图的最短路径（Dijkstra）（Floyd），拓扑排序，生成树代码

使用邻接矩阵存储加权图，无穷大使用常数MAXLEN代表，然后使用Dijkstra方法求取最短路径

 1 #include <stdio.h>
 2 
 3 #define MAXLEN 1000
 4 int cost[7][7];
 5 int dist[7];
 6 
 7 void creategraph(int* node,int num)
 8 {
 9     int from;
10     int to;
11     int i;
12     for(i = 0;i < num; i++)
13     {
14         from = node[i*3];
15         to = node[i*3+1];
16         cost[from][to] = node[i*3+2];
17     }
18 }
19 
20 void shortestpath(int begin,int num)
21 {
22     int selected[7];
23     int min;
24     int s;
25     int i,j;
26     
27     for(i = 2;i <= num;i++)
28     {
29         selected[i] = 0;
30         dist[i] = cost[begin][i];
31     }
32     selected[begin] = 1;
33     dist[begin] = 0;
34     printf("顶点1     2     3     4     5     6\n");
35     for(j = 1;j <= num;j++)
36         printf(" %4d ",dist[j]);
37     printf("\n");
38     for(i = 1;i <= num - 1;i++)
39     {
40         min = MAXLEN;
41         for(j = 1;j <= num;j++)
42             if(min > dist[j] && selected[j] == 0)
43             {
44                 s = j;
45                 min = dist[j];
46             }
47         selected[s] = 1;
48         for(j = 1;j <= num;j++)
49         {
50             if(selected[j] == 0 &&
51                 dist[s] + cost[s][j] < dist[j])
52                 dist[j] = dist[s] + cost[s][j];
53             printf(" %4d ",dist[j]);
54         }
55         printf("\n");
56     }
57 }
58 
59 int main()
60 {
61     int node[7][3] = {
62         { 1, 2, 35},
63         { 2, 3, 45},
64         { 2, 4, 30},
65         { 3, 5, 25},
66         { 4, 5, 45},
67         { 4, 6, 130},
68         { 5, 6, 100},
69     };
70     int i,j;
71     
72     for(i = 1;i <= 6;i++)
73         for(j = 1;j <= 6;j++)
74             cost[i][j] = MAXLEN;
75     creategraph(node,7);
76     printf("加权图的邻接矩阵内容：\n");
77     for(i = 1;i <= 6;i++)
78     {
79         for(j = 1;j <= 6;j++)
80             printf(" %4d ",cost[i][j]);
81         printf("\n");
82     }
83     printf("\n从顶点1到各顶点最近距离计算过程：\n");
84     shortestpath(1,6);
85 }

改用Floyd方法计算各顶点到其他各顶点的最短距离

 1 #include <stdio.h>
 2 
 3 #define MAXLEN 1000
 4 int cost[7][7];
 5 int dist[7][7];
 6 
 7 void creategraph(int* node,int num)
 8 {
 9     int from;
10     int to;
11     int i;
12     for(i = 0;i < num; i++)
13     {
14         from = node[i*3];
15         to = node[i*3+1];
16         cost[from][to] = node[i*3+2];
17         cost[to][from] = node[i*3+2];
18     }
19 }
20 
21 void shortestpath(int num)
22 {
23     int i,j,k;
24     for(i = 1;i <= num;i++)
25         for(j = 1;j <= num;j++)
26             if(i != j)
27                 dist[i][j] = cost[i][j];
28             else
29                 dist[i][j] = 0;
30     for(k = 1;k <= num;k++)
31         for(i = 1;i <= num;i++)
32             for(j = 1;j <= num;j++)
33                 if(dist[i][k] + dist[k][j] < dist[i][j])
34                     dist[i][j] = dist[i][k] + dist[k][j];
35 }
36 
37 int main()
38 {
39     int node[7][3] = {
40         { 1, 2, 35},
41         { 2, 3, 45},
42         { 2, 4, 30},
43         { 3, 5, 25},
44         { 4, 5, 45},
45         { 4, 6, 130},
46         { 5, 6, 100},
47     };
48     int i,j;
49     
50     for(i = 1;i <= 6;i++)
51         for(j = 1;j <= 6;j++)
52             cost[i][j] = MAXLEN;
53     creategraph(node,7);
54     printf("加权图的邻接矩阵内容：\n");
55     for(i = 1;i <= 6;i++)
56     {
57         for(j = 1;j <= 6;j++)
58             printf(" %4d ",cost[i][j]);
59         printf("\n");
60     }
61     shortestpath(6);
62     printf("\n从各顶点到各顶点最近距离：\n");
63     printf("顶点1     2     3     4     5     6\n");
64     for(i = 1;i <= 6;i++)
65     {
66         for(j = 1;j <= 6;j++)
67             printf(" %4d ",dist[i][j]);
68         printf("\n");
69     }
70     
71 }

导入一个包含回路和不包含回路的图，然后将拓扑排序的内容输出来

  1 #include <stdlib.h>
  2 #include <stdio.h>
  3 
  4 #define MAXQUEUE 20
  5 
  6 struct node
  7 {
  8     int vertex;
  9     struct node* nextnode;
 10 };
 11 
 12 typedef struct node* graph;
 13 struct node head1[8];
 14 struct node head2[8];
 15 
 16 int queue[MAXQUEUE];
 17 int front = -1;
 18 int rear = -1;
 19 
 20 void creategraph(graph head,int* node,int num)
 21 {
 22     graph newnode;
 23     graph ptr;
 24     int from;
 25     int to;
 26     int i;
 27     
 28     for(i = 0;i < num;i++)
 29     {
 30         from = node[i*2];
 31         to = node[i*2+1];
 32         head[to].vertex += 1;
 33         newnode = (graph)malloc(sizeof(struct node));
 34         newnode->vertex = to;
 35         newnode->nextnode = NULL;
 36         ptr = &(head[from]);
 37         while(ptr->nextnode != NULL)
 38             ptr = ptr->nextnode;
 39         ptr->nextnode = newnode;
 40     }
 41 }
 42 
 43 int enqueue(int value)
 44 {
 45     if(rear + 1 == front ||
 46       (rear == (MAXQUEUE - 1) && front <= 0))
 47         return -1;
 48     rear++;
 49     if(rear == MAXQUEUE)
 50         rear = 0;
 51     queue[rear] = value;
 52 }
 53 
 54 int dequeue()
 55 {
 56     if(front == rear)
 57         return -1;
 58     front++;
 59     if(front == MAXQUEUE)
 60         front = 0;
 61     return queue[front];
 62 }
 63 
 64 int toposort(graph head,int num)
 65 {
 66     graph ptr;
 67     int i;
 68     
 69     for(i = 1;i <= num;i++)
 70         if(head[i].vertex == 0)
 71             enqueue(i);
 72     while((i = dequeue()) != -1)
 73     {
 74         printf(" %d ",i);
 75         ptr = head[i].nextnode;
 76         while(ptr != NULL)
 77         {
 78             i = ptr->vertex;
 79             head[i].vertex --;
 80             if(head[i].vertex == 0)
 81                 enqueue(i);
 82             ptr = ptr->nextnode;
 83         }
 84     }
 85     printf("\n");
 86     for(i = 1;i <= num;i++)
 87         if(head[i].vertex != 0)
 88             return 1;
 89         return 0;
 90 }
 91 
 92 int main()
 93 {
 94     graph ptr;
 95     int node[10][2] = {
 96         { 3, 2},
 97         { 2, 1},
 98         { 2, 5},
 99         { 2, 6},
100         { 1, 4},
101         { 5, 4},
102         { 7, 4},
103         { 6, 7},
104         { 5, 6},
105         { 7, 5}
106     };
107     int i;
108     for(i = 1;i <= 7;i++)
109     {
110         head1[i].vertex = 0;
111         head1[i].nextnode = NULL;
112         head2[i].vertex = 0;
113         head2[i].nextnode = NULL;
114     }
115     creategraph(head1,node,8);
116     creategraph(head2,node,10);
117     printf("图1 - 含入度的邻接表内容：\n");
118     for(i = 1;i <= 7;i++)
119     {
120         printf("顶点%d(%d) =>",i,head1[i].vertex);
121         ptr = head1[i].nextnode;
122         while(ptr != NULL)
123         {
124             printf(" %d ",ptr->vertex);
125             ptr = ptr->nextnode;
126         }
127         printf("\n");
128     }
129     printf("图1 - 拓扑排序的内容：\n");
130     if(toposort(head1,7))
131         printf("图有回路\n");
132     else
133         printf("图没有回路\n");
134     front = rear = -1;
135     printf("\n图2 - 含入度的邻接表内容：\n");
136     for(i = 1;i <= 7;i++)
137     {
138         printf("顶点%d(%d) =>",i,head2[i].vertex);
139         ptr = head2[i].nextnode;
140         while(ptr != NULL)
141         {
142             printf(" %d ",ptr->vertex);
143             ptr = ptr->nextnode;
144         }
145         printf("\n");
146     }
147     printf("图2 - 拓扑排序的内容：\n");
148     if(toposort(head2,7))
149         printf("图有回路\n");
150     else
151         printf("图没有回路\n");
152     return 0;
153 }

图的最小生成树

  1 #include <stdlib.h>
  2 #include <stdio.h>
  3 
  4 struct edge
  5 {
  6     int from;
  7     int to;
  8     int weight;
  9     struct edge* nextedge;
 10 };
 11 
 12 typedef struct edge* edgelist;
 13 edgelist list = NULL;
 14 int node[6];
 15 
 16 edgelist createedgelist(edgelist list,int* edges,int num)
 17 {
 18     edgelist newnode;
 19     edgelist last;
 20     int i;
 21     
 22     for(i = 0;i < num;i++)
 23     {
 24         newnode = (edgelist)malloc(sizeof(struct edge));
 25         newnode->from = edges[3*i];
 26         newnode->to = edges[3*i+1];
 27         newnode->weight = edges[3*i+2];
 28         newnode->nextedge = NULL;
 29         if(list == NULL)
 30         {
 31             list = newnode;
 32             last = list;
 33         }
 34         else
 35         {
 36             last->nextedge = newnode;
 37             last = newnode;
 38         }
 39     }
 40     return list;
 41 }
 42 
 43 int uniongroup(int from,int to)
 44 {
 45     int to_root;
 46     to_root = to;
 47     while(node[to_root] > 0)
 48         to_root = node[to_root];
 49     node[to_root] = from;
 50 }
 51 
 52 int samegroup(int from,int to)
 53 {
 54     int from_root;
 55     int to_root;
 56     
 57     from_root = from;
 58     while(node[from_root] > 0)
 59         from_root = node[from_root];
 60     to_root = to;
 61     while(node[to_root] > 0)
 62         to_root = node[to_root];
 63     if(from_root == to_root)
 64         return 1;
 65     else
 66         return 0;
 67 }
 68 
 69 void minspantree()
 70 {
 71     edgelist ptr;
 72     
 73     ptr = list;
 74     while(ptr != NULL)
 75     {
 76         if(!samegroup(ptr->from,ptr->to))
 77         {
 78             printf("从顶点： %d 到： %d 权值： %d\n",ptr->from,
 79                    ptr->to,ptr->weight);
 80             uniongroup(ptr->from,ptr->to);
 81         }
 82         ptr = ptr->nextedge;
 83     }
 84 }
 85 
 86 int main()
 87 {
 88     int edges[8][3] = {
 89         { 1, 2, 2},
 90         { 2, 4, 3},
 91         { 1, 4, 4},
 92         { 3, 5, 5},
 93         { 2, 5, 6},
 94         { 2, 3, 8},
 95         { 3, 4, 10},
 96         { 4, 5, 15}
 97     };
 98     int i;
 99     list = createedgelist(list,edges,8);
100     for(i = 1;i <= 5;i++)
101         node[i] = -1;
102     printf("图的最小生成树：\n");
103     minspantree();
104     printf("顶点数组内容：\n");
105     for(i = 1;i <= 5;i++)
106         printf("[%d]",node[i]);
107     printf("\n");
108     return 0;
109 }

posted @ 2021-01-02 22:21 互联星空阅读(198) 评论(0) 收藏举报

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图的最短路径（Dijkstra）（Floyd），拓扑排序，生成树代码

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