Printing Paths in Dijkstra's Shortest Path Algorithm

Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph.
We have discussed Dijkstra's Shortest Path algorithm in the below posts. 

• Dijkstra’s shortest path for adjacency matrix representation
• Dijkstra’s shortest path for adjacency list representation

The implementations discussed above only find shortest distances, but do not print paths. In this post-printing of paths is discussed. 

Example:

Input: Consider below graph and source as 0,

👁 Image

Output

Vertex Distance Path
0 -> 1 4 0 1 
0 -> 2 12 0 1 2 
0 -> 3 19 0 1 2 3 
0 -> 4 21 0 7 6 5 4 
0 -> 5 11 0 7 6 5 
0 -> 6 9 0 7 6 
0 -> 7 8 0 7 
0 -> 8 14 0 1 2 8 

The idea is to create a separate array parent[]. Value of parent[v] for a vertex v stores parent vertex of v in shortest path tree. The parent of the root (or source vertex) is -1. Whenever we find a shorter path through a vertex u, we make u as a parent of the current vertex.

Once we have the parent array constructed, we can print the path using the below recursive function.

void printPath(int parent[], int j)
{
 // Base Case : If j is source
 if (parent[j]==-1)
 return;

 printPath(parent, parent[j]);

 printf("%d ", j);
}

Below is the complete implementation:

Vertex Distance Path
0 -> 1 4 0 1 
0 -> 2 12 0 1 2 
0 -> 3 19 0 1 2 3 
0 -> 4 21 0 7 6 5 4 
0 -> 5 11 0 7 6 5 
0 -> 6 9 0 7 6 
0 -> 7 8 0 7 
0 -> 8 14 0 1 2 8 

Time Complexity:- O(V^2)
Space Complexity:- O(V^2)