C++ Program to Implement Dijkstra’s Algorithm Using Set

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This is a C++ Program to find shortest path. 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.
Below are the detailed steps used in Dijkstra’s algorithm to find the shortest path from a single source vertex to all other vertices in the given graph.
Algorithm
1) Create a set sptSet (shortest path tree set) that keeps track of vertices included in shortest path tree, i.e., whose minimum distance from source is calculated and finalized. Initially, this set is empty.
2) Assign a distance value to all vertices in the input graph. Initialize all distance values as INFINITE. Assign distance value as 0 for the source vertex so that it is picked first.
3) While sptSet doesn’t include all vertices
….a) Pick a vertex u which is not there in sptSetand has minimum distance value.
….b) Include u to sptSet.
….c) Update distance value of all adjacent vertices of u. To update the distance values, iterate through all adjacent vertices. For every adjacent vertex v, if sum of distance value of u (from source) and weight of edge u-v, is less than the distance value of v, then update the distance value of v.

Here is source code of the C++ Program to Implement Dijkstra’s Algorithm Using Set. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. // A C++ program for Dijkstra's single source shortest path algorithm.
  2. // The program is for adjacency matrix representation of the graph
  3.  
  4. #include <stdio.h>
  5. #include <limits.h>
  6.  
  7. // Number of vertices in the graph
  8. #define V 9
  9.  
  10. // A utility function to find the vertex with minimum distance value, from
  11. // the set of vertices not yet included in shortest path tree
  12. int minDistance(int dist[], bool sptSet[])
  13. {
  14.     // Initialize min value
  15.     int min = INT_MAX, min_index;
  16.  
  17.     for (int v = 0; v < V; v++)
  18.         if (sptSet[v] == false && dist[v] <= min)
  19.             min = dist[v], min_index = v;
  20.  
  21.     return min_index;
  22. }
  23.  
  24. // A utility function to print the constructed distance array
  25. int printSolution(int dist[], int n)
  26. {
  27.     printf("Vertex   Distance from Source\n");
  28.     for (int i = 0; i < V; i++)
  29.         printf("%d \t\t %d\n", i, dist[i]);
  30. }
  31.  
  32. // Funtion that implements Dijkstra's single source shortest path algorithm
  33. // for a graph represented using adjacency matrix representation
  34. void dijkstra(int graph[V][V], int src)
  35. {
  36.     int dist[V]; // The output array.  dist[i] will hold the shortest
  37.     // distance from src to i
  38.  
  39.     bool sptSet[V]; // sptSet[i] will true if vertex i is included in shortest
  40.     // path tree or shortest distance from src to i is finalized
  41.  
  42.     // Initialize all distances as INFINITE and stpSet[] as false
  43.     for (int i = 0; i < V; i++)
  44.         dist[i] = INT_MAX, sptSet[i] = false;
  45.  
  46.     // Distance of source vertex from itself is always 0
  47.     dist[src] = 0;
  48.  
  49.     // Find shortest path for all vertices
  50.     for (int count = 0; count < V - 1; count++)
  51.     {
  52.         // Pick the minimum distance vertex from the set of vertices not
  53.         // yet processed. u is always equal to src in first iteration.
  54.         int u = minDistance(dist, sptSet);
  55.  
  56.         // Mark the picked vertex as processed
  57.         sptSet[u] = true;
  58.  
  59.         // Update dist value of the adjacent vertices of the picked vertex.
  60.         for (int v = 0; v < V; v++)
  61.  
  62.             // Update dist[v] only if is not in sptSet, there is an edge from
  63.             // u to v, and total weight of path from src to  v through u is
  64.             // smaller than current value of dist[v]
  65.             if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX && dist[u]
  66.                     + graph[u][v] < dist[v])
  67.                 dist[v] = dist[u] + graph[u][v];
  68.     }
  69.  
  70.     // print the constructed distance array
  71.     printSolution(dist, V);
  72. }
  73.  
  74. // driver program to test above function
  75. int main()
  76. {
  77.     /* Let us create the example graph discussed above */
  78.     int graph[V][V] =
  79.             { { 0, 4, 0, 0, 0, 0, 0, 8, 0 }, { 4, 0, 8, 0, 0, 0, 0, 11, 0 }, {
  80.                     0, 8, 0, 7, 0, 4, 0, 0, 2 },
  81.                     { 0, 0, 7, 0, 9, 14, 0, 0, 0 }, { 0, 0, 0, 9, 0, 10, 0, 0,
  82.                             0 }, { 0, 0, 4, 0, 10, 0, 2, 0, 0 }, { 0, 0, 0, 14,
  83.                             0, 2, 0, 1, 6 }, { 8, 11, 0, 0, 0, 0, 1, 0, 7 }, {
  84.                             0, 0, 2, 0, 0, 0, 6, 7, 0 } };
  85.  
  86.     dijkstra(graph, 0);
  87.  
  88.     return 0;
  89. }

Output:

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$ g++ DijkstraUsingSet.cpp
$ a.out
 
Vertex   Distance from Source
0 		 0
1 		 4
2 		 12
3 		 19
4 		 21
5 		 11
6 		 9
7 		 8
8 		 14
------------------
(program exited with code: 0)
Press return to continue

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter