數據結構之圖的創建（鄰接表）

　　數據結構之圖的基本概念中了解了圖的基本概念，接下來對圖的代碼實現進行詳解。

鄰接無向圖

1. 鄰接表無向圖介紹

　　鄰接表無向圖是指通過鄰接表表示的無向圖。

　　上面的圖G1包含了"A,B,C,D,E,F,G"共7個頂點，而且包含了"(A,C),(A,D),(A,F),(B,C),(C,D),(E,G),(F,G)"共7條邊。

　　上圖右邊的矩陣是G1在內存中的鄰接表示意圖。每一個頂點都包含一條鏈表，該鏈表記錄了"該頂點的鄰接點的序號"。例如，第2個頂點(頂點C)包含的鏈表所包含的節點的數據分別是"0,1,3"；而這"0,1,3"分別對應"A,B,D"的序號，"A,B,D"都是C的鄰接點。就是通過這種方式記錄圖的信息的。

2. 鄰接表無向圖代碼實現

（1）數據結構

struct ENode
{
    int nVindex;  // 該邊所指的頂點的位置
    ENode *pNext; // 指向下一個邊的指針
};

struct VNode
{
    char data;  // 頂點信息
    ENode *pFirstEdge; // 指向第一條依附該頂點的邊
};

（2）圖的創建

listUDG(char *vexs, int vlen, char edges[][2], int elen)
{
    m_nVexNum = vlen;
    m_nEdgNum = elen;

    // 初始化"鄰接表"的頂點
    for (int i = 0; i < vlen; i ++)
    {
        m_mVexs[i].data = vexs[i];
        m_mVexs[i].pFirstEdge = NULL;
    }

    char c1,c2;
    int p1,p2;
    ENode *node1, *node2;
    // 初始化"鄰接表"的邊
    for (int j = 0; j < elen; j ++)
    {
        // 讀取邊的起始頂點和結束頂點
        c1 = edges[j][0];
        c2 = edges[j][1];
        p1 = GetVIndex(c1);
        p2 = GetVIndex(c2);

        node1 = new ENode();
        node1->nVindex = p2;
        if (m_mVexs[p1].pFirstEdge == NULL)
        {
            m_mVexs[p1].pFirstEdge = node1;
        }
        else
        {
            LinkLast(m_mVexs[p1].pFirstEdge, node1);
        }

        node2 = new ENode();
        node2->nVindex = p1;
        if (m_mVexs[p2].pFirstEdge == NULL)
        {
            m_mVexs[p2].pFirstEdge = node2;
        }
        else
        {
            LinkLast(m_mVexs[p2].pFirstEdge, node2);
        }
    }

}

（3）完整代碼

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

#define MAX 100

// 邊
struct ENode
{
    int nVindex;  // 該邊所指的頂點的位置
    ENode *pNext; // 指向下一個邊的指針
};

struct VNode
{
    char data;  // 頂點信息
    ENode *pFirstEdge; // 指向第一條依附該頂點的邊
};

// 無向鄰接表
class listUDG
{
public:
    listUDG(){};
    listUDG(char *vexs, int vlen, char edges[][2], int elen)
    {
        m_nVexNum = vlen;
        m_nEdgNum = elen;

        // 初始化"鄰接表"的頂點
        for (int i = 0; i < vlen; i ++)
        {
            m_mVexs[i].data = vexs[i];
            m_mVexs[i].pFirstEdge = NULL;
        }

        char c1,c2;
        int p1,p2;
        ENode *node1, *node2;
        // 初始化"鄰接表"的邊
        for (int j = 0; j < elen; j ++)
        {
            // 讀取邊的起始頂點和結束頂點
            c1 = edges[j][0];
            c2 = edges[j][1];
            p1 = GetVIndex(c1);
            p2 = GetVIndex(c2);

            node1 = new ENode();
            node1->nVindex = p2;
            if (m_mVexs[p1].pFirstEdge == NULL)
            {
                m_mVexs[p1].pFirstEdge = node1;
            }
            else
            {
                LinkLast(m_mVexs[p1].pFirstEdge, node1);
            }

            node2 = new ENode();
            node2->nVindex = p1;
            if (m_mVexs[p2].pFirstEdge == NULL)
            {
                m_mVexs[p2].pFirstEdge = node2;
            }
            else
            {
                LinkLast(m_mVexs[p2].pFirstEdge, node2);
            }
        }

    }
    ~listUDG()
    {
        ENode *pENode = NULL;
        ENode *pTemp = NULL;
        for (int i = 0; i < m_nVexNum; i ++)
        {
            pENode = m_mVexs[i].pFirstEdge;
            if (pENode != NULL)
            {
                pTemp = pENode;
                pENode = pENode->pNext;

                delete pTemp;
            }
            delete pENode;
        }
    }

    void PrintUDG()
    { 
        ENode *pTempNode = NULL;
        cout << "鄰接無向表:" << endl;
        for (int i = 0; i < m_nVexNum; i ++)
        {
            cout << "頂點:" << GetVIndex(m_mVexs[i].data)<< "-" << m_mVexs[i].data<<  "->";
            pTempNode = m_mVexs[i].pFirstEdge;
            while (pTempNode)
            {
                cout <<pTempNode->nVindex << "->";
                pTempNode = pTempNode->pNext;
            }
            cout << endl;
        }
    }
private:
    // 返回頂點的索引
    int GetVIndex(char ch)
    {
        int i = 0;
        for (; i < m_nVexNum; i ++)
        {
            if (m_mVexs[i].data == ch)
            {
                return i;
            }
        }
        return -1;
    }

    void LinkLast(ENode *pFirstNode, ENode *pNode)
    {
        if (pFirstNode == NULL || pNode == NULL)
        {
            return;
        }
        ENode *pTempNode = pFirstNode;
        while (pTempNode->pNext != NULL)
        {
            pTempNode = pTempNode->pNext;
        }

        pTempNode->pNext = pNode;
    }

private:
    int m_nVexNum;   // 頂點數目
    int m_nEdgNum;   // 邊數目
    VNode m_mVexs[MAX];
};

void main()
{
    char vexs[] = {'A', 'B', 'C', 'D', 'E', 'F', 'G'}; 
    char edges[][2] = { 
        {'A', 'C'},  
        {'A', 'D'},  
        {'A', 'F'},  
        {'B', 'C'},  
        {'C', 'D'},  
        {'E', 'G'},  
        {'F', 'G'}}; 
    int vlen = sizeof(vexs)/sizeof(vexs[0]); 
    int elen = sizeof(edges)/sizeof(edges[0]); 
    listUDG* pG = new listUDG(vexs, vlen, edges, elen); 

    pG->PrintUDG();   // 打印圖 

    return; 
}

鄰接有向圖

1. 鄰接表有向圖介紹

　　鄰接表有向圖是指通過鄰接表表示的有向圖。

　　上面的圖G2包含了"A,B,C,D,E,F,G"共7個頂點，而且包含了"<A,B>,<B,C>,<B,E>,<B,F>,<C,E>,<D,C>,<E,B>,<E,D>,<F,G>"共9條邊。

上　　圖右邊的矩陣是G2在內存中的鄰接表示意圖。每一個頂點都包含一條鏈表，該鏈表記錄了"該頂點所對應的出邊的另一個頂點的序號"。例如，第1個頂點(頂點B)包含的鏈表所包含的節點的數據分別是"2,4,5"；而這"2,4,5"分別對應"C,E,F"的序號，"C,E,F"都屬於B的出邊的另一個頂點。

2. 鄰接表有向圖代碼實現

（1）數據結構

struct ENode
{
    int nVindex;  // 該邊所指的頂點的位置
    ENode *pNext; // 指向下一個邊的指針
};

struct VNode
{
    char data;  // 頂點信息
    ENode *pFirstEdge; // 指向第一條依附該頂點的邊
};

（2）鄰接表有向圖創建

listDG(char *vexs, int vlen, char edges[][2], int elen)
{
    m_nVexNum = vlen;
    m_nEdgNum = elen;

    // 初始化"鄰接表"的頂點
    for (int i = 0; i < vlen; i ++)
    {
        m_mVexs[i].data = vexs[i];
        m_mVexs[i].pFirstEdge = NULL;
    }

    char c1,c2;
    int p1,p2;
    ENode *node1;
    // 初始化"鄰接表"的邊
    for (int j = 0; j < elen; j ++)
    {
        // 讀取邊的起始頂點和結束頂點
        c1 = edges[j][0];
        c2 = edges[j][1];
        p1 = GetVIndex(c1);
        p2 = GetVIndex(c2);

        node1 = new ENode();
        node1->nVindex = p2;
        if (m_mVexs[p1].pFirstEdge == NULL)
        {
            m_mVexs[p1].pFirstEdge = node1;
        }
        else
        {
            LinkLast(m_mVexs[p1].pFirstEdge, node1);
        }
    }
}

（3）完整代碼實現

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

#define MAX 100

// 邊
struct ENode
{
    int nVindex;  // 該邊所指的頂點的位置
    ENode *pNext; // 指向下一個邊的指針
};

struct VNode
{
    char data;  // 頂點信息
    ENode *pFirstEdge; // 指向第一條依附該頂點的邊
};

// 有向鄰接表
class listDG
{
public:
    listDG(){};
    listDG(char *vexs, int vlen, char edges[][2], int elen)
    {
        m_nVexNum = vlen;
        m_nEdgNum = elen;

        // 初始化"鄰接表"的頂點
        for (int i = 0; i < vlen; i ++)
        {
            m_mVexs[i].data = vexs[i];
            m_mVexs[i].pFirstEdge = NULL;
        }

        char c1,c2;
        int p1,p2;
        ENode *node1;
        // 初始化"鄰接表"的邊
        for (int j = 0; j < elen; j ++)
        {
            // 讀取邊的起始頂點和結束頂點
            c1 = edges[j][0];
            c2 = edges[j][1];
            p1 = GetVIndex(c1);
            p2 = GetVIndex(c2);

            node1 = new ENode();
            node1->nVindex = p2;
            if (m_mVexs[p1].pFirstEdge == NULL)
            {
                m_mVexs[p1].pFirstEdge = node1;
            }
            else
            {
                LinkLast(m_mVexs[p1].pFirstEdge, node1);
            }
        }
    }
    ~listDG()
    {
        ENode *pENode = NULL;
        ENode *pTemp = NULL;
        for (int i = 0; i < m_nVexNum; i ++)
        {
            pENode = m_mVexs[i].pFirstEdge;
            if (pENode != NULL)
            {
                pTemp = pENode;
                pENode = pENode->pNext;

                delete pTemp;
            }
            delete pENode;
        }
    }

    void PrintDG()
    { 
        ENode *pTempNode = NULL;
        cout << "鄰接有向表:" << endl;
        for (int i = 0; i < m_nVexNum; i ++)
        {
            cout << "頂點:" << GetVIndex(m_mVexs[i].data)<< "-" << m_mVexs[i].data<<  "->";
            pTempNode = m_mVexs[i].pFirstEdge;
            while (pTempNode)
            {
                cout <<pTempNode->nVindex << "->";
                pTempNode = pTempNode->pNext;
            }
            cout << endl;
        }
    }
private:
    // 返回頂點的索引
    int GetVIndex(char ch)
    {
        int i = 0;
        for (; i < m_nVexNum; i ++)
        {
            if (m_mVexs[i].data == ch)
            {
                return i;
            }
        }
        return -1;
    }

    void LinkLast(ENode *pFirstNode, ENode *pNode)
    {
        if (pFirstNode == NULL || pNode == NULL)
        {
            return;
        }
        ENode *pTempNode = pFirstNode;
        while (pTempNode->pNext != NULL)
        {
            pTempNode = pTempNode->pNext;
        }

        pTempNode->pNext = pNode;
    }

private:
    int m_nVexNum;   // 頂點數目
    int m_nEdgNum;   // 邊數目
    VNode m_mVexs[MAX];
};

void main()
{
    char vexs[] = {'A', 'B', 'C', 'D', 'E', 'F', 'G'}; 
    char edges[][2] = { 
        {'A', 'B'},  
        {'B', 'C'},  
        {'B', 'E'},  
        {'B', 'F'},  
        {'C', 'E'},  
        {'D', 'C'},  
        {'E', 'B'},  
        {'E', 'D'},  
        {'F', 'G'}};  
    int vlen = sizeof(vexs)/sizeof(vexs[0]); 
    int elen = sizeof(edges)/sizeof(edges[0]); 

    listDG *pG = new listDG(vexs, vlen, edges, elen); 

    pG->PrintDG();   // 打印圖 

    return; 
}