Split in Three

input/code.cpp: In function 'bool solve(long long int, long long int)':
input/code.cpp:43:24: warning: suggest parentheses around assignment used as truth value [-Wparentheses]
   return dp[ind][asum] = solve(ind+1, asum);
          ~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~
input/code.cpp:55:24: warning: suggest parentheses around assignment used as truth value [-Wparentheses]
   return dp[ind][asum] = ans;
          ~~~~~~~~~~~~~~^~~~~
input/code.cpp: In function 'void usaco()':
input/code.cpp:15:9: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  freopen("problem.in", "r", stdin);
  ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
input/code.cpp:16:9: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  freopen("problem.out", "w", stdout);
  ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~

#include <bits/stdc++.h>
using namespace std;
void fast() {
	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
}
void ran() {
	srand(chrono::steady_clock::now().time_since_epoch().count());
}
long long get_rand() {
	long long a = rand();
	long long b = rand();
	return a * (RAND_MAX + 1ll) + b;
}
void usaco() {
	freopen("problem.in", "r", stdin); 
	freopen("problem.out", "w", stdout);
}
template<typename T>
using min_pq = priority_queue<T, vector<T>, greater<T>>;
// #define endl '\n'
// #define double long double
#define int long long
// const int MOD = 1000 * 1000 * 1000 + 7;
// const int MOD = 998244353;

const int MXN = 105, MXS = 10005;
int n;
int par[MXN][MXS]; // 0 for no change asum, 1 for change in asum
int assign[MXN];
int dp[MXN][MXS];
int s;

bool solve(int ind, int asum) {
	if (ind == n + 1) {
		if (asum == s/3 - 1) {
			return true;
		}
		return false;
	}
	if (dp[ind][asum] != -1) return dp[ind][asum];
	if (assign[ind] != -1) {
		par[ind][asum] = 0;
		return dp[ind][asum] = solve(ind+1, asum);
	}
	else {
		bool ans = false;
		if (solve(ind+1, asum+ind)) {
			ans = true;
			par[ind][asum] = 1;
		}
		if (solve(ind+1, asum)) {
			ans = true;
			par[ind][asum] = 0;
		}
		return dp[ind][asum] = ans;
	}
}

signed main() {
	
	for (int i=0; i<MXN; i++) {
		for (int j=0; j<MXS; j++) {
			dp[i][j] = -1;
			par[i][j] = -1;
		}
	}

	ran(); fast();

	cin >> n;
	
	s = n * (n+1) / 2;
	
	if (s % 3 == 0) {
		
		memset(assign, -1, sizeof assign);
		
		int L = s / 3;
		for (int i=n; i>=1; i--) {
			if (L >= i) {
				L -= i;
				assign[i] = 2;
			}
		}
		
		solve(1, 0);
		
		int as = 0;
		for (int curr=1; curr<=n; curr++) {
			if (assign[curr] == 2) {
				//
				
			}
			else {
				if (par[curr][as] == 1) {
					as += curr;
					assign[curr] = 1;
				}
				else {
					assign[curr] = 3;
				}
			}
		}
		
		for (int i=1; i<=n; i++) {
			cout << assign[i] << ' ';
		}
		cout << endl;
		
	}
	else {
		cout << "IMPOSSIBLE" << endl;
	}

}

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: ACCEPTED

Test 10

Group: 2

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: ACCEPTED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

Test 14

Group: 2

Verdict: ACCEPTED

Test 15

Group: 2

Verdict: ACCEPTED