class Solution {
 public:
  int makeConnected(int n, vector<vector<int>>& connections) {
    // to connect n nodes, we need at least n - 1 edges
    if (connections.size() < n - 1)
      return -1;

    int numOfConnected = 0;
    vector<vector<int>> graph(n);
    unordered_set<int> seen;

    for (const auto& conn : connections) {
      graph[conn[0]].push_back(conn[1]);
      graph[conn[1]].push_back(conn[0]);
    }

    for (int i = 0; i < n; ++i)
      if (seen.insert(i).second) {
        dfs(graph, i, seen);
        ++numOfConnected;
      }

    return numOfConnected - 1;
  }

 private:
  void dfs(const vector<vector<int>>& graph, int u, unordered_set<int>& seen) {
    for (const int v : graph[u])
      if (seen.insert(v).second)
        dfs(graph, v, seen);
  }
};