Dijkstra’s shortest path algorithm

dij.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;

		for (int v = 0; v < V; v++)
			if (sptSet[v] == false && dist[v] <= min)
			{
				min = dist[v];
				min_index = v;
			}

		return min_index;
	}

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

	// Funtion 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;
			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++)

				// Update dist[v] only if is not in sptSet, there is an
				// edge from u to v, and total weight of path from src to
				// v through u is smaller than current value of dist[v]
				// check - 
				// 1. if the vertex has not been finalized
				// 2. if there exists a path
				// 3. there can be no value greate then v(if it's set to INF). So no need to update
				// 4. the main conditio
				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];
			
			// suppose we want to find minimum distance till a particular node eg at 8
			// if(sptSet[8] == true) 
			//   break;
		}

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

	// 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);
	}
}