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:
1 #include <queue> 2 #include <stack> 3 #include <iostream> 4 using namespace std; 5 6 7 enum GraphType 8 { 9 UNDIR_UNWEIGHT_GRAPH, //无向无权图 10 UNDIR_WEIGHT_GRAPH, //无向带权图 11 DIR_UNWEIGHT_GRAPH, //有向无权图 12 DIR_WEIGHT_GRAPH //有向带权图 13 }; 14 15 //结点颜色代表遍历情况 16 enum ColorType 17 { 18 WHITE, //未访问 19 GRAY, //正在访问，邻接点还没访问完 20 BLACK //访问完毕 21 }; 22 23 template<typename VertexType,typename InfoType> 24 class Graph 25 { 26 public: 27 Graph(int vertexNum, GraphType type) :m_vertexNum(vertexNum), m_type(type), m_arcNum(0) 28 { 29 for (int i = 0; i < MAX_VERTEX_NUM; ++i) 30 { 31 m_vertices[i].firstArc = nullptr; 32 } 33 } 34 35 void Create() 36 { 37 switch (m_type) 38 { 39 case UNDIR_UNWEIGHT_GRAPH: 40 CreateUndirUnweightGraph(); 41 break; 42 case UNDIR_WEIGHT_GRAPH: 43 CreateUndirWeightGraph(); 44 break; 45 case DIR_UNWEIGHT_GRAPH: 46 CreateDirUnweightGraph(); 47 break; 48 case DIR_WEIGHT_GRAPH: 49 CreateDirWeightGraph(); 50 break; 51 default: 52 break; 53 } 54 } 55 56 //输出图的信息 57 void Display() 58 { 59 for (int i = 0; i < m_vertexNum; ++i) 60 { 61 cout << "第" << i + 1 << "个结点为" << m_vertices[i].data << " 邻接表为："; 62 ArcNode* node = m_vertices[i].firstArc; 63 while (node) 64 { 65 cout << "->" << m_vertices[node->vertexIndex].data << "(" << node->info << ")"; 66 node = node->next; 67 } 68 cout << endl; 69 } 70 } 71 72 void BFS() 73 { 74 for (int i = 0; i < m_vertexNum; ++i) 75 { 76 m_vertices[i].color = WHITE; 77 } 78 cout << "图的广度优先遍历为："; 79 BFS(&m_vertices[0]); 80 cout << endl; 81 } 82 83 void DFS() 84 { 85 for (int i = 0; i < m_vertexNum; ++i) 86 { 87 m_vertices[i].color = WHITE; 88 } 89 cout << "图的深度优先遍历为："; 90 DFS(&m_vertices[0]); 91 cout << endl; 92 } 93 private: 94 struct ArcNode 95 { 96 int vertexIndex; //该弧指向的顶点位置 97 struct ArcNode* next; //指向下一个弧 98 InfoType info; //该弧的相关信息，如权重等 99 }; 100 101 struct Vertex 102 { 103 VertexType data; //顶点信息 104 ArcNode* firstArc; //指向第一条依附该节点弧的指针 105 ColorType color; //访问情况 106 }; 107 108 //最大顶点数 109 static const int MAX_VERTEX_NUM = 20; 110 Vertex m_vertices[MAX_VERTEX_NUM]; //顶点列表 111 int m_vertexNum; //当前顶点数量 112 int m_arcNum; //当前弧数量 113 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 114 private: 115 //初始化顶点列表 116 void InitVertices() 117 { 118 cout << "请输入每个顶点的关键字" << endl; 119 VertexType data; 120 for (int i = 0; i < m_vertexNum; ++i) 121 { 122 cin >> data; 123 m_vertices[i].data = data; 124 } 125 } 126 //插入一个表结点 127 void Insert(int headVertex, int tailVertex, InfoType info) 128 { 129 //构造一个邻接表结点，即创建一条弧 130 ArcNode* newNode = new ArcNode; 131 newNode->info = info; 132 newNode->next = nullptr; 133 newNode->vertexIndex = tailVertex; 134 135 //找到邻接表的最后一个节点 136 ArcNode* lastNode = m_vertices[headVertex].firstArc; 137 if (lastNode == nullptr) 138 m_vertices[headVertex].firstArc = newNode; 139 else 140 { 141 while (lastNode->next) 142 { 143 lastNode = lastNode->next; 144 } 145 lastNode->next = newNode; 146 } 147 ++m_arcNum; 148 } 149 150 //创建无向无权图 151 void CreateUndirUnweightGraph() 152 { 153 InitVertices(); 154 cout << "请分别输入每条边的起始结点:" << endl; 155 int head, tail; 156 while (cin >> head >> tail) 157 { 158 //无向图head->tail tail->head插入两次 159 Insert(head, tail, 0); 160 Insert(tail, head, 0); 161 } 162 } 163 //创建无向有权图 164 void CreateUndirWeightGraph() 165 { 166 InitVertices(); 167 cout << "请分别输入每条边的起始结点和权值:" << endl; 168 int head, tail; 169 InfoType weight; 170 while (cin >> head >> tail >> weight) 171 { 172 Insert(head, tail, weight); 173 Insert(tail, head, weight); 174 } 175 } 176 //创建有向无权图 177 void CreateDirUnweightGraph() 178 { 179 InitVertices(); 180 cout << "请分别输入每条边的起始结点值:" << endl; 181 int head, tail; 182 while (cin >> head >> tail) 183 { 184 Insert(head, tail,0); 185 } 186 } 187 //创建有向带权图 188 void CreateDirWeightGraph() 189 { 190 InitVertices(); 191 cout << "请分别输入每条边的起始结点和权值:" << endl; 192 int head, tail; 193 InfoType weight; 194 while (cin >> head >> tail >> weight) 195 { 196 Insert(head, tail, weight); 197 } 198 } 199 200 void BFS(Vertex* vertex) 201 { 202 vertex->color = GRAY; 203 queue<Vertex*> vertices; 204 vertices.push(vertex); 205 while (!vertices.empty()) 206 { 207 Vertex* curVertex = vertices.front(); 208 vertices.pop(); 209 cout << curVertex->data << "->"; 210 ArcNode* node = curVertex->firstArc; 211 while (node) 212 { 213 Vertex* tmpVertex = &m_vertices[node->vertexIndex]; 214 if (tmpVertex->color == WHITE) 215 { 216 tmpVertex->color = GRAY; 217 vertices.push(tmpVertex); 218 } 219 node = node->next; 220 } 221 curVertex->color = BLACK; 222 } 223 } 224 225 void DFS(Vertex* vertex) 226 { 227 vertex->color = GRAY; 228 stack<Vertex*> vertices; 229 vertices.push(vertex); 230 while (!vertices.empty()) 231 { 232 Vertex* curVertex = vertices.top(); 233 vertices.pop(); 234 cout << curVertex->data << "->"; 235 ArcNode* node = curVertex->firstArc; 236 while (node) 237 { 238 Vertex* tmp = &m_vertices[node->vertexIndex]; 239 if (tmp->color == WHITE) 240 { 241 tmp->color = GRAY; 242 vertices.push(tmp); 243 } 244 node = node->next; 245 } 246 curVertex->color = BLACK; 247 } 248 } 249 }; 250 251 int main() 252 { 253 int vertexNum; 254 cout << "请输入要创建的图的结点数："; 255 cin >> vertexNum; 256 Graph<char, int> g(vertexNum,GraphType::UNDIR_UNWEIGHT_GRAPH); 257 g.Create(); 258 g.Display(); 259 g.BFS(); 260 g.DFS(); 261 }
运行结果：(创建的树为算法导论BFS说明图片中的树)
