Split in Three

#include <bits/stdc++.h>
 
using namespace std;
 
#define int long long
#define endl '\n'
#define maxn 200010
const int MOD = 1000000007;
 
void solve() {
    int n;
    cin >> n;
 
    // x - 1
    // x
    // x + 1
 
    // 3 * x = n * (n + 1) // 2
 
    // n * (n + 1) // 6
 
    int tp = n * (n + 1);
    if (tp % 6) {
        cout << "IMPOSSIBLE";
        return;
    }
    vector<int> v1, v2;
    int sum = 0, val = tp / 6 - 1;
    for (int i = 1; i <= n; i++) {
        if (sum + i <= val)sum += i, v1.push_back(i);
        else {
            int need = val - sum;
            int back = (!v1.empty() ? v1.back() : 0);
 
            back += need;
            if (back <= n) {
                if (!v1.empty())
                    v1.pop_back();
                v1.push_back(back);
                break;
            } else {
                cout << "IMPOSSIBLE";
                return;
            }
        }
    }
    val++;
    sum = 0;
    for (int i = 1; i <= n; i++) {
        if (binary_search(v1.begin(), v1.end(), i))continue;
        if (sum + i <= val)sum += i, v2.push_back(i);
        else {
            int need = val - sum;
            int back = (!v2.empty() ? v2.back() : 0);
 
            back += need;
            if (back <= n and !binary_search(v1.begin(), v1.end(), back)) {
                if (!v2.empty())
                    v2.pop_back();
                v2.push_back(back);
                break;
            } else {
                cout << "IMPOSSIBLE";
                return;
            }
        }
    }
    for (int i = 1; i <= n; i++) {
        if (binary_search(v1.begin(), v1.end(), i))cout << 1 << " ";
        else if (binary_search(v2.begin(), v2.end(), i))cout << 2 << " ";
        else cout << 3 << " ";
    }
}
 
int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
 
    int t = 1;
//    cin >> t;
 
    while (t--)
        solve();
    return 0;
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

Test 4

Group: 1, 2

Verdict: WRONG ANSWER

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

Test 7

Group: 1, 2

Verdict: ACCEPTED

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: ACCEPTED

Test 10

Group: 2

Verdict: WRONG ANSWER

Test 11

Group: 2

Verdict: WRONG ANSWER

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: WRONG ANSWER

Test 14

Group: 2

Verdict: WRONG ANSWER

Test 15

Group: 2

Verdict: ACCEPTED