279. 自然数拆分

完全背包模型

二维

#include<iostream>
using namespace std;

const int N = 4010;
const unsigned int mod = 1 << 31;


unsigned int f[N][N];
int n;

int main(){
    cin >> n;
    
    for(int i = 0; i <= n; i ++) f[i][0] = 1;
    
    for(int i = 1; i <= n; i ++)
        for(int j = 1; j <= n; j ++){
            f[i][j] = f[i - 1][j];
            if(j >= i) f[i][j] = (f[i][j] + f[i][j - i]) % mod;
        }
    
    cout << f[n][n] - 1 << endl; // 这里可以写成f[n - 1][n]
    return 0;
}

一维优化

#include<iostream>
using namespace std;

const int N = 4010;
const unsigned int mod = 1 << 31;


unsigned int f[N];
int 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] - 1 << endl;
    return 0;
}