# C Program to Find Shortest Path using Dijkstra’s Algorithm

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This is a C Program to find Dijkstra algorithm. Dijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree. Like Prim’s MST, we generate a SPT (shortest path tree) with given source as root. We maintain two sets, one set contains vertices included in shortest path tree, other set includes vertices not yet included in shortest path tree. At every step of the algorithm, we find a vertex which is in the other set (set of not yet included) and has minimum distance from source.

Here is source code of the C Program to Find the Shortest Path Between Two Vertices Using Dijkstra’s Algorithm. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

1. `#include <stdio.h>`
2. `#include <limits.h>`
3. ` `
4. `// Number of vertices in the graph`
5. `#define V 9`
6. ` `
7. `// A utility function to find the vertex with minimum distance value, from`
8. `// the set of vertices not yet included in shortest path tree`
9. `int minDistance(int dist[], int sptSet[]) {`
10. `    // Initialize min value`
11. `    int min = INT_MAX, min_index;`
12. `    int v;`
13. `    for (v = 0; v < V; v++)`
14. `        if (sptSet[v] == 0 && dist[v] <= min)`
15. `            min = dist[v], min_index = v;`
16. ` `
17. `    return min_index;`
18. `}`
19. ` `
20. `// A utility function to print the constructed distance array`
21. `void printSolution(int dist[], int n) {`
22. `    printf("Vertex   Distance from Source\n");`
23. `    int i;`
24. `    for (i = 0; i < V; i++)`
25. `        printf("%d \t\t %d\n", i, dist[i]);`
26. `}`
27. ` `
28. `// Funtion that implements Dijkstra's single source shortest path algorithm`
29. `// for a graph represented using adjacency matrix representation`
30. `void dijkstra(int graph[V][V], int src) {`
31. `    int dist[V]; // The output array.  dist[i] will hold the shortest`
32. `    // distance from src to i`
33. ` `
34. `    int sptSet[V]; // sptSet[i] will 1 if vertex i is included in shortest`
35. `    // path tree or shortest distance from src to i is finalized`
36. ` `
37. `    // Initialize all distances as INFINITE and stpSet[] as 0`
38. `    int i, count, v;`
39. `    for (i = 0; i < V; i++)`
40. `        dist[i] = INT_MAX, sptSet[i] = 0;`
41. ` `
42. `    // Distance of source vertex from itself is always 0`
43. `    dist[src] = 0;`
44. ` `
45. `    // Find shortest path for all vertices`
46. `    for (count = 0; count < V - 1; count++) {`
47. `        // Pick the minimum distance vertex from the set of vertices not`
48. `        // yet processed. u is always equal to src in first iteration.`
49. `        int u = minDistance(dist, sptSet);`
50. ` `
51. `        // Mark the picked vertex as processed`
52. `        sptSet[u] = 1;`
53. ` `
54. `        // Update dist value of the adjacent vertices of the picked vertex.`
55. `        for (v = 0; v < V; v++)`
56. ` `
57. `            // Update dist[v] only if is not in sptSet, there is an edge from`
58. `            // u to v, and total weight of path from src to  v through u is`
59. `            // smaller than current value of dist[v]`
60. `            if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX && dist[u]`
61. `                    + graph[u][v] < dist[v])`
62. `                dist[v] = dist[u] + graph[u][v];`
63. `    }`
64. ` `
65. `    // print the constructed distance array`
66. `    printSolution(dist, V);`
67. `}`
68. ` `
69. `// driver program to test above function`
70. `int main() {`
71. `    /* Let us create the example graph discussed above */`
72. `    int graph[V][V] =  {{0, 4, 0, 0, 0, 0, 0, 8, 0},`
73. `                        {4, 0, 8, 0, 0, 0, 0, 11, 0},`
74. `                        {0, 8, 0, 7, 0, 4, 0, 0, 2},`
75. `                        {0, 0, 7, 0, 9, 14, 0, 0, 0},`
76. `                        {0, 0, 0, 9, 0, 10, 0, 0, 0},`
77. `                        {0, 0, 4, 0, 10, 0, 2, 0, 0},`
78. `                        {0, 0, 0, 14, 0, 2, 0, 1, 6},`
79. `                        {8, 11, 0, 0, 0, 0, 1, 0, 7},`
80. `                        {0, 0, 2, 0, 0, 0, 6, 7, 0}`
81. `                       };`
82. ` `
83. `    dijkstra(graph, 0);`
84. ` `
85. `    return 0;`
86. `}`

Output:

```\$ gcc Dijkstra.c
\$ ./a.out

Vertex   Distance from Source
0 		 0
1 		 4
2 		 12
3 		 19
4 		 21
5 		 11
6 		 9
7 		 8
8 		 14```

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