Enumeration

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

#define rep(i, a, b) for(int i = a; i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

bool check(int n, int x) {
    int s = 0;
    for (int i = n - 1; i >= 0; i--) {
        if (x >> i & 1) {
            s--;
        } else {
            s++;
        }
        if (s < 0) {
            return false;
        }
    }
    return s == 0;
}

int flip(int val, int x, int y) {
    assert(x != y);
    val ^= (1 << x);
    val ^= (1 << y);
    return val;
}

const int N = 20;

int n;
bool vis[1 << N];

int main() {
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit);
    cin >> n;
    cout << string(n / 2, '(') << string(n / 2, ')') << '\n';
    vis[(1 << (n / 2)) - 1] = true;
    int cur = (1 << (n / 2)) - 1;
    while (true) {
        bool f = true;
        for (int i = 0; i < n - 1; i++) {
            int v = flip(cur, i, i + 1);
            if (check(n, v) && !vis[v]) {
                vis[v] = true;
                cout << i + 1 << ' ' << i + 2 << '\n';
                cur = v;
                f = false;
                break;
            }
        }
        if (f) {
            break;
        }
    }
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: WRONG ANSWER

Test 6

Verdict: WRONG ANSWER

Test 7

Verdict: WRONG ANSWER

Test 8

Verdict: WRONG ANSWER

Test 9

Verdict: WRONG ANSWER

Test 10

Verdict: WRONG ANSWER