C++ 实现MST kruskal's algorithm

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#include<iostream>#include<vector>#include<list>#include<iomanip>#include<algorithm>using namespace std;enum{ INF = INT_MAX };struct Edge{int from;int to;int Wgt;Edge(int _from, int _to, int _Wgt = INF) :from(_from), to(_to), Wgt(_Wgt) {}bool operator <(const Edge & rhs) const {return Wgt < rhs.Wgt;}};int root(vector<int> & Fr, int vrt) {while (Fr[vrt] != -1) {vrt = Fr[vrt];}return vrt;}bool Kruskal(vector<vector<int> > & G, vector<int> & Fr) {//init forest.vector<int>(G.size(), -1).swap(Fr);//build Edge list;list<Edge> EL;for (int i = 0; i < G.size(); ++i) {for (int j = 0; j < G.size(); ++j) {if (G[i][j] != INF && G[i][j] != 0)EL.push_back(Edge(i, j, G[i][j]));}}EL.sort();//ascending order.//spanint Ecnt = 0;while (Ecnt < G.size() - 1 && !EL.empty()) {//extract edge.Edge e(EL.front());EL.pop_front();if (root(Fr, e.from) != root(Fr, e.to)) {++Ecnt;//append edge.Fr[e.to] = e.from;//merge tree.}}if (Ecnt < G.size() - 1) {cout << "Not connected graph." << endl;return false;}elsereturn true;}int main(void) {cout << "Kruskal algorithm." << endl;int n, m;while (cin >> n >> m) {vector<vector<int> > G(n, vector<int>(n, INF));for (int i = 0; i < n; ++i) G[i][i] = 0;//input edges.for (int i = 0; i < m; ++i) {int s, t;cin >> s >> t;cin >> G[s][t];}//display matrix.cout << "Adj: " << endl;for (int i = 0; i < G.size(); ++i) {for (int j = 0; j < G.size(); ++j) {cout << " " << setw(3) << G[i][j];}cout << endl;}cout << endl;vector<int> Fr;if (Kruskal(G, Fr)) {cout << "Parenthoods of the spanning tree:" << endl;for (int i = 0; i < Fr.size(); ++i) {cout << "Vertex: " << i << "   Parent: " << Fr[i] << endl;}}}system("pause");return 0;}

很直观的算法,关键在于森林的构造.

输入样例:

8 32
0 1 10
1 0 10
0 3 10
3 0 10
0 5 14
5 0 14
0 7 11
7 0 11
1 2 10
2 1 10
1 4 7
4 1 7
1 6 7
6 1 7
2 3 11
3 2 11
2 5 9
5 2 9
2 7 8
7 2 8
3 4 12
4 3 12
3 6 15
6 3 15
4 5 13
5 4 13
4 7 16
7 4 16
5 6 13
6 5 13
6 7 12
7 6 12

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