Steps of Working of PriorityQueue:

• Below are the steps explaining how PriorityQueue works internally in the Java Collection Framework:
  1. Creation of PriorityQueue:
     • We create a new PriorityQueue as follows:
       PriorityQueue<Integer> pq = new PriorityQueue<>();
     • A new PriorityQueue object is created internally using a min-heap (implemented via a dynamic array). Initially, it is empty and ready to store elements.

     • _____________________________
       |     |     |     |     |     |
       -----------------------------
       (Index positions of internal array)
                               

  2. Adding Elements (Insertion):
     • We add elements using the add() or offer() method:
       pq.add(30);
pq.add(10);
pq.add(20);
pq.add(40);
     • When an element is inserted, it is added at the end of the array and then adjusted using the heapify-up process to maintain the min-heap property.
     • Let’s see step-by-step how the internal structure forms:
       • Step 1: Add 30 → First element, becomes the root.
         

                   (30)
         
         Internal array:
         ______________________
         | 30 |     |     |     |
         ------------------------
         (Index: 0)
                                         

       • Step 2: Add 10 → Goes to next position (index 1). Now, 10 < 30 → swap occurs to maintain min-heap.

                   (10)
                   /
                 (30)
         
         Internal array:
         ______________________
         | 10 | 30 | | |
         ------------------------
         (Index: 0 1)
                                                                     

       • Step 3: Add 20 → Goes to index 2. 20 > 10 → Heap property valid, no swap required.

                   (10)
                   /   \
                (30)   (20)
         
         Internal array:
         __________________________
         | 10 | 30 | 20 |     |
         --------------------------
         (Index: 0   1    2)
                                         

       • Step 4: Add 40 → Goes to index 3. 40 > 30 → Heap property valid, no swap required.

                   (10)
                   /   \
                (30)   (20)
                /
             (40)
         
         Internal array representation:
         ______________________________________
         | 10 | 30 | 20 | 40 |     |     |
         --------------------------------------
         (Index: 0   1    2    3)
                                         

  3. Retrieving Element (Using peek()):
     • The peek() method retrieves the head element of the PriorityQueue without removing it.
     • The head is always the smallest element (in natural ordering).
     • Example:

     System.out.println(pq.peek()); // Output → 10

     • Internal representation (Heap Structure):

       ______________________________________
       | 10 | 30 | 20 | 40 |    |    |
       --------------------------------------
       ↑
       Head element (smallest)
                               

     • Even though the internal array appears unsorted, the smallest element is always at the head of the queue.
  4. Removing Element (Using poll()):
     • The poll() method removes and returns the head element from the PriorityQueue.
     • After removal, the last element (40) temporarily moves to the root position, and then the heapify-down process restores order.
     • Example:

     System.out.println(pq.poll()); // Output → 10

     • Before removing (10 is head):

       ______________________________________
       | 10 | 30 | 20 | 40 |    |    |
       --------------------------------------
       ↑
       Head element (to be removed)
                               

     • After removing 10 and reordering heap:

       ______________________________________
       | 20 | 30 | 40 |    |    |    |
       --------------------------------------
       ↑
       New head (smallest after reordering)
                               

     • The PriorityQueue automatically maintains its heap structure internally after each removal.
  5. Custom Ordering (Using Comparator):
     • By default, PriorityQueue arranges elements in ascending order (min-heap).
     • You can create a max-heap using a custom comparator:
       PriorityQueue<Integer> pq = new PriorityQueue<>((a, b) -> b - a);
     • In a max-heap, the largest element has the highest priority and becomes the root:

                 (40)
                 /   \
              (30)   (20)
              /
           (10)
       
       Internal array representation:
       ______________________________________
       | 40 | 30 | 20 | 10 |     |     |
       --------------------------------------
       (Index: 0   1    2    3)
                               

PriorityQueue is Good for:

1. Automatic element ordering:
   • PriorityQueue automatically arranges elements in their natural order (for Comparable objects) or based on a custom Comparator.
   • Ideal for problems where elements must be processed according to priority, not just insertion order.
2. Efficient retrieval of highest/lowest priority element:
   • peek() and poll() always operate on the head element (the smallest or highest priority).
   • Useful in algorithms like Dijkstra’s shortest path, Huffman coding, and task scheduling systems.
3. Good for dynamic data processing:
   • As new elements are inserted, the heap structure automatically adjusts using heapify-up and heapify-down operations.
   • Ensures that the most important element is always accessible at O(1) time.
4. Flexible ordering (Min-Heap or Max-Heap):
   • By default, PriorityQueue is a Min-Heap.
   • You can create a Max-Heap using:

     PriorityQueue<Integer> pq = new PriorityQueue<>((a, b) -> b - a);

PriorityQueue is Not Good for:

1. Random access or traversal:
   • PriorityQueue does not allow efficient random access to elements.
   • Internally backed by a heap, not an ordered list — so accessing arbitrary elements is O(n).
2. Preserving insertion order:
   • Elements are ordered by priority, not by the order of insertion.
   • Not suitable when insertion order matters, e.g., for FIFO structures.
3. Thread safety:
   • PriorityQueue is not thread-safe.
   • Use PriorityBlockingQueue for concurrent or multithreaded environments.
4. Null elements not allowed:
   • Adding null throws a NullPointerException.
   • Because null cannot be compared with other elements.

Summary Table: