图相关算法：最小生成树

• P算法（基于点）

• #include<iostream>
  #include<vector>
  #include<limits>
  using namespace std;
  
  int MiniSpanTree_Prim(int numVex, vector<vector<int>>arc)
  {
  	int sum = 0;
  	vector<int>adjvex(numVex);
  	vector<int>lower(numVex);
  	adjvex[0] = 0;
  	lower[0] = 0;
  	for (int i = 1; i < numVex; i++)
  	{
  		lower[i] = arc[0][i];
  	}
  	for (int i = 1; i < numVex; i++)
  	{
  		int Min = INT_MAX;
  		int j = 1;
  		int k = 0;
  		while (j < numVex)
  		{
  			if (lower[j] && lower[j] < Min)
  			{
  				Min = lower[j];
  				k = j;
  			}
  			j++;
  		}
  		sum += Min;
  		cout << adjvex[k] << " " << k << endl;
  		lower[k] = 0;
  		for (j = 0; j < numVex; j++)
  		{
  			if (lower[j] && arc[k][j] < lower[j])
  			{
  				lower[j] = arc[k][j];
  				adjvex[j] = k;
  			}
  		}
  	}
  	return sum;
  }
  int main()
  {
  	int numVex, numEdge;
  	//创建图
  	cout << "请输入图中的点数和边数：" << endl;
  	cin >> numVex >> numEdge;
  	/*cout << "请输入点的信息：" << endl;
  	vector<char>Vexs(numVex);
  	for (int i = 0; i < numVex; i++)
  	{
  		cin >> Vexs[i];
  	}*/
  	vector<vector<int>>arc(numVex, vector<int>(numVex, INT_MAX));
  	cout << "请输入边的信息(两个端点，权值）：" << endl;
  	for (int i = 0; i < numEdge; i++)
  	{
  		int e1, e2, weight;
  		cin >> e1 >> e2 >> weight;
  		//无向图
  		arc[e1][e2] = weight;
  		arc[e2][e1] = weight;
  	}
  
  	//最小生成树
  	cout << "组成最小生成树的边有：" << endl;
  	int Min = MiniSpanTree_Prim(numVex, arc);
  	cout << "最小生成树的权值为：" << endl;
  	cout << Min << endl;
  	return 0;
  }

• K算法 （基于边）

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
struct Edge
{
	int begin;
	int end;
	int weight;
};
bool Mycom(Edge e1, Edge e2)
{
	return e1.weight < e2.weight;
}
int find(int i, vector<int>parent)
{
	while (parent[i] > 0)
	{
		i = parent[i];
	}
	return i;
}
int MiniSpanTree_K(vector<Edge>& edge, int numVex)
{
	int sum = 0;
	vector<int>parent(numVex);
	for (int i = 0; i < edge.size(); i++)
	{
		int n = find(edge[i].begin, parent);
		int m = find(edge[i].end, parent);
		if (n != m)
		{
			parent[n] = m;
			cout << edge[i].begin << " " << edge[i].end << endl;
			sum += edge[i].weight;
		}
	}
	return sum;
}
int main()
{
	int numVex, numEdge;
	cout << "请输入图中的点数和边数：" << endl;
	cin >> numVex >> numEdge;
	vector<Edge>edge(numEdge);
	cout << "请输入边的信息：" << endl;
	for (int i = 0; i < numEdge; i++)
	{
		cin >> edge[i].begin >> edge[i].end >> edge[i].weight;
	}
	sort(edge.begin(), edge.end(), Mycom);
	//最小生成树 - K算法
	cout << "组成最小生成树的边有：" << endl;
	int ret = MiniSpanTree_K(edge, numVex);
	cout << "最小生成树的权值为：" << endl;
	cout << ret << endl;

	return 0;
}