拓扑排序

  1 #include <iostream>
  2 using namespace std;
  3 #define    MAX_VERTEX_NUM 10//最大顶点个数
  4 
  5 //创建队列
  6 struct Queue
  7 {
  8     int rear;
  9     int front;
 10     int size;
 11     int cap;
 12     int *array;
 13 };
 14 Queue* CreateQueue()
 15 {
 16     Queue *Q = (Queue*)malloc(sizeof(Queue));
 17     Q->rear = -1; Q->front = 0;
 18     Q->size = 0; Q->cap = MAX_VERTEX_NUM ;
 19     Q->array = (int*)malloc(sizeof(int)*MAX_VERTEX_NUM);
 20     return Q;
 21 }
 22 bool isempty(Queue* Q)//队列是否为空
 23 {
 24     return Q->size==0;
 25 }
 26 bool isfull(Queue* Q)
 27 {
 28     return Q->size == Q->cap;
 29 }
 30 void Enqueue(Queue *Q,int v)//入队
 31 {
 32     if (isfull(Q))
 33         return;
 34     Q->rear++; Q->size++;
 35     Q->array[Q->rear] = v;
 36 }
 37 int Dequeue(Queue* Q)//出队
 38 {
 39     if (isempty(Q))
 40         return 0;
 41     int a = Q->array[Q->front];
 42     Q->front++; Q->size--;
 43     return a;
 44 }
 45 
 46 //创建图(邻接表)
 47 struct ENode//边结点
 48 {
 49     int index;//边所指向的点的序号
 50     int info;//记录权值
 51     struct ENode* next;//指向下一条边
 52 };
 53 struct VNode//顶点结点
 54 {
 55     char data;//顶点名称
 56     ENode* first;//指向顶点的第一个邻边
 57 };
 58 struct AGraph//记录图的信息
 59 {
 60     int vexnum, arcnum;//顶点数和边数
 61     VNode p[MAX_VERTEX_NUM];//顶点数组
 62 };
 63 
 64 int LocateVex(AGraph *G, char ch)
 65 {
 66     for (int i = 0; i < G->vexnum; i++)
 67         if (ch == G->p[i].data)
 68         {
 69             return i;
 70             break;
 71         }
 72     return -1;
 73 }
 74 //创建邻接表
 75 void CreateAGraph(AGraph *G)
 76 {
 77     int i, j, info;
 78     char v1, v2;
 79     cout << "请输入顶点个数：" << endl; cin >> G->vexnum;
 80     cout << "请输入边的个数：" << endl; cin >> G->arcnum;
 81     cout << "构造顶点：" << endl;
 82     for (int i = 0; i < G->vexnum; i++)//构造顶点数组
 83     {
 84         cin >> G->p[i].data;
 85         G->p[i].first = NULL;
 86     }
 87     cout << "构造邻接表：" << endl;
 88     for (int k = 0; k < G->arcnum; k++)
 89     {
 90         cin >> v1 >> v2 >> info;
 91         i = LocateVex(G, v1);
 92         j = LocateVex(G, v2);
 93         ENode *E = (ENode*)malloc(sizeof(ENode));
 94         E->index = j;
 95         E->info = info;
 96         E->next = G->p[i].first;//头插法
 97         G->p[i].first = E;
 98     }
 99 }
100 //求每个顶点的入度
101 int Indegree[MAX_VERTEX_NUM] = { 0 };//记录入度
102 void VexIndegree(AGraph *G)
103 {
104     for (int i = 0; i < G->vexnum; i++)
105     {
106         if (G->p[i].first != NULL)
107         {
108             ENode* e = G->p[i].first;
109             while (e != NULL)
110             {
111                 Indegree[e->index]++;
112                 e = e->next;
113             }
114         }
115     }
116 }
117 
118 //拓扑排序
119 void Topsort(AGraph *G)
120 {
121     Queue *Q = CreateQueue();
122     VexIndegree(G);
123     for (int i = 0; i < G->vexnum; i++)//先将入度为0的点全部入队
124     {
125         if (Indegree[i] == 0)
126             Enqueue(Q, LocateVex(G,G->p[i].data));
127     }
128     while (!isempty(Q))//当队列不空
129     {
130         
131         int v=Dequeue(Q);//出队
132         if (G->p[v].first != NULL)//若v的存在邻接点
133         {
134             ENode* e = G->p[v].first;
135             while (e != NULL)
136             {
137                 if (--Indegree[e->index] == 0)//将v的邻接点的入度皆减1，若为0，则入队
138                     Enqueue(Q, e->index);
139                 e = e->next;
140             }
141         }
142     }
143     cout << "拓扑排序：" << endl;
144     for (int i = 0; i < G->vexnum; i++)
145         cout << Q->array[i] << " ";
146 }
147 int main()
148 {
149     AGraph* G = (AGraph*)malloc(sizeof(AGraph));
150     CreateAGraph(G);
151     Topsort(G);
152     system("pause");
153     return 0;
154 }