Kolmijako

#include <iostream>
#include <vector>
 
using namespace std;
 
vector<int> a;
vector<int> b;
vector<int> c;
int sumA;
int sumB;
int sumC;
 
int ans[101];
 
int n;
bool found = false;
 
void search(int i) {
  if (i > n) {
    // check
    if (sumA == sumB-1 && sumB == sumC-1) {
      found = true;
    }
 
    return;
  }
 
  a.push_back(i);
  sumA += i;
  search(i+1);
  if (found) return;
  sumA -= i;
  a.pop_back();
 
  b.push_back(i);
  sumB += i;
  search(i+1);
  if (found) return;
  sumB -= i;
  b.pop_back();
 
  c.push_back(i);
  sumC += i;
  search(i+1);
  if (found) return;
  sumC -= i;
  c.pop_back();
}
 
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  
  cin>>n;
 
  search(1);
 
  if (!found) {
    cout << "IMPOSSIBLE";
  } else {
    for (int i : a) {
      ans[i] = 1;
    }
    for (int i : b) {
      ans[i] = 2;
    }
    for (int i : c) {
      ans[i] = 3;
    }
 
    for (int i = 1; i <= n; i++) cout << ans[i] << " ";
  }
}

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: ACCEPTED

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: TIME LIMIT EXCEEDED

Test 10

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 11

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 12

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 13

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 2

Verdict: TIME LIMIT EXCEEDED