j*3-1)/2])%mod+mod)%mod;
                if(i-j*(j*3+1)/2>=0)
                dp[i]=((dp[i]+((j+1)%2==0?1:-1)*dp[i-j*(j*3+1)/2])%mod+mod)%mod;
                else break;
            }
        }
        printf("%d\n",dp[n]);
    }
    return 0;
}