C++ 实现MST kruskal's algorithm

#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.

	//span
	int 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;
	}
	else
		return 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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C++ 实现MST kruskal's algorithm