Split in Three

///By Stephan Ramirez [email protected]
#include<bits/stdc++.h>
#define ms(a,v) memset(a,v,sizeof a)
#define ll long long
using namespace std;
int vis[200];
int n;
int sm;
int a,b,c;
int dp[102][10100];
int can(int pos, int num){
	if(num==0)
		return 1;
	if(num<0)
		return 0;
	if(pos==0)
		return 0;
	int &ans=dp[pos][num];
	if(ans!=-1)
		return ans;
	
	ans=can(pos-1,num) ;
	if(vis[pos]==-1)
		ans|= can(pos-1,num-pos);
	return ans;
}
vector<int> aux;
void backtrack(int pos,int num){
	if(num==0)
		return ;
	if(num<0)
		return ;
	if(pos==0)
		return ;
	if(can(pos-1,num)==1){
		backtrack(pos-1,num);
		return;
	}	
	aux.push_back(pos);
	backtrack(pos-1,num-pos);
}
int main(){
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	#ifdef LOCAL
		freopen("in.txt","r",stdin);
		//freopen("out.txt","w",stdout)	;
	#endif
	cin>>n;
	sm=((n+1)*n)/2;
	if(sm%3!=0){
		cout<<"IMPOSSIBLE\n";
		return 0;
	}
	b=sm/3;
	a=b-1;
	c=b+1;
	int s[3]={b,a,c};
	int id[3]={2,1,3};
	ms(vis,-1);
	for(int i=0;i<3;i++){

		ms(dp,-1);
		if(can(n,s[i])==0){
			cout<<"IMPOSSIBLE\n";
			return 0;
		}
		aux.clear();
		backtrack(n,s[i]);
		for(int j: aux){
			vis[j]=id[i];
		}
	}
	for(int i=1;i<=n;i++)
		cout<<vis[i]<<" ";
	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: 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