c++ - 使用带两个链表的邻接表的深度优先搜索 C++ 实现

Question

我是一名大学生，这是我第一次在这里提问。首先感谢您抽出时间阅读。我们有一个关于图形的项目。到目前为止，我通过 matrix 和 adjacency list 创建了图形。我的邻接列表版本由 2 个链表组成(只是为了允许添加尽可能多的顶点)。现在我正在尝试进行 Depth First Search 。我做了一些研究，认真地我不太了解，所以我按照自己的想法行事，但我不确定它是否正确，或者复杂性是否为 O(V+E) v 指的是顶点，E 指的是edges.. 任何人都可以阅读它并告诉我它是否正确？如果是，那么复杂度 O(V+E) 是多少？PS:请只使用 c++，因为它是我唯一知道的语言。非常感谢您的帮助

我在DFS做的是

1-执行遍历所有顶点并在每个顶点上调用 DFS 的 while 循环2- 在每个顶点上，调用 DFS，顶点的颜色将为灰色 ('g')3-另一个遍历目标顶点(边)子节点的 while 循环4-在每个 children 上，另一个 while 循环将通过 search-> value == child->value
搜索相应的边5-当它找到顶点时它会再次调用 DFS(所以重复步骤 2 到 5)6-完成后，一个接一个地给顶点涂上黑色

代码如下:

边缘节点.h

class EdgeNode
{
public:
    int value;
    EdgeNode *Next;
};

顶点节点.h

#include "EdgeNode.h"
class VertexNode
{
public:
    int value;
    int parentIndex;
    char color;
    EdgeNode *Child;
    VertexNode *Next;
};

图.h

#include "VertexNode.h"

class Graph{
public:

    int NbVertex;
    int time;
    VertexNode *s;
    Graph();
    void AddVertex(int value);
    bool AddEdge(int parentIndex, int value);
    void PrintVertex();
    void PrintGraph();
    void DepthFirstSearch();
    void DFS(VertexNode *V);


};

图表.cpp

#include <iostream>
#include "Graph.h"
#include <string>
using namespace std;


Graph::Graph()
{
    s = NULL;
    NbVertex = 0;
}

void Graph::AddVertex(int value)
{
    if (NbVertex == 0)
    {
        s = new VertexNode;
        s->value = value;
        s->parentIndex = NbVertex+1;
        s->color = 'w';
        s->Child = NULL;
        s->Next = NULL;
    }

    else
    {
        VertexNode *z = s;
        while (z->Next != NULL)
        {
            z = z->Next;
        }
        z->Next = new VertexNode;
        z->Next->parentIndex = NbVertex+1;
        z->Next->color = 'w';
        z->Next->value = value;
        z->Next->Child = NULL;
        z->Next->Next = NULL;
    }


    NbVertex++;
}


bool Graph::AddEdge(int parentIndex, int value)
{
    if (NbVertex == 0)
        cout << "Graph is empty" << endl;

    VertexNode *z = s;

        while (z != NULL)
        {
            if (z->parentIndex == parentIndex)
            {


                if (z->Child == NULL)
                {
                    EdgeNode *y = new EdgeNode;
                    y->value = value;
                    y->Next = NULL;
                    z->Child = y;

                }

                else
                {
                    EdgeNode *y = z->Child;
                    while (y->Next != NULL)
                    {
                        if (y->value == value)
                        {
                            cout << "The edge already exists"<<endl;
                            return false;
                        }

                        y = y->Next;
                    }
                    y->Next = new EdgeNode;
                    y->Next->value = value;
                    y->Next->Next = NULL;

                }

                return true;

            }

            z = z->Next;

        }

        cout << "The index was not found" << endl;
    return false;

}


void Graph :: PrintVertex()
{
    VertexNode *z = s;
    int count = 1;
    while (z != NULL)
    {
        cout << "vertex " << count << " : " << endl;
        cout << "Value : " << z->value << endl;
        cout << "Index : " << z->parentIndex << endl;
        cout << "Next : " << z->Next << endl;
        cout << "Child : " << z->Child << endl;
        cout << "Color : "  << z->color << endl;
        cout << endl;
        count++;
        z = z->Next;
    }

    cout << "time is : " << time;
}


void Graph::PrintGraph()
{
    VertexNode *z = s;
    int countVertex = 1;
    while (z != NULL)
    {
        cout << "vertex " << countVertex << " : " << endl;
        cout << "Value : " << z->value << endl;
        cout << "Index : " << z->parentIndex << endl;
        cout << "Next : " << z->Next << endl;
        cout << "Child : " << z->Child << endl;
        cout << endl;
        countVertex++;
        if (z->Child != NULL)
        {
            int countChild=1;
            EdgeNode *y = z->Child;
            while (y != NULL)
            {
                cout << "Child " << countChild << " : " << endl;
                cout << "Value : " << y->value << endl;
                cout <<"Next : " << y->Next << endl;
                cout << "-------------------"<<endl;
                countChild++;
                y = y->Next;
            }

        }

        cout << "*************************************"<<endl;

        z = z->Next;
    }
}



void Graph :: DepthFirstSearch()
{
    time = 0;
    VertexNode *z = s;
    while (z != NULL)
    {
        if (z->color == 'w')
        {
            DFS(z);
        }
        z = z->Next;
    }

}
void Graph::DFS(VertexNode *V)
{
    cout << "(" << V->value;
    V->color = 'g';
    time++;

    EdgeNode *Y = V->Child;
    while (Y != NULL)
    {
        VertexNode *Search = s;
        while (Search != NULL)
        {
            if (Search->value == Y->value)
            {
                if (Search->color == 'w')
                {
                    DFS(Search);
                }
                /*else
                {
                    Search->color = 'b';
                }*/
            }

            Search = Search->Next;

        }

        Y = Y->Next;
    }

    V->color = 'b';
    time++;
    cout << V->value << ")";
}

这是DFS

void Graph :: DepthFirstSearch()
{
    time = 0;
    VertexNode *z = s;
    while (z != NULL)
    {
        if (z->color == 'w')
        {
            DFS(z);
        }
        z = z->Next;
    }

}
void Graph::DFS(VertexNode *V)
{
    cout << "(" << V->value;
    V->color = 'g';
    time++;

    EdgeNode *Y = V->Child;
    while (Y != NULL)
    {
        VertexNode *Search = s;
        while (Search != NULL)
        {
            if (Search->value == Y->value)
            {
                if (Search->color == 'w')
                {
                    DFS(Search);
                }
                /*else
                {
                    Search->color = 'b';
                }*/
            }

            Search = Search->Next;

        }

        Y = Y->Next;
    }

    V->color = 'b';
    time++;
    cout << V->value << ")";
}

Answer 1

我不知道你的项目应该如何组织，但是用邻接表构建的图的代码大约需要 10 行。

快速查看一下，您的 DFS 似乎是正确的。理论上，DFS(或 BFS)时间是 O(V + E)，因为它会通过所有顶点和所有边(总计 O(|V| + |E|)。

如果您关心代码阅读和组织，请继续，但如果您更喜欢更少的代码，我相信您可以找到更小的图形实现。

有一个 5 行的 DFS 实现可以正常工作。

void DFS(graph G, int v){
    mark[v] = true;
    cout<<"Visiting "<<v<<endl;
    for(auto u : G[v]) //this means "for all u in the adjacence list of v"
        if(!mark[u]) DFS(G, u);
}