Java Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time

This Java program is to Implement weighted graph and find shortest path from one source vertex to every other vertex. Dijkstra’s Algorithm can be used to achieve this goal.

Here is the source code of the Java Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

//This is a java program to find the shortest path from one vertex to all other vertex

```
import java.util.HashSet;
```

import java.util.InputMismatchException;

```
import java.util.Iterator;
```
```
import java.util.Scanner;
```
```
import java.util.Set;
```
```
 
```
```
public class Shortest_Path_to_AllVertex
```
```
{
```
```
    private int          distances[];
```
```
    private Set<Integer> settled;
```
```
    private Set<Integer> unsettled;
```

    private int          number_of_nodes;

    private int          adjacencyMatrix[][];

```
 
```

    public Shortest_Path_to_AllVertex(int number_of_nodes)

```
    {
```

        this.number_of_nodes = number_of_nodes;

        distances = new int[number_of_nodes + 1];

        settled = new HashSet<Integer>();

        unsettled = new HashSet<Integer>();

        adjacencyMatrix = new int[number_of_nodes + 1][number_of_nodes + 1];

```
    }
```
```
 
```

    public void shortestPath(int adjacency_matrix[][], int source)

```
    {
```
```
        int evaluationNode;
```

        for (int i = 1; i <= number_of_nodes; i++)

            for (int j = 1; j <= number_of_nodes; j++)

                adjacencyMatrix[i][j] = adjacency_matrix[i][j];

```
 
```

        for (int i = 1; i <= number_of_nodes; i++)

```
        {
```

            distances[i] = Integer.MAX_VALUE;

```
        }
```
```
 
```
```
        unsettled.add(source);
```
```
        distances[source] = 0;
```
```
        while (!unsettled.isEmpty())
```
```
        {
```

            evaluationNode = getNodeWithMinimumDistanceFromUnsettled();

            unsettled.remove(evaluationNode);

            settled.add(evaluationNode);

            evaluateNeighbours(evaluationNode);

```
        }
```
```
    }
```
```
 
```

    private int getNodeWithMinimumDistanceFromUnsettled()

```
    {
```
```
        int min;
```
```
        int node = 0;
```
```
 
```

        Iterator<Integer> iterator = unsettled.iterator();

```
        node = iterator.next();
```
```
        min = distances[node];
```

        for (int i = 1; i <= distances.length; i++)

```
        {
```
```
            if (unsettled.contains(i))
```
```
            {
```

                if (distances[i] <= min)

```
                {
```
```
                    min = distances[i];
```
```
                    node = i;
```
```
                }
```
```
            }
```
```
        }
```
```
        return node;
```
```
    }
```
```
 
```

    private void evaluateNeighbours(int evaluationNode)

```
    {
```
```
        int edgeDistance = -1;
```
```
        int newDistance = -1;
```
```
 
```

        for (int destinationNode = 1; destinationNode <= number_of_nodes; destinationNode++)

```
        {
```

            if (!settled.contains(destinationNode))

```
            {
```

                if (adjacencyMatrix[evaluationNode][destinationNode] != Integer.MAX_VALUE)

```
                {
```

                    edgeDistance = adjacencyMatrix[evaluationNode][destinationNode];

                    newDistance = distances[evaluationNode] + edgeDistance;

                    if (newDistance < distances[destinationNode])

```
                    {
```

                        distances[destinationNode] = newDistance;

```
                    }
```

                    unsettled.add(destinationNode);

```
                }
```
```
            }
```
```
        }
```
```
    }
```
```
 
```

    public static void main(String... arg)

```
    {
```
```
        int adjacency_matrix[][];
```
```
        int number_of_vertices;
```
```
        int source = 0;
```

        Scanner scan = new Scanner(System.in);

```
        try
```
```
        {
```

            System.out.println("Enter the number of vertices");

            number_of_vertices = scan.nextInt();

            adjacency_matrix = new int[number_of_vertices + 1][number_of_vertices + 1];

```
 
```

            System.out.println("Enter the Weighted Matrix for the graph");

            for (int i = 1; i <= number_of_vertices; i++)

```
            {
```

                for (int j = 1; j <= number_of_vertices; j++)

```
                {
```

                    adjacency_matrix[i][j] = scan.nextInt();

```
                    if (i == j)
```
```
                    {
```

                        adjacency_matrix[i][j] = 0;

```
                        continue;
```
```
                    }
```

                    if (adjacency_matrix[i][j] == 0)

```
                    {
```

                        adjacency_matrix[i][j] = Integer.MAX_VALUE;

```
                    }
```
```
                }
```
```
            }
```
```
 
```

            System.out.println("Enter the source ");

```
            source = scan.nextInt();
```
```
 
```

            Shortest_Path_to_AllVertex sp = new Shortest_Path_to_AllVertex(

                    number_of_vertices);

            sp.shortestPath(adjacency_matrix, source);

```
 
```

            System.out.println("The Shorted Path from " + source

                    + " to all other nodes are: ");

            for (int i = 1; i <= sp.distances.length - 1; i++)

```
            {
```
```
 
```

                System.out.println(source + " to " + i + " is "

                        + sp.distances[i]);

```
            }
```

        } catch (InputMismatchException inputMismatch)

```
        {
```

            System.out.println("Wrong Input Format");

```
        }
```
```
        scan.close();
```
```
    }
```
```
}
```

Output:

$ javac Shortest_Path_to_AllVertex.java
$ java Shortest_Path_to_AllVertex
 
Enter the number of vertices
5
Enter the Weighted Matrix for the graph
0 9 6 5 3 
0 0 0 0 0
0 2 0 4 0
0 0 0 0 0
0 0 0 0 0
Enter the source 
1
The Shorted Path from 1 to all other nodes are: 
1 to 1 is 0
1 to 2 is 8
1 to 3 is 6
1 to 4 is 5
1 to 5 is 3

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