数据结构基础(20) --图的存储结构

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图的结构定义

图是由一个顶点集 V 和一个弧集 E构成的数据结构。

Graph = (V , E )

其中，E ＝ {<v,w>| v,w∈V 且 P(v,w)} <v,w>表示从 v 到 w 的一条弧，并称 v 为弧尾，w 为弧头。谓词 P(v,w) 定义了弧 <v,w>的意义或信息。

由顶点集和边集构成的图称作无向图。

如果”弧”是有方向的，则称由顶点集和弧集构成的图为有向图。

邻接矩阵

定义:矩阵的元素为

有向图的邻接矩阵为非对称矩阵, 而无向图的邻接矩阵为对称矩阵;

//无向图的邻接矩阵const int MAX_VERTS = 20;//顶点template <typename Type>class Vertex{public:    Vertex(const Type &_node = Type())        : node(_node) {}private:    Type node;};//图template <typename Type>class Graph{public:    Graph();    ~Graph();    void addVertex(const Type &vertex);    void addEdge(int start, int end);    void printMatrix();private:    Vertex<Type>* vertexList[MAX_VERTS];    int nVerts;    int adjMatrix[MAX_VERTS][MAX_VERTS];};

template <typename Type>Graph<Type>::Graph():nVerts(0){    for (int i = 0; i < MAX_VERTS; ++i)        for (int j = 0; j < MAX_VERTS; ++j)            adjMatrix[i][j] = 0;}template <typename Type>Graph<Type>::~Graph(){    for (int i = 0; i < nVerts; ++i)        delete vertexList[i];}

template <typename Type>void Graph<Type>::addVertex(const Type &vertex){    vertexList[nVerts ++] = new Vertex<Type>(vertex);}template <typename Type>void Graph<Type>::addEdge(int start, int end){    //无向图    adjMatrix[start][end] = 1;    adjMatrix[end][start] = 1;}

template <typename Type>void Graph<Type>::printMatrix(){    for (int i = 0; i < nVerts; ++i)    {        for (int j = 0; j < nVerts; ++j)            cout << adjMatrix[i][j] << ' ';        cout << endl;    }}

//测试代码int main(){    Graph<char> g;    g.addVertex('A');   //0    g.addVertex('B');   //1    g.addVertex('C');   //2    g.addVertex('D');   //3    g.addVertex('E');   //4    g.addEdge(0, 1);    //A-B    g.addEdge(0, 3);    //A-D    g.addEdge(1, 0);    //B-A    g.addEdge(1, 4);    //B-E    g.addEdge(2, 4);    //C-E    g.addEdge(3, 0);    //D-A    g.addEdge(3, 4);    //D-E    g.addEdge(4, 1);    //E-B    g.addEdge(4, 2);    //E-C    g.addEdge(4, 3);    //E-D    g.printMatrix();    return 0;}

邻接表

注意:在有向图的邻接表中不易找到指向该顶点的弧。

//无向图的邻接表template <typename Type>class Graph{public:    Graph(int _size = 10);    ~Graph();    void addVertex(const Type &vertex);    void addEdge(int start, int end);    void printVertex();    void printAdjList();private:    Type *vertexList;    list<int> *headNode;    int size;    int nVertex;};

template <typename Type>Graph<Type>::Graph(int _size):size(_size), nVertex(0){    vertexList = new Type[size];    headNode = new list<int>[size];}template <typename Type>Graph<Type>::~Graph(){    delete []vertexList;    delete []headNode;}

template <typename Type>void Graph<Type>::addVertex(const Type &vertex){    vertexList[nVertex ++] = vertex;}template <typename Type>void Graph<Type>::addEdge(int start, int end){    headNode[start].push_back(end);}

template <typename Type>void Graph<Type>::printVertex(){    cout << vertexList[0];    for (int i = 1; i < nVertex; ++i)        cout << ' ' << vertexList[i];    cout << endl;}template <typename Type>void Graph<Type>::printAdjList(){    for (int i = 0; i < nVertex; ++i)    {        cout << i;        for (list<int>::iterator iter = headNode[i].begin();                iter != headNode[i].end();                ++iter)            cout << " -> " << *iter;        cout << endl;    }}

//测试代码int main(){    Graph<char> g;    g.addVertex('A');   //0    g.addVertex('B');   //1    g.addVertex('C');   //2    g.addVertex('D');   //3    g.addVertex('E');   //4    g.printVertex();    g.addEdge(0, 1);    //A-B    g.addEdge(0, 3);    //A-D    g.addEdge(1, 0);    //B-A    g.addEdge(1, 4);    //B-E    g.addEdge(2, 4);    //C-E    g.addEdge(3, 0);    //D-A    g.addEdge(3, 4);    //D-E    g.addEdge(4, 1);    //E-B    g.addEdge(4, 2);    //E-C    g.addEdge(4, 3);    //E-D    g.printAdjList();    return 0;}

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