P1010 [NOIP1998 普及组] 幂次方

// Problem: P1010 [NOIP1998 普及组] 幂次方
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P1010
// Memory Limit: 125 MB
// Time Limit: 1000 ms
// User: Pannnn

#include <bits/stdc++.h>

using namespace std;

template<class T>
void debugVector(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>
void debugMatrix2(const T &a) {
    for (size_t i = 0; i < a.size(); ++i) {
        debugVector(a[i]);
    }
}

template<class T>
using matrix2 = vector<vector<T>>;

template<class T>
vector<vector<T>> getMatrix2(size_t n, size_t m, T init = T()) {
    return vector<vector<T>>(n, vector<T>(m, init));
}

template<class T>
using matrix3 = vector<vector<vector<T>>>;

template<class T>
vector<vector<vector<T>>> getMatrix3(size_t x, size_t y, size_t z, T init = T()) {
    return vector<vector<vector<T>>>(x, vector<vector<T>>(y, vector<T>(z, init)));
}

vector<int> genBigInteger(string a) {
    vector<int> res;
    for (int i = a.size() - 1; i >= 0; --i) {
        res.push_back(a[i] - '0');
    }
    return res;
}

void printBigInteger(vector<int> a) {
    for (size_t i = a.size() - 1; i >= 0; --i) {
        cout << a[i];
    }
}

vector<int> addBigInteger(vector<int> a, vector<int> b) {
    vector<int> res;
    int pre = 0;
    for (size_t i = 0; i < a.size() || i < b.size() || pre; ++i) {
        if (i < a.size()) pre += a[i];
        if (i < b.size()) pre += b[i];
        res.push_back(pre % 10);
        pre /= 10;
    }
    return res;
}

void convert(int n) {
    if (n == 0) {
        cout << "0";
        return;
    }
    // 取出二进制表示中为1的位号，即括号内的数
    vector<int> mi;
    for (int i = 0; n; ++i, n >>= 1) {
        if (n & 1) {
            mi.push_back(i);
        }
    }
    // 反转，先输出高位
    reverse(mi.begin(), mi.end());
    // debugVector(mi);
    for (int i = 0; i < mi.size(); ++i) {
        cout << "2";
        if (mi[i] != 1) {
            cout << "(";
            convert(mi[i]);
            cout << ")";
        }
        if (i != mi.size() - 1) {
            cout << "+";
        }
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    int n;
    cin >> n;
    convert(n);
    
    return 0;
}