is_tree.cpp

#include <iostream>
#include <stack>
#include <unordered_map>
#include <vector>
using namespace std;

int dfs(const vector<vector<int>> &g) {
  int connected = 1;
  vector<bool> visited(g.size(), 0);
  stack<int> q;
  q.push(0);
  visited[0] = true;
  while (!q.empty()) {
    int t = q.top();
    q.pop();

    for (auto c : g[t]) {
      if (!visited[c]) {
        q.push(c);
        visited[c] = true;
        ++connected;
      }
    }
  }

  return connected;
}

int main() {
  int n, m;
  cin >> n >> m;
  if (m == n - 1) {
    vector<vector<int>> g(n, vector<int>());
    for (int i = 0; i < m; ++i) {
      int v1, v2;
      cin >> v1 >> v2;

      // for undirected graph
      g[v1 - 1].push_back(v2 - 1);
      g[v2 - 1].push_back(v1 - 1);
    }
    (dfs(g) == n) ? cout << "YES\n" : cout << "NO\n";
  } else {
    cout << "NO\n";
  }
  return 0;
}