标签：struct subsets int graph Kruskal 最小 edges edge 代码
1 // C program for Kruskal's algorithm to find Minimum
2 // Spanning Tree of a given connected, undirected and
3 // weighted graph
4 #include <stdio.h>
5 #include <stdlib.h>
6 #include <string.h>
7
8 // a structure to represent a weighted edge in graph
9 struct Edge {
10 int src, dest, weight;
11 };
12
13 // a structure to represent a connected, undirected
14 // and weighted graph
15 struct Graph {
16 // V-> Number of vertices, E-> Number of edges
17 int V, E;
18
19 // graph is represented as an array of edges.
20 // Since the graph is undirected, the edge
21 // from src to dest is also edge from dest
22 // to src. Both are counted as 1 edge here.
23 struct Edge* edge;
24 };
25
26 // Creates a graph with V vertices and E edges
27 struct Graph* createGraph(int V, int E)
28 {
29 struct Graph* graph = (struct Graph*)(malloc(sizeof(struct Graph)));
30 graph->V = V;
31 graph->E = E;
32
33 graph->edge = (struct Edge*)malloc(sizeof( struct Edge)*E);
34
35 return graph;
36 }
37
38 // A structure to represent a subset for union-find
39 struct subset {
40 int parent;
41 int rank;
42 };
43
44 // A utility function to find set of an element i
45 // (uses path compression technique)
46 int find(struct subset subsets[], int i)
47 {
48 // find root and make root as parent of i
49 // (path compression)
50 if (subsets[i].parent != i)
51 subsets[i].parent
52 = find(subsets, subsets[i].parent);
53
54 return subsets[i].parent;
55 }
56
57 // A function that does union of two sets of x and y
58 // (uses union by rank)
59 void Union(struct subset subsets[], int x, int y)
60 {
61 int xroot = find(subsets, x);
62 int yroot = find(subsets, y);
63
64 // Attach smaller rank tree under root of high
65 // rank tree (Union by Rank)
66 if (subsets[xroot].rank < subsets[yroot].rank)
67 subsets[xroot].parent = yroot;
68 else if (subsets[xroot].rank > subsets[yroot].rank)
69 subsets[yroot].parent = xroot;
70
71 // If ranks are same, then make one as root and
72 // increment its rank by one
73 else
74 {
75 subsets[yroot].parent = xroot;
76 subsets[xroot].rank++;
77 }
78 }
79
80 // Compare two edges according to their weights.
81 // Used in qsort() for sorting an array of edges
82 int myComp(const void* a, const void* b)
83 {
84 struct Edge* a1 = (struct Edge*)a;
85 struct Edge* b1 = (struct Edge*)b;
86 return a1->weight > b1->weight;
87 }
88
89 // The main function to construct MST using Kruskal's
90 // algorithm
91 void KruskalMST(struct Graph* graph)
92 {
93 int V = graph->V;
94 struct Edge
95 result[V]; // Tnis will store the resultant MST
96 int e = 0; // An index variable, used for result[]
97 int i = 0; // An index variable, used for sorted edges
98
99 // Step 1: Sort all the edges in non-decreasing
100 // order of their weight. If we are not allowed to
101 // change the given graph, we can create a copy of
102 // array of edges
103 qsort(graph->edge, graph->E, sizeof(graph->edge[0]),
104 myComp);
105
106 // Allocate memory for creating V ssubsets
107 struct subset* subsets
108 = (struct subset*)malloc(V * sizeof(struct subset));
109
110 // Create V subsets with single elements
111 for (int v = 0; v < V; ++v) {
112 subsets[v].parent = v;
113 subsets[v].rank = 0;
114 }
115
116 // Number of edges to be taken is equal to V-1
117 while (e < V - 1 && i < graph->E) {
118 // Step 2: Pick the smallest edge. And increment
119 // the index for next iteration
120 struct Edge next_edge = graph->edge[i++];
121
122 int x = find(subsets, next_edge.src);
123 int y = find(subsets, next_edge.dest);
124
125 // If including this edge does't cause cycle,
126 // include it in result and increment the index
127 // of result for next edge
128 if (x != y) {
129 result[e++] = next_edge;
130 Union(subsets, x, y);
131 }
132 // Else discard the next_edge
133 }
134
135 // print the contents of result[] to display the
136 // built MST
137 printf(
138 "Following are the edges in the constructed MST\n");
139 int minimumCost = 0;
140 for (i = 0; i < e; ++i)
141 {
142 printf("%d -- %d == %d\n", result[i].src,
143 result[i].dest, result[i].weight);
144 minimumCost += result[i].weight;
145 }
146 printf("Minimum Cost Spanning tree : %d",minimumCost);
147 return;
148 }
149
150 // Driver program to test above functions
151 int main()
152 {
153 /* Let us create following weighted graph
154 10
155 0--------1
156 | \ |
157 6| 5\ |15
158 | \ |
159 2--------3
160 4 */
161 int V = 4; // Number of vertices in graph
162 int E = 5; // Number of edges in graph
163 struct Graph* graph = createGraph(V, E);
164
165 // add edge 0-1
166 graph->edge[0].src = 0;
167 graph->edge[0].dest = 1;
168 graph->edge[0].weight = 10;
169
170 // add edge 0-2
171 graph->edge[1].src = 0;
172 graph->edge[1].dest = 2;
173 graph->edge[1].weight = 6;
174
175 // add edge 0-3
176 graph->edge[2].src = 0;
177 graph->edge[2].dest = 3;
178 graph->edge[2].weight = 5;
179
180 // add edge 1-3
181 graph->edge[3].src = 1;
182 graph->edge[3].dest = 3;
183 graph->edge[3].weight = 15;
184
185 // add edge 2-3
186 graph->edge[4].src = 2;
187 graph->edge[4].dest = 3;
188 graph->edge[4].weight = 4;
189
190 KruskalMST(graph);
191
192 return 0;
193 }
$gcc -o main *.c
$main
Following are the edges in the constructed MST 2 -- 3 == 4 0 -- 3 == 5 0 -- 1 == 10 Minimum Cost Spanning tree : 19
标签：struct,subsets,int,graph,Kruskal,最小,edges,edge,代码 来源： https://www.cnblogs.com/hulianxingkong/p/15201777.html
本站声明： 1. iCode9 技术分享网（下文简称本站）提供的所有内容，仅供技术学习、探讨和分享； 2. 关于本站的所有留言、评论、转载及引用，纯属内容发起人的个人观点，与本站观点和立场无关； 3. 关于本站的所有言论和文字，纯属内容发起人的个人观点，与本站观点和立场无关； 4. 本站文章均是网友提供，不完全保证技术分享内容的完整性、准确性、时效性、风险性和版权归属；如您发现该文章侵犯了您的权益，可联系我们第一时间进行删除； 5. 本站为非盈利性的个人网站，所有内容不会用来进行牟利，也不会利用任何形式的广告来间接获益，纯粹是为了广大技术爱好者提供技术内容和技术思想的分享性交流网站。