由于图的基本操作的代码较多，我放到这一章来写。图可以用两种方法来存储，但是本人偏爱链表的表示方法，所以以下代码也都是是基于邻接链表的存储方式。
1 /* 2 以下存储结构参考严蔚敏版数据结构，不懂的可以翻阅查看 3 */ 4 const int UNDIGRAPH = 0; //无向图 5 const int DIGRAPH = 1; //有向图 6 const int MAX_VERTEX_NUM = 20; 7 8 typedef struct ArchNode 9 { 10 int vertexIndex; //该弧指向顶点在图中顶点数组的索引，对应vertexs[20]的下标 11 ArchNode *nextarc; //指向下一条弧的指针 12 InfoTypde info; //比如弧的权重 13 }ArchNode; 14 15 typedef struct Vertex 16 { 17 VertexType data; //顶点信息 18 ArchNode *firstarc; //指向第一条弧的指针 19 }Vertex; 20 21 //这样定义图有个坏处，一旦定义好，图中结点的个数就固定了！ 22 typedef struct Graph 23 { 24 Vertex *vertexs[MAX_VERTEX_NUM]; //存储顶点的数组,存放的是指向顶点的指针 25 int vexNum; //当前图中的定点数 26 int arcNum; //当前图中的弧的个数 27 int kind; //图的种类，有向图还是无向图 28 }Graph;
//图的创建
1 /* 2 初始条件：kind是图的类型，目前有有向图和无向图 两种. 3 返回值 ：无。---大部分函数都无返回值，是对图的引用进行操作的 4 */ 5 void createGraph(Graph *&G,int kind) 6 { 7 if(G) G = NULL; 8 G = (Graph *)malloc(sizeof(struct Graph)); 9 assert(NULL != G); 10 for(int i = 0; i < MAX_VERTEX_NUM; ++i) 11 { 12 G->vertexs[i] = NULL; //初始化指向顶点的指针为NULL 13 } 14 G->kind = kind; //设置图的种类 15 G->vexNum = 0; //初始化图中顶点的个数 16 G->arcNum = 0; //初始化图中弧的个数 17 }
//图的销毁
1 /* 2 初始条件：G存在 3 返回值 ：无。---大部分函数都无返回值，是对图的引用进行操作的 4 */ 5 void destoryGraph(Graph *&G) 6 { 7 ArchNode *cur,*next; 8 if(NULL == G) 9 return; 10 //遍历顶点 11 for(int i = 0; i < G->vexNum; ++i) 12 { 13 if(!G->vertexs[i]) 14 continue; 15 next = G->vertexs[i]->firstarc; 16 cur = G->vertexs[i]->firstarc; 17 while(cur) 18 { 19 next = cur->nextarc; 20 free(cur); 21 cur = next; 22 } 23 G->vertexs[i]->firstarc = NULL; 24 } 25 free(G); 26 G = NULL; 27 }
//向图中增加结点
1 //向图中增加结点 2 /* 3 初始条件：G存在，data是结点的数据值 4 */ 5 void addVertexToGraph(Graph *&G,VertexType data) 6 { 7 if(G->vexNum >= MAX_VERTEX_NUM) 8 { 9 cout << "Too many vertex!" << endl; 10 return ; 11 } 12 for(int i = 0; i < G->vexNum; ++i) 13 { 14 if(!G->vertexs[i]) 15 continue; 16 if(G->vertexs[i]->data == data) 17 { 18 cout << "Already exists!" << endl; 19 return; //不允许重复 20 } 21 } 22 Vertex *pVeterx; 23 pVeterx = (Vertex *)malloc(sizeof(struct Vertex)); 24 pVeterx->data = data; 25 pVeterx->firstarc = NULL; 26 G->vertexs[G->vexNum] = pVeterx; 27 G->vexNum++; 28 }
//从图中删除一个结点
1 void delVertexFromGraph(Graph *&G,VertexType data) 2 { 3 bool haveThisVertex = false; 4 ArchNode *cur,*next,*temp,*pre; 5 Vertex *anotherVertex; 6 if(NULL == G) 7 return; 8 if(G->vexNum <= 0) 9 { 10 cout << "Have no vertex!" << endl; 11 return ; 12 } 13 for(int i = 0; i < G->vexNum; ++i) 14 { 15 if(!G->vertexs[i]) 16 continue; 17 if(G->vertexs[i]->data == data) 18 { 19 haveThisVertex = true; 20 //以下循环用来删除顶点所指向的弧链表 21 next = cur = G->vertexs[i]->firstarc; 22 if(G->kind == DIGRAPH) //如果是有向图 23 { 24 while(cur) 25 { 26 next = cur->nextarc; 27 free(cur); 28 G->arcNum --; //弧的个数减一 29 cur = next; 30 } 31 G->vertexs[i] = NULL; 32 } 33 else if(G->kind == UNDIGRAPH) //如果是无向图，这个麻烦点 34 { 35 while(cur) 36 { 37 //找到待删除的弧的另一个结点，将它的弧链表中指向被删除结点的弧也删掉 38 anotherVertex = G->vertexs[cur->vertexIndex]; //找到待删除弧对应的另一个结点 39 temp = anotherVertex->firstarc,pre = NULL; 40 while(temp) //这个循环是为了删除另一个结点中保存弧信息 41 { 42 if(temp->vertexIndex == i) 43 { 44 //如果是首节点 45 if(NULL == pre) //或者if(NULL == pre) 46 { 47 anotherVertex->firstarc = temp->nextarc; 48 free(temp); 49 } 50 else 51 { 52 pre->nextarc = temp->nextarc; 53 free(temp); 54 } 55 break; //找到即停止循环 56 } 57 pre = temp; 58 temp = temp->nextarc; 59 } 60 next = cur->nextarc; 61 free(cur); 62 G->arcNum --; //弧的个数减一 63 cur = next; 64 } 65 G->vertexs[i] = NULL; 66 } 67 for(int j = i; j < G->vexNum - 1; ++j) 68 { 69 G->vertexs[j] = G->vertexs[j + 1]; 70 } 71 G->vertexs[j] = NULL; // 72 G->vexNum-- ; //结点的个数减一 73 break; 74 } 75 } 76 if(!haveThisVertex) 77 cout << "没有该结点！" << endl; 78 }
//从图中查找一个值为指定值的结点的索引
1 //初始条件：G存在，data是指定结点的数据值 2 int findVertexIndexInGraph(const Graph *G,VertexType data) 3 { 4 if(NULL == G) 5 return -1; 6 for(int i = 0; i < G->vexNum; ++i) 7 { 8 if(!G->vertexs[i]) 9 continue; 10 if(G->vertexs[i]->data == data) 11 { 12 return i; 13 break; 14 } 15 } 16 return -1; 17 }
//向图中增加一条弧，有有向图和无向图之分
1 //初始条件：G存在，指定起始点，和弧的权重 2 void addArchToGraph(Graph *&G,VertexType startData,VertexType endData,InfoTypde weight = 0) 3 { 4 ArchNode *pArchNode,*cur; 5 //先要找到start和end 6 if(NULL == G) 7 return; 8 int startVertexIndex = findVertexIndexInGraph(G,startData); 9 int endVertexIndex = findVertexIndexInGraph(G,endData); 10 cur = G->vertexs[startVertexIndex]->firstarc; 11 while(cur) 12 { 13 if(cur->vertexIndex == endVertexIndex) 14 { 15 cout << "Already have this arch!" << endl; 16 return ; 17 } 18 cur = cur->nextarc; 19 } 20 if(startVertexIndex >= 0 && endVertexIndex >= 0) 21 { 22 if(G->kind == DIGRAPH) //如果是有向图 23 { 24 pArchNode = (ArchNode *)malloc(sizeof(struct ArchNode)); //创建一个弧结点 25 pArchNode->info = weight; 26 pArchNode->nextarc = NULL; 27 pArchNode->vertexIndex = endVertexIndex; 28 cur = G->vertexs[startVertexIndex]->firstarc; 29 if(NULL == cur) 30 { 31 G->vertexs[startVertexIndex]->firstarc = pArchNode; 32 } 33 else 34 { 35 while(cur->nextarc) 36 { 37 cur = cur->nextarc; 38 } 39 cur->nextarc = pArchNode; 40 } 41 G->arcNum ++; //弧的条数加一 42 } 43 else if(G->kind == UNDIGRAPH) //如果是无向图 44 { 45 pArchNode = (ArchNode *)malloc(sizeof(struct ArchNode)); //创建一个弧结点 46 pArchNode->info = weight; 47 pArchNode->nextarc = NULL; 48 pArchNode->vertexIndex = endVertexIndex; 49 cur = G->vertexs[startVertexIndex]->firstarc; 50 if(NULL == cur) 51 { 52 G->vertexs[startVertexIndex]->firstarc = pArchNode; 53 } 54 else 55 { 56 while(cur->nextarc) 57 { 58 cur = cur->nextarc; 59 } 60 cur->nextarc = pArchNode; 61 } 62 pArchNode = (ArchNode *)malloc(sizeof(struct ArchNode)); //再创建一个弧结点 63 pArchNode->info = weight; 64 pArchNode->nextarc = NULL; 65 pArchNode->vertexIndex = startVertexIndex; 66 cur = G->vertexs[endVertexIndex]->firstarc; 67 if(NULL == cur) 68 { 69 G->vertexs[endVertexIndex]->firstarc = pArchNode; 70 } 71 else 72 { 73 while(cur->nextarc) 74 { 75 cur = cur->nextarc; 76 } 77 cur->nextarc = pArchNode; 78 } 79 G->arcNum ++; //弧的条数加一 80 } 81 } 82 else 83 { 84 cout << "起点或终点不存在！" << endl; 85 return ; 86 } 87 }
//从图中删除一条弧
1 //初始条件：G存在，指定要删除弧连接的两个顶点 2 void delArchFromGraph(Graph *&G,VertexType startData,VertexType endData) 3 { 4 ArchNode *cur,*pre; 5 //先要找到start和end 6 if(NULL == G) 7 return; 8 int startVertexIndex = findVertexIndexInGraph(G,startData); 9 int endVertexIndex = findVertexIndexInGraph(G,endData); 10 if(startVertexIndex >= 0 && endVertexIndex >= 0) 11 { 12 if(G->kind == DIGRAPH) 13 { 14 cur = G->vertexs[startVertexIndex]->firstarc,pre = NULL; 15 while(cur) 16 { 17 if(cur->vertexIndex == endVertexIndex) 18 { 19 break; 20 } 21 pre = cur; 22 cur = cur->nextarc; 23 } 24 if(NULL == cur) 25 { 26 cout << "这两个结点之间没有弧！" << endl; 27 return ; 28 } 29 else 30 { 31 if(NULL == pre) //是首节点 32 G->vertexs[startVertexIndex]->firstarc = cur->nextarc; 33 else 34 pre->nextarc = cur->nextarc; 35 free(cur); 36 G->arcNum --; 37 } 38 } 39 else if(G->kind == UNDIGRAPH) 40 { 41 cur = G->vertexs[startVertexIndex]->firstarc,pre = NULL; 42 while(cur) 43 { 44 if(cur->vertexIndex == endVertexIndex) 45 { 46 break; 47 } 48 pre = cur; 49 cur = cur->nextarc; 50 } 51 if(NULL == cur) 52 { 53 cout << "这两个结点之间没有弧！" << endl; 54 return ; 55 } 56 else 57 { 58 if(NULL == pre) //是首节点 59 G->vertexs[startVertexIndex]->firstarc = cur->nextarc; 60 else 61 pre->nextarc = cur->nextarc; 62 free(cur); 63 //G->arcNum --; 64 } 65 66 cur = G->vertexs[endVertexIndex]->firstarc,pre = NULL; 67 while(cur) 68 { 69 if(cur->vertexIndex == startVertexIndex) 70 { 71 break; 72 } 73 pre = cur; 74 cur = cur->nextarc; 75 } 76 if(NULL == cur) 77 { 78 cout << "这两个结点之间没有弧！" << endl; 79 return ; 80 } 81 else 82 { 83 if(NULL == pre) //是首节点 84 G->vertexs[endVertexIndex]->firstarc = cur->nextarc; 85 else 86 pre->nextarc = cur->nextarc; 87 free(cur); 88 G->arcNum --; 89 } 90 } 91 } 92 else 93 { 94 cout << "起点或终点不存在！" << endl; 95 return ; 96 } 97 }
//深度优先遍历
1 //初始条件：图G存在 2 void DFSdetails(const Graph *G,int i,int satusArr[]) 3 { 4 ArchNode *cur; 5 if(satusArr[i] == 1 ) 6 return; 7 cout << G->vertexs[i]->data << " "; 8 satusArr[i] = 1; 9 cur = G->vertexs[i]->firstarc; 10 while(cur) 11 { 12 DFSdetails(G,cur->vertexIndex,satusArr); 13 cur = cur->nextarc; 14 } 15 } 16 17 void DFS(const Graph *G) 18 { 19 int satusArr[MAX_VERTEX_NUM] = {0}; 20 cout << "深度优先遍历："; 21 if(NULL == G) 22 return; 23 for(int i = 0; i < G->vexNum; ++i) 24 { 25 DFSdetails(G,i,satusArr); 26 } 27 cout << endl; 28 }