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- // A C++ program for Dijkstra's single source shortest path algorithm.
- // The program is for adjacency matrix representation of the graph
- #include <limits.h>
- #include <stdio.h>
- // Number of vertices in the graph
- #define V 9
- // A utility function to find the vertex with minimum distance value, from
- // the set of vertices not yet included in shortest path tree
- int minDistance(int dist[], bool sptSet[])
- {
- // Initialize min value
- int min = INT_MAX, min_index;
- for (int v = 0; v < V; v++)
- if (sptSet[v] == false && dist[v] <= min)
- min = dist[v], min_index = v;
- return min_index;
- }
- // A utility function to print the constructed distance array
- int printSolution(int dist[])
- {
- printf("Vertex \t\t Distance from Source\n");
- for (int i = 0; i < V; i++)
- printf("%d \t\t %d\n", i, dist[i]);
- }
- // Function that implements Dijkstra's single source shortest path algorithm
- // for a graph represented using adjacency matrix representation
- void dijkstra(int graph[V][V], int src)
- {
- int dist[V]; // The output array. dist[i] will hold the shortest
- // distance from src to i
- bool sptSet[V]; // sptSet[i] will be true if vertex i is included in shortest
- // path tree or shortest distance from src to i is finalized
- // Initialize all distances as INFINITE and stpSet[] as false
- for (int i = 0; i < V; i++)
- dist[i] = INT_MAX, sptSet[i] = false;
- // Distance of source vertex from itself is always 0
- dist[src] = 0;
- // Find shortest path for all vertices
- for (int count = 0; count < V - 1; count++) {
- // Pick the minimum distance vertex from the set of vertices not
- // yet processed. u is always equal to src in the first iteration.
- int u = minDistance(dist, sptSet);
- // Mark the picked vertex as processed
- sptSet[u] = true;
- // Update dist value of the adjacent vertices of the picked vertex.
- for (int v = 0; v < V; v++)
- // Update dist[v] only if is not in sptSet, there is an edge from
- // u to v, and total weight of path from src to v through u is
- // smaller than current value of dist[v]
- if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX
- && dist[u] + graph[u][v] < dist[v])
- dist[v] = dist[u] + graph[u][v];
- }
- // print the constructed distance array
- printSolution(dist);
- }
- // driver program to test above function
- int main()
- {
- /* Let us create the example graph discussed above */
- int graph[V][V] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
- { 4, 0, 8, 0, 0, 0, 0, 11, 0 },
- { 0, 8, 0, 7, 0, 4, 0, 0, 2 },
- { 0, 0, 7, 0, 9, 14, 0, 0, 0 },
- { 0, 0, 0, 9, 0, 10, 0, 0, 0 },
- { 0, 0, 4, 14, 10, 0, 2, 0, 0 },
- { 0, 0, 0, 0, 0, 2, 0, 1, 6 },
- { 8, 11, 0, 0, 0, 0, 1, 0, 7 },
- { 0, 0, 2, 0, 0, 0, 6, 7, 0 } };
- dijkstra(graph, 0);
- return 0;
- }
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