P1028 [NOIP2001 普及组] 数的计算

// Problem: P1028 [NOIP2001 普及组] 数的计算
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P1028
// Memory Limit: 125 MB
// Time Limit: 1000 ms
// User: Pannnn

#include <bits/stdc++.h>

using namespace std;

template<class T>
void printVector(const T &a) {
    cout << "[ ";
    for (size_t i = 0; i < a.size(); ++i) {
        cout << a[i] << (i == a.size() - 1 ? " " : ", ");
    }
    cout << "]" << endl;
}

template<class T>
vector<vector<T>> matrix2(size_t n, size_t m, T init) {
    return vector<vector<T>>(n, vector<T>(m, init));
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    /*
        对于一个数n，令其可以得到的数的个数为f(n);
        f(n) = 1 + f(1) + f(2) + ... + f(k); k <= n / 2;
        递归式，其中f(1) = 1;
        
        使用递归超时，多个数重复计算，改为递推
    */
    int n;
    cin >> n;
    vector<int> f(n + 1);
    f[0] = f[1] = 1;
    for (int i = 2; i <= n; ++i) {
        int sum = 1;
        for (int j = 1; j <= i / 2; ++j) {
            sum += f[j];
        }
        f[i] = sum;
    }
    // printVector(f);
    cout << f[n] << endl;
    return 0;
}