3-Coloring

#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

string to_string(string s) {
    return '"' + s + '"';
}
 
string to_string(const char* s) {
    return to_string((string) s);
}
 
string to_string(bool b) {
    return (b ? "true" : "false");
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}
 
void debug_out() {
    cerr << endl;
}
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
 
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

const int N = 1e5 + 5;

int n, e[N];
vector<int> adj[N];
int col[N];

void dfs(int u, int c) {
    col[u] = c;
    for (int v : adj[u]) {
        if (col[v]) continue;
        dfs(v, 3 - c);
    }
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit); // RTE if input wrong datatype

    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> e[i];
        adj[e[i]].push_back(i);
        adj[i].push_back(e[i]);
    }

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

    for (int i = 1; i <= n; i++) {
        bool found = false;
        for (int v : adj[i]) {
            if (col[v] == col[i]) {
                found = true;
                break;
            }
        }
        if (found) {
            col[i] = 3;
        }
    }

    // for (int i = 1; i <= n; i++) {
    //     for (int v : adj[i]) {
    //         assert(col[i] != col[v]);
    //     }
    // }

    for (int i = 1; i <= n; i++) {
        cout << col[i] << ' ';
    }
}

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