图遍历与A*算法

嘿，我是AI学生，我要尝试我的作业是实现A*算法来遍历一个图。我使用c++代码，我现在所做的是下面的代码，这只是一个图形类+ insertedge和顶点函数。但现在我很困惑如何定义成本函数(f= h(n) + g(n))…

也任何代码参考或解释如何A*的工作图将帮助我。我在谷歌上找到的是关于通过a*寻路的，它没有遍历图。

#include <iostream>
using namespace std;
class Graph;
class node {
    friend class Graph;
private:
    char data;
    int cost;
    node *next;
    node *vlist;
    bool goal;
    bool visited;
public:
    node(char d,int c, bool g){
        cost = c;
        goal = g;
        next = NULL;
        data = d;
        vlist = NULL;
        visited = false;
    }
};
class Graph {
private:
    node *Headnodes;
    char n;
public:
    Graph ()
    {
        Headnodes = NULL;
    }
    void InsertVertex(char n, int c, bool g);
    void InsertEdge(char n, char m, int c);
    void PrintVertices();
    void Expand(char n);
};
/////////////////
//  INSERTION  //
/////////////////
void Graph::InsertVertex(char n, int c, bool g){
    node *temp = new node(n,c,g);
    if(Headnodes==NULL)
    {
        Headnodes=temp;
        return;
    }
    node *t=Headnodes;
    while(t->vlist!=NULL)
        t=t->vlist;
    t->vlist=temp;
}
void Graph::InsertEdge(char n, char m, int c){
    int temp_cost = 0;
    if(Headnodes==NULL)
        return;
    node *x=Headnodes;
    while(x!=NULL){
        if(x->data==m)
            temp_cost = (x->cost+c);
        x = x->vlist;
    }
    node *t=Headnodes;
    node *temp=new node(m,temp_cost,false);
    while(t!=NULL){
        if(t->data==n){
            node *s=t;
            while(s->next!=NULL)
                s=s->next;
            s->next=temp;
        }
        t=t->vlist;
    }
}
int min_cost = 1000;
bool enough = false;
void Graph::PrintVertices(){
    node *t=Headnodes;
    while(t!=NULL){
        cout<<t->data<<"t";
        t=t->vlist;
    }
}
void Graph::Expand(char n){
    cout << n << "t";
    char temp_min;
    node *t=Headnodes;
    while(t!=NULL){
        if(t->data==n && t->visited == false){
            t->visited = true;
            if (t->goal)
                return;
            while(t->next!=NULL){
                if (t->next->cost <= min_cost){
                    min_cost=t->next->cost;
                    temp_min = t->next->data;
                }
                t = t->next;
            }
        }
        t=t->vlist;
    }
    Expand(temp_min);
}
int main(){
    Graph g;
    g.InsertVertex('A',5,false);
    g.InsertVertex('B',1,false);
    g.InsertVertex('C',9,false);
    g.InsertVertex('D',5,false);
    g.InsertVertex('E',1,false);
    g.InsertVertex('F',3,false);
    g.InsertVertex('G',2,false);
    g.InsertVertex('J',1,false);
    g.InsertVertex('K',0,true);
    g.InsertEdge('A','B',2);
    g.InsertEdge('A','C',1);
    g.InsertEdge('B','A',2);
    g.InsertEdge('B','D',1);
    g.InsertEdge('B','E',1);
    g.InsertEdge('C','A',1);
    g.InsertEdge('C','F',1);
    g.InsertEdge('C','G',1);
    g.InsertEdge('E','J',3);
    g.InsertEdge('E','K',3);
    g.PrintVertices();
    cout<<"nn";
    g.Expand('A');
    return 0;
}