矢量问题 (std::out_of_range）

这是我问题的描述：

该计划的说明：
我正在C++中实现一个程序，该程序测试 Prim 的算法以查找最小生成树。该程序的目标是计算为选定数量的随机图找到最小生成树所需的秒数。

到目前为止，我做了什么？
我完成了整个程序的函数和头文件的实现。由于源代码很小，为了清楚起见，我决定将其粘贴到此邮件中，以便更好地可视化问题。

问题：
出于某种原因，我在应用程序运行时遇到了某种"超出范围"的矢量问题。问题标记在（"Prim_and_Kruskal_Algorithms.cpp"）文件中。

请求帮助：
如果有人能帮助我发现问题，我将不胜感激。我已经用这个问题内联了源代码。

源代码：

（Undirected_Graph.h） 文件：

#ifndef UNDIRECTED_GRAPH_H
#define UNDIRECTED_GRAPH_H
#include <vector>
using std::vector;
#include <climits>
class Edge;
class Node
{
    public:
        Node(int);                 //The constructor.
        int id;                    //For the id of the node.
        bool visited;              //For checking visited nodes.
        int distance;
        vector <Edge*> adj;       //The adjacent nodes.
};
class Edge
{
    public:
        Edge(Node*, Node*, int);   //The constructor.
        Node* start_Node;          //The start_Node start of the edge.
        Node* end_Node;            //The end of the edge.
        int w;                     //The weight of the edge.
        bool isConnected(Node* node1, Node* node2)  //Checks if the nodes are connected.
        {
            return((node1 == this->start_Node && node2 == this->end_Node) ||
                   (node1 == this->end_Node   && node2 == this->start_Node));
        }
};
class Graph
{
    public:
        Graph(int);                    //The Constructor.
        int max_Nodes;                 //Maximum Number of allowed Nodes.
        vector <Edge*> edges_List;     //For storing the edges of the graph.
        vector <Node*> nodes_List;     //For storing the nodes of the graph.
        void insertEdge(int, int, int);
        int getNumNodes();
        int getNumEdges();
};
#endif

（Undirected_Graph.cpp）文件：

#include "Undirected_Graph.h"
Node::Node(int id_Num)
{
    id = id_Num;
    visited = 0;
    distance = INT_MAX;
}
Edge::Edge(Node* a, Node* b, int weight)
{
    start_Node = a;
    end_Node = b;
    w = weight;
}
Graph::Graph(int size)
{
    max_Nodes = size;
    for (int i = 1; i <= max_Nodes; ++i)
    {
        Node* temp = new Node(i);
        nodes_List.push_back(temp);
    }
}
void Graph::insertEdge(int x, int y, int w)
{
    Node* a = nodes_List[x-1];
    Node* b = nodes_List[y-1];
    Edge* edge1 = new Edge(a, b, w);
    Edge* edge2 = new Edge(b, a, w);
    edges_List.push_back(edge1);
    a->adj.push_back(edge1);
    b->adj.push_back(edge2);
}
int Graph::getNumNodes()
{
    return max_Nodes;
}
int Graph::getNumEdges()
{
    return edges_List.size();
}

（Prim_and_Kruskal_Algorithms.h） 文件：

#ifndef PRIM_AND_KRUSKAL_ALGORITHMS_H
#define PRIM_AND_KRUSKAL_ALGORITHMS_H
class PKA
{
    private:
    //inline void generateRandomGraph();
    protected:
    //-No Protected Data Members in this Class.
    public:
        void runAlgorithms();
        void prim();
};
#endif

（Prim_and_Kruskal_Algorithms.cpp） 文件*（问题出在此文件中，标记如下）：*

#include "Prim_and_Kruskal_Algorithms.h"
#include "Undirected_Graph.h"
#include <iostream>
using std::cout;
using std::cin;
using std::endl;
#include <cstdlib>
using std::rand;
using std::srand;
#include <ctime>
using std::time;
//=============================================================================
//============Global Variables and Settings for the program====================
//=============================================================================
const int numIterations = 1; //How many times the Prim function will run.
const int numNodes = 10;     //The number of nodes in each graph.
const int numEdges = 9;      //The number of edges for each graph.
const int sRandWeight = 1;   //The "start" range of the weight of each edge in the graph.
const int eRandWeight = 100; //The "end" range of the weight of each edge in the graph.
//=============================================================================
//=============================================================================
//=============================================================================
void PKA::runAlgorithms()   //Runs the Algorithms
{
        srand( time(0) );
    cout << "------------------------------" << endl;
        //Calling the Functions:
        cout << "nRunning the Prim's Algorithms:nPlease wait till the completion of the execution time" << endl;
        //===============================================
        //Start the clock for Prim's Algorithm:
        clock_t start, finish;
        start = clock();
        for(int iter1 = 1; iter1 <= numIterations; ++iter1)
        {
            prim();
        }
        //Stop the clock for Prim and print the results:
    finish = clock();
        cout << "ntThe execution time of Prim's Algorithm:t" << ((double)(finish - start) / CLOCKS_PER_SEC) << " s";
    return;
}
void PKA::prim()
{
    //=============================================================================
    //=============================Generating A Random Graph=======================
    //=============================================================================
    //Randomizing Values:
    //===============================================
    int randStartNode = rand() % numNodes;     //Generation a random start node.
    int randEndNode = rand() % numNodes;       //Generating a random end node.
    int randWeight;               //Random weight for the edge.
    while(randEndNode == randStartNode)   //Checking if both randomized nodes are equal.
    {
        randEndNode = (rand() % numNodes);
    }
    //===============================================
    Graph myGraph(numNodes);
    for(int i = 0; i < numEdges; ++i)
    {
        //Generating a random weight:
        randWeight =  sRandWeight + rand() % eRandWeight;
        //Inserting a new Edge:
        myGraph.insertEdge(randStartNode, randEndNode, randWeight);
    }

    //=============================================================================
    //=============================================================================
    //=============================================================================
    int currentNode = 0;           //The current Node being under investigation.
    int adjCounter = NULL;         //How many adjacent nodes do we have for the current node.
    int minDistance = NULL;        
    int minIndex = 0;
    myGraph.nodes_List[0]->distance = 0;   //Indicate the start node.
    myGraph.nodes_List[0]->visited = 1;    //The starting node is already considered as a visited node.
    for(int i = 0; i < numNodes - 1; i++)
    {
        //Determine how many adjacent nodes there are for the current node:
        adjCounter = myGraph.nodes_List[currentNode]->adj.size();
        if(adjCounter == 0) //If there are no adjacent nodes to the current node:
        {
            myGraph.nodes_List[currentNode]->adj.at(minIndex)->end_Node->visited = 1;
                    cout << "n*******Not all nodes are connected!*******" << endl;
            continue;
        }
        minDistance = myGraph.nodes_List[currentNode]->adj.at(0)->w;
        minIndex = 0;
        for(int counter = 0; adjCounter > 0; adjCounter--, counter++)
        {
            if(myGraph.nodes_List[currentNode]->adj[counter]->end_Node->visited == false)
            {
                if(myGraph.nodes_List[currentNode]->distance > myGraph.nodes_List[currentNode]->adj[counter]->w)
                {
                    myGraph.nodes_List[currentNode]->distance = myGraph.nodes_List[currentNode]->adj[counter]->w;
                }
                if(minDistance > myGraph.nodes_List[currentNode]->adj[counter]->w)
                {
                    minDistance = myGraph.nodes_List[currentNode]->adj[counter]->w;
                    minIndex = counter;
                }
            }
        }
                //======================================================================================
                //=========================The Problem is in the following two lines====================
        //======================================================================================
        //Mark the current node as visited:
        myGraph.nodes_List[currentNode]->adj.at(minIndex)->end_Node->visited = 1;
        //Switching to the next node that we have just visited:
        currentNode = myGraph.nodes_List[currentNode]->adj.at(minIndex)->start_Node->id;
        //======================================================================================
        //======================================================================================
        //======================================================================================
    }
}

（Client_Code.cpp） 文件：用于测试程序。

#include "Prim_and_Kruskal_Algorithms.h"
#include <iostream>
using std::cout;
using std::endl;
int main()
{
    cout << "nWelcome to the Prim and Kruskal Algorithms Comparison!" << endl;
    cout << "nPlease wait until the completion of the algorithms." << endl;
    PKA myPKA;                //Creating an object of the class.
    myPKA.runAlgorithms();    //Running the Algorithm.
    cout << "nnThe program terminated successfully!" << endl;
    return 0;
}