title: null-pointer exception when coding bellmanFord algo
body: <p>i have a null pointer exception in my computePaths() method, please help me find the reason why. below is my code and below my code is the output i have</p>
  
  <p>Vertex class:</p>
  
  <pre><code>class Vertex implements Comparable&lt;Vertex&gt; {
      String name;
      Double minDistance = Double.POSITIVE_INFINITY;
      Vertex previous;
      Edge[] adjacencies;
  
      public String toString() {
          return name;
      }
  
      public Vertex(String argName) {
          name = argName;
      }
  
      @Override
      public int compareTo(Vertex other) {
          return Double.compare(minDistance, other.minDistance);
      }
  
  }
  </code></pre>
  
  <p>Edge class:</p>
  
  <pre><code>class Edge {
      Double weight;
      Vertex target;
  
      public Edge(Vertex argTarget, Double argWeight) {
          target = argTarget;
          weight = argWeight;
      }
  }
  </code></pre>
  
  <p>Class for the algorithm:</p>
  
  <pre><code>public class BellmanFord {
      public static void computePaths(Vertex source, Vertex[] vertices) {
          source.minDistance = 0.0;
          PriorityQueue&lt;Vertex&gt; vq = new PriorityQueue&lt;Vertex&gt;();
          vq.add(source);
  
          for (int i = 1; i &lt; vertices.length - 1; i++) {
  
              while (!vq.isEmpty()) {
  
                  Vertex u = vq.poll();
                  for (Edge e : u.adjacencies) {
                      Vertex v = e.target;
                      System.out.println(u + " " + e.target);
                      Double weight = e.weight;
                      Double distanceThroughU = u.minDistance + weight;
                      if (distanceThroughU &lt; v.minDistance) {
                          vq.remove(v);
                          v.minDistance = distanceThroughU;
                          v.previous = u;
                          vq.add(v);
                      }
                  }
              }
          }
      }
  
      public static List&lt;Vertex&gt; getShortestPathTo(Vertex target) {
          List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
          for (Vertex v = target; v != null; v = v.previous) {
              path.add(v);
          }
          Collections.reverse(path);
          return path;
      }
  
      public static void main(String[] args) {
          Vertex a = new Vertex("A");
          Vertex b = new Vertex("B");
          Vertex c = new Vertex("C");
          Vertex d = new Vertex("D");
          Vertex e = new Vertex("E");
  
          a.adjacencies = new Edge[] { new Edge(b, -1.0), new Edge(c, 4.0) };
          b.adjacencies = new Edge[] { new Edge(d, 2.0), new Edge(c, 3.0), new Edge(e, 2.0) };
          d.adjacencies = new Edge[] { new Edge(b, 1.0) };
          e.adjacencies = new Edge[] { new Edge(d, -3.0) };
  
          Vertex[] vertices = { b, c, d, e };
          computePaths(a, vertices);
  
          for (Vertex v : vertices) {
              System.out.println(" distance to " + v.toString() + " is " + v.minDistance);
              System.out.println("path is " + getShortestPathTo(v));
          }
      }
  }
  </code></pre>
  
  <p>and here is my output</p>
  
  <pre><code>A B
  A C
  B D
  B C
  B E
  D B
  E D
  D B
  Exception in thread "main" java.lang.NullPointerException
      at BellmanFord.computePaths(BellmanFord.java:50)
      at BellmanFord.main(BellmanFord.java:106)
  </code></pre>
  
  <p>so line 50 is  <code>for(Edge e : u.adjacencies)</code> and line 106 is <code>computePaths(a,vertices);</code></p>