[Algorithm] Prim's Algorithm의 시간 복잡도에 관한 질문

void Graph::prim() const {
    // assume that G has at least one vertex.
    const int n = _vertices.count();
    Graph tree(n);
 
 
 
    Array<bool> visited(n);
    for (int i = 0; i < n; ++i) {
        visited[i] = false;
    }
    visited[0] = true;
 
 
 
    int edge_count = 0;
    for (int i = 0; edge_count < n - 1; ++i) {
        int min_cost = INT_MAX;
        int src = -1, dst = -1;
 
        for (int j = 0; j < n; ++j) {
            if (visited[j] == false)
                continue;
 
            const Vertex &vertex = _vertices[j];
            const std::vector<Edge> &adjList = vertex.adjacencyList();
            for (int k = 0, adjCount = adjList.size(); k < adjCount; ++k) {
                const Edge &edge = adjList[k];
                // check src/dst included
                if (visited[edge.destination()])
                    continue;
                // check cost is minimum
                else if (min_cost > edge.cost()) {
                    src = edge.source();
                    dst = edge.destination();
                    min_cost = edge.cost();
                }
            }
        }
        if (src < 0)
            break; // there's no such edge
 
        tree.link(src, dst, min_cost);
        visited[dst] = true;
        ++edge_count;
    }
    if (edge_count != n - 1) {
        std::cout << "no spanning tree" << std::endl;
        return;
    }
 
    tree.setAction(show_visited_vertex);
    tree.dfs(0);
    tree.setAction(nullptr);
}