https://codeforces.net/contest/2013/problem/C

Hi everyone,
I’m trying to solve the problem using a recursive approach, but I’m running into issues. My iterative solution works perfectly and gets accepted, but when I try to implement it recursively, the solution doesn’t behave as expected.

I suspect there might be an issue with how I’m handling the recursion termination or updating the string in the recursive calls, but I’m not sure.

Here’s the iterative solution that works.

Here’s the recursive solution that I’m struggling with:

#include <bits/stdc++.h>
using namespace std;

int f(string &s1, string &s2, int i, int n, bool first) {
    if ((s1.size() + s2.size()) > n or (i >= (2 * n)))
        return -1;
    cout << "? " << s1 + s2 << endl;

    int check;
    cin >> check;
    if (first) {
        if (check) {
            s2 = s1 + s2;
            return 1;
        } else {
            if (s1 == "0") {
                s1 = "1";
                return 1 + f(s1, s2, i + 1, n, first);
            } else {
                return -1;
            }
        }
    } else {
        if (check) {
            s1 = s1 + s2;
            return 1;
        } else {
            if (s2 == "0") {
                s2 = "1";
                return 1 + f(s1, s2, i + 1, n, first);
            } else {
                return -1;
            }
        }
    }
}

void tTestCase() {
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        string s = "";
        int i = 0;

        while (i < (2 * n) and i >= 0) {
            string t = "0";
            int temp = f(t, s, i, n, true);
            if (temp <= 0)
                break;
            i += temp;
        }
        while (i < (2 * n) and i >= 0) {
            string t = "0";
            int temp = f(s, t, i, n, false);
            if (temp <= 0) {
                break;
            }
            i += temp;
        }
        if (s.size() != n)
            s = s + "1";
        cout << "! " << s << endl;
    }
}

void solve() { tTestCase(); }

int main() { solve(); }

Could someone help me debug this and point out what might be going wrong? I’d appreciate any guidance to fix the recursive approach while keeping the logic consistent with the iterative one.

Thanks in advance!