Create Dijkstra.c

Dijkstra.c

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+#include <stdio.h>
+#include <limits.h>
+#include <stdbool.h>
+// Number of vertices in the graph
+#define V 14
+
+// 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;
+}
+
+// Function to print shortest path from source to j
+// using parent array
+void printPath(int parent[], int j)
+{
+    // Base Case : If j is source
+    if (parent[j]==-1)
+        return;
+
+    printPath(parent, parent[j]);
+
+    printf("%d ", j);
+}
+
+// A utility function to print the constructed distance
+// array
+int printSolution(int dist[], int n, int parent[])
+{
+    int src = 0;
+    printf("Vertex\t  Distance\tPath");
+    for (int i = 1; i < V; i++)
+    {
+        printf("\n%d -> %d \t\t %d\t\t%d ", src, i, dist[i], src);
+        printPath(parent, i);
+    }
+}
+
+// Funtion 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
+
+    // sptSet[i] will true if vertex i is included / in shortest
+    // path tree or shortest distance from src to i is finalized
+    bool sptSet[V];
+
+    // Parent array to store shortest path tree
+    int parent[V];
+
+    // Initialize all distances as INFINITE and stpSet[] as false
+    for (int i = 0; i < V; i++)
+    {
+        parent[0] = -1;
+        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 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] + graph[u][v] < dist[v])
+            {
+                parent[v]  = u;
+                dist[v] = dist[u] + graph[u][v];
+            }  
+    }
+
+    // print the constructed distance array
+    printSolution(dist, V, parent);
+}
+
+// driver program to test above function
+int main()
+{
+    /* Let us create the example graph discussed above */
+    int graph[V][V] = {{0, 4, 5, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0},
+
+{4, 0, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+{5, 9, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ,0}, 
+{0, 1, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0},
+{0, 0, 0, 1, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0},   // Choosing the vertex 0 as source 
+{8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0},
+{0, 0, 0 ,3 ,0, 5, 0, 1, 0, 0, 0, 0, 0, 0},
+{0, 0, 0, 0, 0, 0 ,1 ,0, 0, 0, 0, 0, 0, 0},
+{0, 0, 1, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0},
+{0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 0, 9, 1, 0},
+{0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 6, 0},
+{0, 0, 0, 0, 0, 0, 0, 0 ,0 ,9 ,1 ,0 ,0 ,4},
+{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0},
+{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0},
+                      };
+
+    dijkstra(graph, 0);
+
+    return 0;
+}