struct Edge {char vertex1;char vertex2;int weight;Edge(char v1, char v2, int w):vertex1(v1), vertex2(v2), weight(w) {}
};struct Graph {vector<char> vertice;vector<Edge> edges;
};unordered_map<char, char> PARENT;
unordered_map<char, int> RANK;char find(char vertex) {if (PARENT[vertex] == vertex) return PARENT[vertex];elsereturn find(PARENT[vertex]);
}void MST(Graph& g) {vector<Edge> res;for (auto c : g.vertice) {PARENT[c] = c;RANK[c] = 0;}sort(g.edges.begin(), g.edges.end(), [](Edge x, Edge y) {return x.weight < y.weight;});   // O(E*log(E))for (Edge e : g.edges) {         // O(E)char root1 = find(e.vertex1);  // 最差O(E)，因为有记录深度，Find可以认为很快char root2 = find(e.vertex2);if (root1 != root2) {res.push_back(e);if (RANK[root1] > RANK[root2]) {PARENT[root2] = root1;RANK[root1]++;} else {PARENT[root1] = root2;RANK[root2]++;}}}for (Edge e : res) {cout << e.vertex1 << " -- " << e.vertex2 << "  " << e.weight << endl;}
}void Union( char vertex_1, char vertex_2 ) {
}int main() {char t[] = {'a', 'b', 'c', 'd', 'e', 'f'};Graph g;g.vertice = vector<char>(t, t + sizeof(t)/sizeof(t[0]));g.edges.push_back(Edge('a', 'b', 4));  // 稀疏图用链来表示(E = O(V)) g.edges.push_back(Edge('a', 'f', 2));  // 如果是密集图(E = O(V*V)), 用矩阵来表示g.edges.push_back(Edge('f', 'b', 5));  // 大部分感兴趣的图是稀疏的g.edges.push_back(Edge('c', 'b', 6));g.edges.push_back(Edge('c', 'f', 1));g.edges.push_back(Edge('f', 'e', 4));g.edges.push_back(Edge('d', 'e', 2));g.edges.push_back(Edge('d', 'c', 3));MST(g);return 0;
}