数据结构之图(图的基本操作)

来源：互联网发布：查看图片软件编辑：程序博客网时间：2024/04/26 14:21

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 Vertex16 {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 Graph23 {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NULL13     }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                             else51                             {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             else34             {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             else55             {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             else72             {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     else83     {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             else30             {31                 if(NULL == pre)    //是首节点32                     G->vertexs[startVertexIndex]->firstarc = cur->nextarc;33                 else34                     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             else57             {58                 if(NULL == pre)    //是首节点59                     G->vertexs[startVertexIndex]->firstarc = cur->nextarc;60                 else61                     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             else82             {83                 if(NULL == pre)    //是首节点84                     G->vertexs[endVertexIndex]->firstarc = cur->nextarc;85                 else86                     pre->nextarc = cur->nextarc;87                 free(cur);88                 G->arcNum --;89             }90         }91     }92     else93     {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 }

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