ShortestPath.java

// A Java program for Dijkstra's single source shortest path algorithm. 
// The program is for adjacency matrix representation of the graph 
import java.util.*; 
import java.lang.*; 
import java.io.*; 

class ShortestPath { 
	// A utility function to find the vertex with minimum distance value, 
	// from the set of vertices not yet included in shortest path tree 
	static final int V = 9; 
  
	int minDistance(int dist[], Boolean sptSet[]) 
	{ 
		// Initialize min value 
		int min = Integer.MAX_VALUE, min_index = -1; 
    //looking for each vertex that is not visited and find the sortest path one.
    // so it will go from left to right 0, 1,2,3 but will pick one that has lesser weight so 3 can have lesser distance from 0 so it will iterate every time and picked
    // the shortet unpicked v
		for (int v = 0; v < V; v++) 
			if (sptSet[v] == false && dist[v] <= min) { 
				min = dist[v]; 
				min_index = v; 
			} 
    // its index is most needed so that we can look up in to main graph matrix.
		return min_index; 
	} 

	// A utility function to print the constructed distance array 
	void printSolution(int dist[]) 
	{ 
		System.out.println("Vertex \t\t Distance from Source"); 
		for (int i = 0; i < V; i++) 
			System.out.println(i + " \t\t " + dist[i]); 
	} 

	// Function that implements Dijkstra's single source shortest path 
	// algorithm for a graph represented using adjacency matrix 
	// representation 
	void dijkstra(int graph[][], int src) 
	{ 
		int dist[] = new int[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 
		Boolean sptSet[] = new Boolean[V]; 

		// Initialize all distances as INFINITE and stpSet[] as false 
		for (int i = 0; i < V; i++) { 
			dist[i] = Integer.MAX_VALUE; // that will tell which is not proccessed means if any distance in Integer.MAX_VALUE that means there is not perfect route to it.
			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++) 

			
        // it should not visited and must have route to it and  dist[u] present it is reachable or not. 
        // dist[u] + graph[u][v] < dist[v] // this means to reach at dist[v] do we have any shorter way if yes then replace it.
				if (!sptSet[v] && graph[u][v] != 0 && dist[u] != Integer.MAX_VALUE && dist[u] + graph[u][v] < dist[v]) 
					dist[v] = dist[u] + graph[u][v]; 
		} 

		// print the constructed distance array 
		printSolution(dist); 
	} 

	// Driver method 
	public static void main(String[] args) 
	{ 
		/* Let us create the example graph discussed above */
		int graph[][] = new int[][] { { 0, 4, 0, 0, 0, 0, 0, 8, 0 }, 
									{ 4, 0, 8, 0, 0, 0, 0, 11, 0 }, 
									{ 0, 8, 0, 7, 0, 4, 0, 0, 2 }, 
									{ 0, 0, 7, 0, 9, 14, 0, 0, 0 }, 
									{ 0, 0, 0, 9, 0, 10, 0, 0, 0 }, 
									{ 0, 0, 4, 14, 10, 0, 2, 0, 0 }, 
									{ 0, 0, 0, 0, 0, 2, 0, 1, 6 }, 
									{ 8, 11, 0, 0, 0, 0, 1, 0, 7 }, 
									{ 0, 0, 2, 0, 0, 0, 6, 7, 0 } }; 
		ShortestPath t = new ShortestPath(); 
		t.dijkstra(graph, 0); 
	} 
} 
// This code is contributed by Aakash Hasija