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import java.util.Arrays;

public class Main {

  private static final int INF = Integer.MAX_VALUE;

  public void dijkstra(int[][] graph, int source) {
    int n = graph.length;
    int[] dist = new int[n]; // array to store shortest distances
    boolean[] visited = new boolean[n]; // array to mark visited nodes
    int[] pred = new int[n]; // array to store predecessors
    
    Arrays.fill(dist, INF); // initialize distances as infinity
    dist[source] = 0; // distance from source to source is 0

    for (int i = 0; i < n - 1; i++) {  
      // select the vertex with the minimum distance
      int u = minDistance(dist, visited);
      visited[u] = true; // mark the vertex as visited

      // update distances of adjacent vertices
      for (int v = 0; v < n; v++) {
        if (!visited[v] && graph[u][v] != 0 && dist[u] != INF && dist[u] + graph[u][v] < dist[v]) {
          dist[v] = dist[u] + graph[u][v];
          pred[v] = u; // store predecessor
        }
      }
    }
    printPathAndDistances(source, dist, pred); // print the shortest path and distances
  }

  // helper function to find the vertex with the minimum distance
  private int minDistance(int[] dist, boolean[] visited) {
    int minDist = INF;
    int minVertex = -1;
    
    for (int i = 0; i < dist.length; i++) {
      if (!visited[i] && dist[i] < minDist) {
        minDist = dist[i];
        minVertex = i;
      }
    }
    return minVertex;
  }

  // helper function to print the shortest path and distances
  private void printPathAndDistances(int source, int[] dist, int[] pred) {
    System.out.println("Shortest distances from the source:");
    for (int i = 0; i < dist.length; i++) {
      System.out.println("Vertex " + i + ": " + dist[i]);
      if (dist[i] != INF) {
        System.out.print("Path: " + i);
        int predVertex = pred[i];
        while (predVertex != source) {
          System.out.print(" <- " + predVertex);
          predVertex = pred[predVertex];
        }
        System.out.println(" <- " + source);
      }
    }
  }

  public static void main(String[] args) {
    int[][] graph = {
      { 0, 2, 0, 1, 0 },
      { 2, 0, 4, 3, 0 },
      { 0, 4, 0, 0, 6 },
      { 1, 3, 0, 0, 5 },
      { 0, 0, 6, 5, 0 },
    };
    Main dijkstra = new Main();
    dijkstra.dijkstra(graph, 0);
  }
}
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