3-Coloring

#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define pb push_back
#define VI vector<int>
#define AR(x) array<int, x>
#define MX vector<VI >
#define all(x) x.begin(), x.end()
#define IOS cin.tie(0)->sync_with_stdio(0)

using namespace std;

int main(){

    int n;
    cin >> n;

    VI e(n+1);
    MX g(n+1);
    for(int i=1; i<=n; i++){
        cin >> e[i];
        g[e[i]].pb(i);
        g[i].pb(e[i]);
    }

    VI ans(n+1);
    auto dfs = [&](auto &&dfs, int i) -> void {
        bool t = 0;
        for(int j : g[i]){
            if(ans[j] == ans[i]){
                t = 1;
            } else {
                if(!ans[j]){
                    ans[j] = ans[i]^3;
                    dfs(dfs, j);
                }
            }
        }
        if(t) ans[i] = 3;
    };

    for(int i=1; i<=n; i++){
        if(!ans[i]){
            ans[i] = 1;
            dfs(dfs, i);
        }
    }

    for(int i=1; i<=n; i++) cout << ans[i] << ' ';

    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED