我可以在O（M log N）时间内完成此操作吗？

Question

所以我正在实现Dijkstra的算法，我在尝试减少它的运行时遇到了麻烦。理想情况下，O（M log N）运行时会很棒。

这是我的代码：

import static jdk.nashorn.internal.runtime.regexp.joni.Syntax.Java;

import java.util.Scanner;

public class Dijkstra {
  public static void main(String[] args) {

     int [][] A = new int[50010][60];
     int [][] W = new int[50010][60];
     int []   deg = new int[50010];


     int N, M, S;

     Scanner scan = new Scanner(System.in);
     N = scan.nextInt(); // # cities
     M = scan.nextInt(); // # train routes
     S = scan.nextInt(); // capital city
     // System.out.println(N + " " + M + " " + S);


     for(int i = 1; i <=N; ++i) {
       deg[i] = 0;  // initialize the degree of each vertex to 0
     }

     for(int i = 1; i <= M; ++i) {
       int u, v, w;
       u = scan.nextInt(); // origin
       v = scan.nextInt(); // destination
       w = scan.nextInt(); // # days
       // System.out.println(u + " " + v + " " + w);
       A[u][deg[u]] = v; // adding an edge (u,v) to the graph
       W[u][deg[u]] = w; // set its weight to w
       deg[u]++; // increase degree of vertex u by 1
     }

     //for(int i = 1; i <= N; ++i) {
     //  System.out.println("vertex:" + i + "'s neighbors");
     //  for(int j = 0; j < deg[i]; ++j) {
     //    System.out.println(A[i][j] + " " + W[i][j]);
     //  }
     //}

     // compute distance from U to S by Dijkstra's algorithm
     // Dijkstra's algorithm
     for(int U = 1; U <= N; ++U) {

       // initialization
       int[] visited = new int[50010];
       int[] dist = new int[50010];
       for(int V = 1; V <= N; ++V) {
         dist[V] = 100000000;
         visited[V] = 0;
       }

       // actual algorithm
       dist[U] = 0;
       for(int k = 1; k <= N; ++k) {
         // repeat the following N times

         //find an unvisited vertex with minimum distance
         int min = 100000000;
         int minVertex = 1;
         for(int i = 1; i<=N; ++i) {
           if(visited[i] == 0 && dist[i] < min) {
             min = dist[i];
             minVertex = i;
           }
         }

         visited[minVertex] = 1;
         // relax the edges that are adjacent to minVertex to update the           shortest path distance to
         // neighbors of minVertex

         for(int j = 0; j<deg[minVertex]; ++j) {
           // A[minVertex][j] is the j-th neighbor of minVertex
           // W[minVertex][j] is the weight of the corresponding edge
           int newDist = dist[minVertex] + W[minVertex][j];
           if (newDist < dist[A[minVertex][j]]) {
             dist[A[minVertex][j]] = newDist;
           }
         }


       }

       if(dist[S] == 100000000) {
         System.out.print("-1 ");
       }
       else {
         System.out.print(dist[S] + " ");
       }


     }

     System.out.println("");

   }


 }

我无法让它在O（M log N）时间运行。我知道我必须在某个地方实施堆，但我不知道在哪里。

非常感谢任何帮助。