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1 // A C program for Prim's Minimum
2 // Spanning Tree (MST) algorithm. The program is
3 // for adjacency matrix representation of the graph
4 #include <limits.h>
5 #include <stdbool.h>
6 #include <stdio.h>
7 // Number of vertices in the graph
8 #define V 5
9
10 // A utility function to find the vertex with
11 // minimum key value, from the set of vertices
12 // not yet included in MST
13 int minKey(int key[], bool mstSet[])
14 {
15 // Initialize min value
16 int min = INT_MAX, min_index;
17
18 for (int v = 0; v < V; v++)
19 if (mstSet[v] == false && key[v] < min)
20 min = key[v], min_index = v;
21
22 return min_index;
23 }
24
25 // A utility function to print the
26 // constructed MST stored in parent[]
27 int printMST(int parent[], int graph[V][V])
28 {
29 printf("Edge \tWeight\n");
30 for (int i = 1; i < V; i++)
31 printf("%d - %d \t%d \n", parent[i], i, graph[i][parent[i]]);
32 }
33
34 // Function to construct and print MST for
35 // a graph represented using adjacency
36 // matrix representation
37 void primMST(int graph[V][V])
38 {
39 // Array to store constructed MST
40 int parent[V];
41 // Key values used to pick minimum weight edge in cut
42 int key[V];
43 // To represent set of vertices included in MST
44 bool mstSet[V];
45
46 // Initialize all keys as INFINITE
47 for (int i = 0; i < V; i++)
48 key[i] = INT_MAX, mstSet[i] = false;
49
50 // Always include first 1st vertex in MST.
51 // Make key 0 so that this vertex is picked as first vertex.
52 key[0] = 0;
53 parent[0] = -1; // First node is always root of MST
54
55 // The MST will have V vertices
56 for (int count = 0; count < V - 1; count++) {
57 // Pick the minimum key vertex from the
58 // set of vertices not yet included in MST
59 int u = minKey(key, mstSet);
60
61 // Add the picked vertex to the MST Set
62 mstSet[u] = true;
63
64 // Update key value and parent index of
65 // the adjacent vertices of the picked vertex.
66 // Consider only those vertices which are not
67 // yet included in MST
68 for (int v = 0; v < V; v++)
69
70 // graph[u][v] is non zero only for adjacent vertices of m
71 // mstSet[v] is false for vertices not yet included in MST
72 // Update the key only if graph[u][v] is smaller than key[v]
73 if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v])
74 parent[v] = u, key[v] = graph[u][v];
75 }
76
77 // print the constructed MST
78 printMST(parent, graph);
79 }
80
81 // driver program to test above function
82 int main()
83 {
84 /* Let us create the following graph
85 2 3
86 (0)--(1)--(2)
87 | / \ |
88 6| 8/ \5 |7
89 | / \ |
90 (3)-------(4)
91 9 */
92 int graph[V][V] = { { 0, 2, 0, 6, 0 },
93 { 2, 0, 3, 8, 5 },
94 { 0, 3, 0, 0, 7 },
95 { 6, 8, 0, 0, 9 },
96 { 0, 5, 7, 9, 0 } };
97
98 // Print the solution
99 primMST(graph);
100
101 return 0;
102 }
$gcc -o main *.c
$main
Edge Weight
0 - 1 2
1 - 2 3
0 - 3 6
1 - 4 5
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