拓扑排序(有向图)
作者：互联网
拓扑排序步骤：
1.在有向图中选一个没有前驱的顶点且输出之。
2.从图中删除该顶点和所有以它为尾的弧。
思考：
1.采用图的十字链表存储结构，可以方便的查找结点的出度和入度。
2.拓扑排序不唯一。
实现：
1 void TopoSort(OLGraph G)
2 {
3 int i = 0;
4 int count = 0;
5 SeqStack S;
6 ArcNode* P = NULL;
7 int indegree[MAXVEX] = { 0 };
8
9 for (i = 0; i < G.vexnum; i++)//求各个顶点入度并存入indegree数组
10 {
11 P = G.vertex[i].head;
12 while (P)
13 {
14 indegree[i]++;
15 P = P->hnext;
16 }
17 }
18
19 S.top = -1;//初始化栈
20 for (i = 0; i < G.vexnum; i++)
21 {
22 if (indegree[i] == 0)
23 {
24 PushStack(&S, i);
25 }
26 }
27
28 while (S.top != -1)//非空栈
29 {
30 count++;
31 PopStack(&S, &i);
32 printf("%c", G.vertex[i].vexdata);
33 for (P = G.vertex[i].tail; P; P = P->tnext)//对所有弧尾为i的边，其弧头点入度减1
34 {
35 i = P->headvex;
36 indegree[i]--;
37 if (indegree[i] == 0)
38 {
39 PushStack(&S, i);
40 }
41 }
42 }
43
44 if (count < G.vexnum)
45 {
46 printf("该有向网有回路");
47 }
48 }
源代码：
1 #define _CRT_SECURE_NO_WARNINGS
2 #include <stdio.h>
3 #include <stdlib.h>
4 #define MAXVEX 20
5
6 typedef struct ArcNode
7 {
8 int tailvex;
9 int headvex;
10 struct ArcNode* tnext;
11 struct ArcNode* hnext;
12 }ArcNode;
13
14 typedef struct VexNode
15 {
16 char vexdata;
17 ArcNode* tail;
18 ArcNode* head;
19 }VexNode;
20
21 typedef struct
22 {
23 int vexnum;
24 int arcnum;
25 VexNode vertex[MAXVEX];
26 }OLGraph;//Orthogonal List Graph
27
28 typedef struct
29 {
30 int top;
31 int elem[MAXVEX];
32 }SeqStack;//定长顺序栈
33
34 void PushStack(SeqStack* S, int elem)
35 {
36 if (S->top == MAXVEX - 1)
37 {
38 printf("栈满");
39 exit(1);
40 }
41 else
42 {
43 S->top++;
44 S->elem[S->top] = elem;
45 }
46 }
47
48 void PopStack(SeqStack* S, int* elem)
49 {
50 if (S->top == -1)
51 {
52 printf("栈空");
53 exit(1);
54 }
55 else
56 {
57 (*elem) = S->elem[S->top];
58 S->top--;
59 }
60 }
61
62 void TopoSort(OLGraph G)
63 {
64 int i = 0;
65 int count = 0;
66 SeqStack S;
67 ArcNode* P = NULL;
68 int indegree[MAXVEX] = { 0 };
69
70 for (i = 0; i < G.vexnum; i++)//求各个顶点入度并存入indegree数组
71 {
72 P = G.vertex[i].head;
73 while (P)
74 {
75 indegree[i]++;
76 P = P->hnext;
77 }
78 }
79
80 S.top = -1;//初始化栈
81 for (i = 0; i < G.vexnum; i++)
82 {
83 if (indegree[i] == 0)
84 {
85 PushStack(&S, i);
86 }
87 }
88
89 while (S.top != -1)//非空栈
90 {
91 count++;
92 PopStack(&S, &i);
93 printf("%c", G.vertex[i].vexdata);
94 for (P = G.vertex[i].tail; P; P = P->tnext)//对所有弧尾为i的边，其弧头点入度减1
95 {
96 i = P->headvex;
97 indegree[i]--;
98 if (indegree[i] == 0)
99 {
100 PushStack(&S, i);
101 }
102 }
103 }
104
105 if (count < G.vexnum)
106 {
107 printf("该有向网有回路");
108 }
109 }
110
111
112 //返回顶点vex在十字链表G中的位置
113 int LocateVex(OLGraph G, char vex)
114 {
115 int i = 0;
116 for (i = 0; i < G.vexnum; i++)
117 {
118 if (G.vertex[i].vexdata == vex)
119 {
120 return i;
121 }
122 }
123 return -1;
124 }
125
126 void Create(OLGraph* G)
127 {
128 int i = 0, j = 0, k = 0;
129 char tail = '\0';
130 char head = '\0';
131 ArcNode* P = NULL;
132 ArcNode* Pre = NULL;
133
134 printf("请输入顶点数和边数(逗号分隔)：");
135 scanf("%d%*c%d", &G->vexnum, &G->arcnum);
136
137 for (i = 0; i < G->vexnum; i++)
138 {
139 printf("请输入第%d个顶点：", i + 1);
140 scanf(" %c", &G->vertex[i].vexdata);//%c前有一空格用于吸收空白字符
141 G->vertex[i].tail = NULL;
142 G->vertex[i].head = NULL;
143 }
144
145 for (k = 0; k < G->arcnum; k++)
146 {
147 printf("请输入第%d条边的两端点(逗号分隔)：", k + 1);
148 scanf(" %c%*c%c", &tail, &head);
149 i = LocateVex(*G, tail);
150 j = LocateVex(*G, head);
151
152 P = (ArcNode*)calloc(1, sizeof(ArcNode));
153 P->tailvex = i;
154 P->headvex = j;
155
156 if (G->vertex[i].tail == NULL)//链接到相同弧尾域
157 {
158 G->vertex[i].tail = P;
159 }
160 else
161 {
162 Pre = G->vertex[i].tail;
163 while (Pre->tnext)
164 {
165 Pre = Pre->tnext;
166 }
167 Pre->tnext = P;
168 }
169
170 if (G->vertex[j].head == NULL)//链接到相同弧头域
171 {
172 G->vertex[j].head = P;
173 }
174 else
175 {
176 Pre = G->vertex[j].head;
177 while (Pre->hnext)
178 {
179 Pre = Pre->hnext;
180 }
181 Pre->hnext = P;
182 }
183 }
184 }
185
186 int main(void)
187 {
188 OLGraph G;
189 Create(&G);
190 TopoSort(G);
191 system("pause");
192 return 0;
193 }
源代码
标签：Pre,有向图,int,indegree,拓扑,vertex,++,ArcNode,排序 来源： https://www.cnblogs.com/lvhui123/p/15851794.html