图的创建和遍历(BFS/DFS)

     图的表示方法主要有邻接矩阵和邻接表。其中邻接表最为常用，因此这里便以邻接表为例介绍一下图的创建及遍历方法。

     创建图用到的结构有两种：顶点及弧

struct ArcNode
    {
        int vertexIndex;        //该弧指向的顶点位置
        struct ArcNode* next;    //指向下一个弧
        InfoType info;            //该弧的相关信息，如权重等
    };

    struct Vertex
    {
        VertexType data;    //顶点信息
        ArcNode* firstArc;    //指向第一条依附该节点弧的指针
        ColorType color;    //访问情况
    };

　　其中ColorType是一个枚举，遍历的时候才会用到。图的创建比较简单，直接看代码很容易理解，这里不再详细说了。 图的深度和广度遍历直接看算法导论中的两张图就明白了 ：

//结点颜色代表遍历情况
enum ColorType
{
    WHITE,    //未访问
    GRAY,    //正在访问，邻接点还没访问完
    BLACK    //访问完毕
};

代码:

#include <queue>
#include <stack>
#include <iostream>
using namespace std;


enum GraphType
{    
    UNDIR_UNWEIGHT_GRAPH,        //无向无权图
    UNDIR_WEIGHT_GRAPH,            //无向带权图
    DIR_UNWEIGHT_GRAPH,            //有向无权图
    DIR_WEIGHT_GRAPH            //有向带权图    
};

//结点颜色代表遍历情况
enum ColorType
{
    WHITE,    //未访问
    GRAY,    //正在访问，邻接点还没访问完
    BLACK    //访问完毕
};

template<typename VertexType,typename InfoType>
class Graph
{
public:
    Graph(int vertexNum, GraphType type) :m_vertexNum(vertexNum), m_type(type), m_arcNum(0)
    {
        for (int i = 0; i < MAX_VERTEX_NUM; ++i)
        {
            m_vertices[i].firstArc = nullptr;
        }
    }

    void Create()
    {
        switch (m_type)
        {
        case UNDIR_UNWEIGHT_GRAPH:
            CreateUndirUnweightGraph();
            break;
        case UNDIR_WEIGHT_GRAPH:
            CreateUndirWeightGraph();
            break;
        case DIR_UNWEIGHT_GRAPH:
            CreateDirUnweightGraph();
            break;
        case DIR_WEIGHT_GRAPH:
            CreateDirWeightGraph();
            break;
        default:
            break;
        }
    }

    //输出图的信息
    void Display()
    {
        for (int i = 0; i < m_vertexNum; ++i)
        {
            cout << "第" << i + 1 << "个结点为" << m_vertices[i].data << " 邻接表为：";
            ArcNode* node = m_vertices[i].firstArc;
            while (node)
            {
                cout << "->" << m_vertices[node->vertexIndex].data << "(" << node->info << ")";
                node = node->next;
            }
            cout << endl;
        }
    }

    void BFS()
    {
        for (int i = 0; i < m_vertexNum; ++i)
        {
            m_vertices[i].color = WHITE;
        }
        cout << "图的广度优先遍历为：";
        BFS(&m_vertices[0]);
        cout << endl;
    }

    void DFS()
    {
        for (int i = 0; i < m_vertexNum; ++i)
        {
            m_vertices[i].color = WHITE;
        }
        cout << "图的深度优先遍历为：";
        DFS(&m_vertices[0]);
        cout << endl;
    }
private:
    struct ArcNode
    {
        int vertexIndex;        //该弧指向的顶点位置
        struct ArcNode* next;    //指向下一个弧
        InfoType info;            //该弧的相关信息，如权重等
    };

    struct Vertex
    {
        VertexType data;    //顶点信息
        ArcNode* firstArc;    //指向第一条依附该节点弧的指针
        ColorType color;    //访问情况
    };

    //最大顶点数
    static const int MAX_VERTEX_NUM = 20;
    Vertex m_vertices[MAX_VERTEX_NUM];    //顶点列表
    int m_vertexNum;    //当前顶点数量
    int m_arcNum;        //当前弧数量
    GraphType m_type;    //图类型：有向无权图、有向带权图、无向无权图、无向无权图
private:
    //初始化顶点列表
    void InitVertices()
    {
        cout << "请输入每个顶点的关键字" << endl;
        VertexType data;
        for (int i = 0; i < m_vertexNum; ++i)
        {
            cin >> data;
            m_vertices[i].data = data;
        }
    }
    //插入一个表结点
    void Insert(int headVertex, int tailVertex, InfoType info)
    {
        //构造一个邻接表结点，即创建一条弧
        ArcNode* newNode = new ArcNode;
        newNode->info = info;
        newNode->next = nullptr;
        newNode->vertexIndex = tailVertex;

        //找到邻接表的最后一个节点
        ArcNode* lastNode = m_vertices[headVertex].firstArc;
        if (lastNode == nullptr)
            m_vertices[headVertex].firstArc = newNode;
        else
        {
            while (lastNode->next)
            {
                lastNode = lastNode->next;
            }
            lastNode->next = newNode;
        }
        ++m_arcNum;
    }

    //创建无向无权图
    void CreateUndirUnweightGraph()
    {
        InitVertices();
        cout << "请分别输入每条边的起始结点:" << endl;
        int head, tail;
        while (cin >> head >> tail)
        {
            //无向图head->tail tail->head插入两次
            Insert(head, tail, 0);
            Insert(tail, head, 0);
        }
    }
    //创建无向有权图
    void CreateUndirWeightGraph()
    {
        InitVertices();
        cout << "请分别输入每条边的起始结点和权值:" << endl;
        int head, tail;
        InfoType weight;
        while (cin >> head >> tail >> weight)
        {
            Insert(head, tail, weight);
            Insert(tail, head, weight);
        }
    }
    //创建有向无权图
    void CreateDirUnweightGraph()
    {
        InitVertices();
        cout << "请分别输入每条边的起始结点值:" << endl;
        int head, tail;
        while (cin >> head >> tail)
        {
            Insert(head, tail,0);
        }
    }
    //创建有向带权图 
    void CreateDirWeightGraph()
    {
        InitVertices();
        cout << "请分别输入每条边的起始结点和权值:" << endl;
        int head, tail;
        InfoType weight;
        while (cin >> head >> tail >> weight)
        {
            Insert(head, tail, weight);
        }
    }

    void BFS(Vertex* vertex)
    {
        vertex->color = GRAY;
        queue<Vertex*> vertices;
        vertices.push(vertex);
        while (!vertices.empty())
        {
            Vertex* curVertex = vertices.front();
            vertices.pop();
            cout << curVertex->data << "->";
            ArcNode* node = curVertex->firstArc;
            while (node)
            {
                Vertex* tmpVertex = &m_vertices[node->vertexIndex];
                if (tmpVertex->color == WHITE)
                {
                    tmpVertex->color = GRAY;
                    vertices.push(tmpVertex);
                }
                node = node->next;
            }
            curVertex->color = BLACK;
        }
    }

    void DFS(Vertex* vertex)
    {
        vertex->color = GRAY;
        stack<Vertex*> vertices;
        vertices.push(vertex);
        while (!vertices.empty())
        {
            Vertex* curVertex = vertices.top();
            vertices.pop();
            cout << curVertex->data << "->";
            ArcNode* node = curVertex->firstArc;
            while (node)
            {
                Vertex* tmp = &m_vertices[node->vertexIndex];
                if (tmp->color == WHITE)
                {
                    tmp->color = GRAY;
                    vertices.push(tmp);
                }
                node = node->next;
            }
            curVertex->color = BLACK;
        }                
    }
};

int main()
{
    int  vertexNum;
    cout << "请输入要创建的图的结点数：";
    cin >> vertexNum;
    Graph<char, int> g(vertexNum,GraphType::UNDIR_UNWEIGHT_GRAPH);
    g.Create();
    g.Display();
    g.BFS();
    g.DFS();
}

运行结果：(创建的树为算法导论BFS说明图片中的树)