detect cycle in undirected graph

/*    Never let anyone dull your sparkle...    */
#include <bits/stdc++.h>
using namespace std;

// type definition
#define int long long
using i64 = int64_t;
typedef pair<int, int> ii;
// constants
constexpr int N = 2e6 + 2;
constexpr int INF = 0x3f3f3f3f;
constexpr int MOD = 1e9 + 7;
constexpr float PI = 3.14;
// possible moves
constexpr int dx[8] = {1, 1, -1, -1, 0, 0, 1, -1};
constexpr int dy[8] = {1, 0, -1, 0, 1, -1, -1, 1};
// shortcuts
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define endl '\n'
#define sz(x) i64(x.size())
#define all(x) begin(x), end(x)
#define rall(x) begin(x), end(x), greater<int>()
// loop definition
#define FOR(i, n, m) for (int i = n; i <= m; ++i)
#define FORD(i, n, m) for (int i = n; i >= m; --i)

int n, m;
std::vector<int> g[N];

bool BFS(int s, vector<bool> &visited) {
    vector<int> parent(n, -1);
    queue<int> q;
    visited[s] = true;
    q.push(s);
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        for (int v : g[u]) {
            if (!visited[v]) {
                visited[v] = true;
                q.push(v);
                parent[v] = u;
            }
            else if (parent[u] != v)
                return true;
        }
    }
    return false;
}

bool isCyclic() {
    vector<bool> visited(n, false);
    FOR(i, 1, n) {
        if (!visited[i] && BFS(i, visited)) {
            return true;
        }
    }
    return false;
}
int32_t main(void) {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    //freopen("main.INP", "r", stdin);
    //freopen("main.OUT", "w", stdout);

    cin >> n >> m;
    while (m--) {
        int x, y; cin >> x >> y;
        g[x].pb(y);
        g[y].pb(x);
    }

    cout << (isCyclic() ? "YES" : "NO");
    return 0;
}