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Print All Paths in Dijkstra's Shortest Path Algorithm
Objective: Given a graph and a source vertex write an algorithm to find the shortest path from the source vertex to all the vertices and print the paths all well.
Example:
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We will use the same approach with some extra steps to print the paths from the source vertex to all the vertices.
Use the parent [] to keep track of parent vertices. Say if parent[x] = y then for vertex ‘x' the parent vertex is ‘y' which means the shortest path to vertex ‘x' goes via vertex ‘y', i.e ‘source>y>x'
The parent of source vertex will be 1.
Once the algorithm is completed, the parent [] will have all the information to print the path. Use recursion to print the paths.
public void printPathUtil(int parent[], int destination){
//if vertex is source then stop recursion
if(parent[destination] == 1) {
System.out.print("0 ");
return;
}
printPathUtil(parent, parent[destination]);
System.out.print(destination + " ");
}
Complete Code:
Output:
Dijkstra Algorithm: (With all paths) 0> 0: distance=0 Path : 0 0> 1: distance=4 Path : 0 2 1 0> 2: distance=3 Path : 0 2 0> 3: distance=6 Path : 0 2 1 3 0> 4: distance=8 Path : 0 2 1 3 4 0> 5: distance=14 Path : 0 2 1 3 4 5
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