Sine之舞 C++递归

#include <iostream>
#include <string>
using namespace std;
string s;
void dfs(int begin, int num)
{
    if (begin == num)
    {
        cout << "sin(" << begin << ")";
        return;
    }
        if (begin % 2 != 1)
        {    
            cout << "sin(" << begin << "+";
        }    
        else
        {
            cout << "sin(" << begin << "-";
        }
        dfs(begin+1, num);
        cout << ")";
}
void Sn(int n, int num)
{
    if (n == 1)
    {
        int k = 1;
        dfs(k, n);
        cout << "+" << num;
    }
    else
    {
        int k = 1;
        cout << "(";
        Sn(n-1, num+1);
        cout << ")";
        dfs(k, n);
        cout << "+" << num;
    }
}
int main(void)
{
    int num;
    cin >> num;
//    s = "sin("
    Sn(num, 1);
    cout << s << endl;
    return 0;
}