【数据结构与算法】带权有向图

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MyGraph.h

#pragma once#include <iostream>#include <stack>#include <queue>using namespace std;// 邻接矩阵// 带权有向图const int MAXSIZE = 20;const int INFINITE = 100;template <class T>class CMyGraph{public:    CMyGraph();    ~CMyGraph();private:    T vertexArray[MAXSIZE] = {0};               // 顶点集合    int edge[MAXSIZE][MAXSIZE];                 // 边集合    int numVertex = 0;                          // 顶点的数量    int numEdge = 0;                            // 边的数量private:    bool isGraphEmpty(void) const;      // 图是否为空    bool isGraphFull(void) const;       // 图是否满了    int getVertexPos(const T& vertex);  // 得到顶点的位置,若不存在则返回-1    void errorMessage(int i);           // 错误信息public:    int GetNumOfVertices(void) const;       // 获得顶点的数量    int GetNumOfEdge(void) const;           // 边的数量    int GetWeight(const T& vertex1, const T& vertex2);  //得到边的权重    void InsertVertex(const T& vertex);                                         // 插入顶点    void InsertEdge(const T& vertex1, const T& vertex2, const int weight);      // 插入边    void DeleteVertex(const T& vertex);     // 删除顶点    void DeleteEdge(const T& vertex1, const T& vertex2); // 删除边    void Display(void);         // 显示图    T* DepthFirstSearch(const T& beginVertex);  //深度优先搜索    T* BreathFirestSearch(const T& beginVertex);//广度优先搜索    bool PathConnect(const T& vertex1, const T& vertex2);   //两顶点之间是否联通};

MyGraph.cpp

#include "MyGraph.h"template<class T>CMyGraph<T>::CMyGraph(){    for (int i = 0; i < MAXSIZE; i++) {        for (int j = 0; j < MAXSIZE; j++) {            if (i == j) {                edge[i][j] = 0;            }            else {                edge[i][j] = INFINITE;            }        }    }}template<class T>CMyGraph<T>::~CMyGraph(){}template<class T>bool CMyGraph<T>::isGraphEmpty(void) const{    if (0 == numVertex) {        return true;    }    return false;}template<class T>bool CMyGraph<T>::isGraphFull(void) const{    if (MAXSIZE == numVertex) {        return true;    }    return false;}template<class T>int CMyGraph<T>::getVertexPos(const T & vertex){    for (int i = 0; i < numVertex; i++) {        if (vertex == vertexArray[i]) {            return i;        }    }    return -1;}template<class T>void CMyGraph<T>::errorMessage(int i){    switch (i)    {    case 1:        cout << "图已满" << endl; break;    case 2:        cout << "图为空" << endl; break;    case 3:        cout << "顶点已存在" << endl; break;    case 4:        cout << "顶点不存在" << endl; break;    case 5:        cout << "权值超最大值" << endl; break;    case 6:        cout << "不允许两个顶点相同" << endl; break;    default:        break;    }}template<class T>int CMyGraph<T>::GetNumOfVertices(void) const{    return numVertex;}template<class T>int CMyGraph<T>::GetNumOfEdge(void) const{    return numEdge;}template<class T>int CMyGraph<T>::GetWeight(const T & vertex1, const T & vertex2){    if (vertex1 == vertex2) {        errorMessage(6);        return 0;    }    int pos1 = getVertexPos(vertex1);    int pos2 = getVertexPos(vertex2);    if (-1 == pos1 || -1 == pos2) {        errorMessage(4);        return INFINITE;    }    return edge[pos1][pos2];}template<class T>void CMyGraph<T>::InsertVertex(const T & vertex){    if (isGraphFull()) {        errorMessage(1);        return;    }    if (-1 != getVertexPos(vertex)) {        errorMessage(3);        return;    }    vertexArray[numVertex] = vertex;    numVertex++;}template<class T>void CMyGraph<T>::InsertEdge(const T & vertex1, const T & vertex2, const int weight){    if (vertex1 == vertex2) {        errorMessage(6);        return;    }    int pos1 = getVertexPos(vertex1);    int pos2 = getVertexPos(vertex2);    if (-1 == pos1 || -1 == pos2) {        errorMessage(4);        return;    }    if (weight >= INFINITE) {        errorMessage(5);        return;    }    edge[pos1][pos2] = weight;    numEdge++;}template<class T>void CMyGraph<T>::DeleteVertex(const T & vertex){    if (isGraphEmpty()) {        errorMessage(2);        return;    }    int pos = getVertexPos(vertex);    if (-1 == pos) {        errorMessage(4);        return;    }    if (pos == MAXSIZE - 1) {        for (int i = 0; i < MAXSIZE - 1; i++) {            edge[i][pos] = INFINITE;            edge[pos][i] = INFINITE;        }    }    else {        for (int i = pos; i < MAXSIZE - 1; i++) {            vertexArray[i] = vertexArray[i + 1];        }        for (int i = 0; i < MAXSIZE - 1; i++) {            edge[i][pos] = edge[i][pos + 1];            edge[pos][i] = edge[pos + 1][i];        }    }    numVertex--;}template<class T>void CMyGraph<T>::DeleteEdge(const T & vertex1, const T & vertex2){    if (vertex1 == vertex2) {        errorMessage(6);        return;    }    int pos1 = getVertexPos(vertex1);    int pos2 = getVertexPos(vertex2);    if (-1 == pos1 || -1 == pos2) {        errorMessage(4);        return;    }    edge[pos1][pos2] = INFINITE;    numEdge--;}template<class T>void CMyGraph<T>::Display(void){    cout << "顶点集合：" << endl;;    for (int i = 0; i < numVertex; i++) {        cout << vertexArray[i] << "  ";    }    cout << endl << "--------" << endl;    cout << "边集合：" << endl;;    for (int i = 0; i < numVertex; i++) {        for (int j = 0; j < numVertex; j++) {            cout << edge[i][j] << "  ";        }        cout << endl;    }}template<class T>T* CMyGraph<T>::DepthFirstSearch(const T& beginVertex) {        T* DFS_visitList = new T[MAXSIZE]{};        stack<T> visitStack;        int length = 0;        T temp = beginVertex;        while (1) {            int k = getVertexPos(temp);            if (-1 == k) {                errorMessage(4);                return nullptr;            }            int i = 0;            for (; i < length; i++) {                if (temp == DFS_visitList[i]) {                    break;                }            }            if (i == length)            {                DFS_visitList[length] = temp;                length++;                for (int j = 0; j < numVertex; j++) {                    if (k == j) {                        continue;                    }                    else if (INFINITE != edge[k][j]) {                        visitStack.push(vertexArray[j]);                    }                }            }            if (visitStack.empty()) {                return DFS_visitList;            }            temp = visitStack.top();            visitStack.pop();        }}template<class T>T * CMyGraph<T>::BreathFirestSearch(const T & beginVertex){    queue<T> visitQueue;    int length = 0;    T* BFS_visitList = new T[MAXSIZE]{};    T Temp = beginVertex;    while (1) {        int k = getVertexPos(Temp);        if (-1 == k) {            errorMessage(4);            return nullptr;        }        int i = 0;        for (; i < length; i++) {            if (Temp == BFS_visitList[i]) {                break;            }        }        if (i == length) {            BFS_visitList[length] = Temp;            length++;            for (int i = 0; i < numVertex; i++) {                if (k == i) {                    continue;                }                else if (INFINITE != edge[k][i]) {                    visitQueue.push(vertexArray[i]);                }            }        }        if (visitQueue.empty()) {            return BFS_visitList;        }        Temp = visitQueue.front();        visitQueue.pop();    }}template<class T>bool CMyGraph<T>::PathConnect(const T & vertex1, const T & vertex2){    T* list = DepthFirstSearch(vertex1);    if (nullptr == list) {        return false;    }    while (NULL != *list) {        if (vertex2 == *list) {            return true;        }        list++;    }    return false;}

源.cpp

#include "MyGraph.h"#include "MyGraph.cpp"void main() {    CMyGraph<char> mg;    mg.InsertVertex('a');    mg.InsertVertex('b');    mg.InsertVertex('c');    mg.InsertVertex('d');    mg.InsertVertex('e');    mg.DeleteVertex('a');    mg.InsertEdge('a', 'b', 10);    mg.InsertEdge('b', 'c', 20);    mg.InsertEdge('b', 'd', 12);    mg.InsertEdge('d', 'e', 65);    mg.Display();    cout << "---" << endl;    cout << "深度优先遍历:";    char* DFS_List = mg.DepthFirstSearch('a');    if (nullptr != DFS_List) {        cout << DFS_List << endl;    }    cout << "---" << endl;    cout << "广优先遍历:";    char* BFS_List = mg.BreathFirestSearch('a');    if (nullptr != BFS_List) {        cout << BFS_List << endl;    }    cout << "---" << endl;    cout << "a,e是否连通: "<< mg.PathConnect('a','e') << endl;    cout << "e,a是否连通: " << mg.PathConnect('e', 'a') << endl;    system("pause");}

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