acwing 900 整数划分 2022/05/10

#include <iostream>

using namespace std;

const int N = 1e3 + 7, mod = 1e9 + 7;

int f[N][N];

int main() {
    int n;
    cin >> n;

    for (int i = 0; i <= n; i ++) {
        f[i][0] = 1; // 容量为0时，前 i 个物品全不选也是一种方案
    }

    for (int i = 1; i <= n; i ++) {
        for (int j = 0; j <= n; j ++) {
            f[i][j] = f[i - 1][j];
            if (j >= i) f[i][j] = (f[i - 1][j] + f[i][j - i]) % mod;
        }
    }

    cout << f[n][n] << endl;
}

#include <iostream>
#include <algorithm>

using namespace std;
const int N = 1010, mod = 1e9+7;
int n;
int f[N];

int main()
{
    cin >> n;
    
    f[0] = 1;
    
    for(int i = 1; i <= n; ++i)
        for(int j = i; j <= n; ++j)
            f[j] = (f[j] + f[j-i]) % mod;
            
    cout << f[n] << endl;
    
    return 0;
}