public class PrioQueue<Key extends Comparable<Key>>
{
   public Key[] pq;
   public int N;

   public PrioQueue(int cap)
   {
      pq = (Key[]) new Comparable[ cap + 1 ];
   }

   public int size()
   {
      return N;
   }

   public boolean isEmpty()
   {
      return N == 0 ;
   }

   public void insert(Key key)
   {
      N++;                // One more entry
      pq[N] = key;        // Insert in left most open position

      filterUp(N);        // Filter up....
   }

   public Key peek()
   {
      return pq[1];
   }

   public Key poll()
   {
      Key r = pq[1];       // Save return value

      exchange( 1, N );	   // Exchange root with left most entry at lowest level
      N--;                 // One less entry

      filterDown(1);       // Filter root node down

      return r;
   }

   /* ================================= helper functions =========== */

   private void filterUp( int k )
   {
      int parent;

      parent = k/2;

      while ( k > 1 /* not root */ && greater( parent, k) )
      {
	 exchange( k, parent );		// Exchange with parent

	 k = parent;			// Go up 1 level
	 parent = k/2;			// Update it's parent 
      }
   }

   private void filterDown( int k )
   {
      int c1, c2;

      while ( 2*k <= N )
      {
	 c1 = 2*k;         // c1 = left child
	 c2 = c1 + 1;	   // c2 = right child

         if ( c2 <= N && greater(c1, c2) )
            c1 = c2;                     // c1 = smallest child

         if ( ! greater( k, c1 ) )
	    break;                  // In order, stop

         exchange(k, c1);           // Exchange parent with smallest child

         k = c1;		    // Continue down the tree
      }
   }


   private boolean greater( int i, int j )
   {
      return pq[i].compareTo(pq[j]) > 0 ;
   }

   private void exchange(int i, int j)
   {
      Key h;

      h = pq[i];
      pq[i] = pq[j];
      pq[j] = h;
   }

   /* ============================ Print */

   void printPQ()
   {
      System.out.println("vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv");
      showR( 1, 0 );
      System.out.println("^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^");
   }

   public void showR(int t, int h)
   {
      if (t > N)
         return;

      showR(2*t+1, h+1);
      printnode(t, h);
      showR(2*t, h+1);
   }

   public void printnode(int x, int h)
   {
      for (int i = 0; i < h; i++)
         System.out.print("    ");

      System.out.println("[" + pq[x] + "]");
   }

}