普里姆（Prim）算法

/*********************普里姆(Prim)算法******************/
//网类
template<class Type>
class NetGraph
{
private:
    Type vexs[MAX];//顶点表
    int  arc[MAX][MAX];//邻接矩阵
    int numVertexes, numEdges;//当前网中节点、边数量

    int getPosition(Type el);//获取数据el在顶点表中的位置
    Type readType();//外界读取一个数据
public:
    NetGraph();//创建网图
    ~NetGraph(){}//析构函数
    void print();//打印邻接矩阵
    void MiniSpanTree_Prim();//Prim算法生成最小生成树
};
//获取数据el在顶点表中的位置
template<class Type>
int NetGraph<Type>::getPosition(Type el)
{
    int i;
    for (i = 0; i < this->numVertexes; i++)
    {
        if (this->vexs[i] == el)
            return i;
    }
    return -1;
}
//外界读取一个数据
template<class Type>
Type NetGraph<Type>::readType()
{
    Type ch;
    cout << "Input a edge data: ";
    cin >> ch;
    return ch;
}
//创建网图(手动输入)
template<class Type>
NetGraph<Type>::NetGraph()
{
    int i,j;
    Type c1, c2;
    int p1, p2;
    int weight;//用于存储权值
    cout << "Input Vertexes number: ";
    cin >> this->numVertexes;
    cout << "Input Edge number: ";
    cin >> this->numEdges;
    //检测顶点、边输入合法性
    if (this->numVertexes < 1 || this->numEdges<1 || this->numEdges> this->numVertexes*(this->numVertexes - 1))
    {
        cout << "Error input!" << endl;
        return;
    }
    //顶点初始化
    for (i = 0; i < this->numVertexes; i++)
    {
        cout << "Input a Type data" << i + 1 << ": ";
        cin >> this->vexs[i];
    }
    //邻接矩阵初始化
    for (i = 0; i < this->numVertexes; i++)
    {
        for (j = 0; j < this->numVertexes; j++)
        {
            if (i == j)
                this->arc[i][j] = 0;
            else
                this->arc[i][j] = 65535;
        }
    }
    //边初始化
    for (i = 0; i < this->numEdges; i++)
    {
        c1 = readType();
        c2 = readType();

        p1 = getPosition(c1);
        p2 = getPosition(c2);
        if (p1 == -1 || p2 == -1 || p1 == p2)
        {
            cout << "Earror Input!" << endl;
            return;
        }
        cout << "Input a weight value: ";
        cin >> weight;

        this->arc[p1][p2] = weight;
        this->arc[p2][p1] = weight;
    }
}
//打印邻接矩阵
template<class Type>
void NetGraph<Type>::print()
{
    cout << "******************************" << endl;
    cout << "打印邻接矩阵" << endl;
    int i, j;
    for (i = 0; i < this->numVertexes; i++)
    {
        for (j = 0; j < this->numVertexes; j++)
            cout << this->arc[i][j] << '\t';
        cout << endl;
    }
}
//Prim算法生成最小生成树
template<class Type>
void NetGraph<Type>::MiniSpanTree_Prim()
{
    int min, i, j, k;
    int adjvex[MAX];//保存相关顶点下标
    int lowcost[MAX];//保存相关顶点间边的权值

    lowcost[0] = 0;//初始化第一个权值为0，即第一个元素加入生成树
    adjvex[0] = 0;//初始化第一个顶点下表为0

    for (i = 1; i < this->numVertexes; i++)
    {
        lowcost[i] = this->arc[0][i];//将第一个元素与之有关的权值存入数组
        adjvex[i] = 0;//初始化都为第一个元素的下标
    }
    for (i = 0; i < this->numVertexes; i++)
    {
        min = 65535;//初始化最小权值为65535
        j = 1; k = 0;
        while (j < this->numVertexes)
        {
            if (lowcost[j] != 0 && lowcost[j] < min)
            {
                min = lowcost[j];
                k = j;
            }
            j++;
        }
        cout << "(" << adjvex[k] << ", " << k << ") ";
        lowcost[k] = 0;//当前顶点的权值设置为0，表示此顶点已经完成任务
        for (j = 1; j < this->numVertexes; j++)
        {
            if (lowcost[j] != 0 && this->arc[k][j] < lowcost[j])
            {
                lowcost[j] = this->arc[k][j];
                adjvex[j] = k;
            }
        }
    }
}
//测试程序
int main()
{
    NetGraph<char> graph;
    graph.print();
    graph.MiniSpanTree_Prim();
    return 0;
}