Priority Queue Introduction and Concept in DSA Java - Execution Trace

Concept Flow - Priority Queue Introduction and Concept

Create empty priority queue

↓

Insert element with priority

↓

Place element in queue based on priority

↓

Remove element with highest priority

↓

Return element and adjust queue

↓

Repeat insert/remove as needed

Shows how elements enter the priority queue by priority and how the highest priority element is removed first.

Execution Sample

DSA Java

PriorityQueue<Integer> pq = new PriorityQueue<>();
pq.add(30);
pq.add(10);
pq.add(20);
System.out.println(pq.poll());

Adds three numbers to the priority queue and removes the smallest (highest priority) element.

Execution Table

Step	Operation	Nodes in Queue	Pointer Changes	Visual State
1	Create empty queue	[]	head=null	null
2	Add 30	[30]	head=30	30
3	Add 10	[10, 30]	head=10	10 -> 30
4	Add 20	[10, 20, 30]	head=10	10 -> 20 -> 30
5	Poll (remove highest priority)	[20, 30]	head=20	20 -> 30
6	Print polled element	[20, 30]	head=20	10 printed
7	End	[20, 30]	head=20	20 -> 30

💡 Polling removes the smallest element 10, queue adjusts with 20 as new head.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	Final
pq (queue elements)	[]	[30]	[10, 30]	[10, 20, 30]	[20, 30]	[20, 30]
head (smallest element)	null	30	10	10	20	20

Key Moments - 3 Insights

Why does the smallest number come out first when polling?

Because PriorityQueue in Java by default orders elements by natural order, so the smallest element has the highest priority and is at the head (see execution_table step 5).

What happens to the queue after polling an element?

The polled element is removed and the queue reorders itself to keep the next smallest element at the head (see execution_table step 5 and 7).

Is the internal order of elements always sorted like a list?

No, the internal structure is a heap, so only the head is guaranteed to be the smallest; other elements are partially ordered (see visual state in execution_table).

Visual Quiz - 3 Questions

Look at the execution_table, what is the head of the queue after adding 10 and 30?

A 10

B 30

C 20

D null

💡 Hint

Check execution_table row 3 for head value after adding 10.

At which step does the queue remove the smallest element?

A Step 3

B Step 5

C Step 4

D Step 2

💡 Hint

Look for 'Poll' operation in execution_table.

If we add 5 instead of 30 first, what would be the new head after adding 10 and 5?

A 10

B 30

C 5

D null

💡 Hint

PriorityQueue orders by smallest element; see variable_tracker for head changes.

Concept Snapshot

Priority Queue stores elements with priorities.
The element with highest priority (smallest number by default) is removed first.
Insertion places elements to keep priority order.
Polling removes and returns the highest priority element.
Implemented as a heap internally for efficiency.

Full Transcript

A Priority Queue is a special queue where elements come out in order of priority, not just arrival. In Java, the PriorityQueue class orders elements by their natural order, so the smallest element has the highest priority. When you add elements, they are placed internally so the smallest is always at the front. When you remove (poll), the smallest element is taken out and the queue adjusts to keep the next smallest at the front. This is efficient because it uses a heap structure internally. The example code adds 30, 10, and 20, then polls the queue to remove the smallest element, which is 10. The queue then contains 20 and 30, with 20 as the new head.

Practice

1. What is the main characteristic of a Priority Queue compared to a regular queue?

easy

A. Elements are dequeued based on their priority, not just order of insertion

B. Elements are always dequeued in the order they were inserted

C. It only stores elements of the same value

D. It does not allow duplicate elements

Solution

1. Step 1: Understand queue behavior

   A regular queue removes elements in the order they were added (FIFO).

2. Step 2: Understand priority queue behavior

   A priority queue removes elements based on priority, not insertion order.

3. Final Answer:

   Elements are dequeued based on their priority, not just order of insertion -> Option A

4. Quick Check:

   Priority Queue = Priority-based removal [OK]

Hint: Priority queue removes highest priority first, not oldest [OK]

Common Mistakes:

• Confusing priority queue with FIFO queue
• Thinking priority queue sorts elements permanently
• Assuming duplicates are not allowed

2. Which of the following is the correct way to declare a Priority Queue of integers in Java?

easy

A. PriorityQueue<int> pq = new PriorityQueue<>();

B. PriorityQueue<Integer> pq = new PriorityQueue<>();

C. PriorityQueue pq = new PriorityQueue<int>();

D. PriorityQueue<Integer> pq = new PriorityQueue<int>();

Solution

1. Step 1: Use wrapper class for generics

   Java generics require wrapper classes, so use Integer, not int.

2. Step 2: Correct generic syntax

   Use diamond operator <> on the right side without type inside.

3. Final Answer:

   PriorityQueue<Integer> pq = new PriorityQueue<>(); -> Option B

4. Quick Check:

   Use wrapper Integer and diamond operator [OK]

Hint: Use wrapper classes (Integer) with generics, not primitives [OK]

Common Mistakes:

• Using primitive types (int) with generics
• Specifying type twice on right side
• Not using diamond operator

3. What will be the output of the following Java code?

import java.util.*;
public class TestPQ {
  public static void main(String[] args) {
    PriorityQueue<Integer> pq = new PriorityQueue<>();
    pq.add(30);
    pq.add(10);
    pq.add(20);
    System.out.print(pq.poll() + ", " + pq.poll() + ", " + pq.poll());
  }
}

medium

A. 10, 20, 30

B. 30, 20, 10

C. 20, 10, 30

D. 10, 30, 20

Solution

1. Step 1: Understand PriorityQueue default order

   Java's PriorityQueue by default is a min-heap, so smallest element is removed first.

2. Step 2: Trace poll() calls

   Elements added: 30, 10, 20. Poll removes 10, then 20, then 30.

3. Final Answer:

   10, 20, 30 -> Option A

4. Quick Check:

   Min-heap poll order = 10, 20, 30 [OK]

Hint: PriorityQueue.poll() returns smallest element first by default [OK]

Common Mistakes:

• Assuming insertion order is preserved
• Thinking PriorityQueue is max-heap by default
• Confusing poll() with peek()

4. Identify the error in the following code snippet that uses a Priority Queue in Java:

import java.util.PriorityQueue;
public class Demo {
  public static void main(String[] args) {
    PriorityQueue pq = new PriorityQueue();
    pq.add("apple");
    pq.add(10);
    System.out.println(pq.poll());
  }
}

medium

A. PriorityQueue requires initial capacity in constructor

B. PriorityQueue must be imported from java.util.concurrent package

C. PriorityQueue cannot mix different data types like String and Integer

D. PriorityQueue does not support add() method

Solution

1. Step 1: Check PriorityQueue type safety

   Without generics, PriorityQueue stores Objects but cannot compare different types.

2. Step 2: Mixing String and Integer causes ClassCastException

   Adding both String and Integer causes runtime error when ordering elements.

3. Final Answer:

   PriorityQueue cannot mix different data types like String and Integer -> Option C

4. Quick Check:

   Mixed types cause runtime error in PriorityQueue [OK]

Hint: PriorityQueue elements must be mutually comparable [OK]

Common Mistakes:

• Ignoring type safety and mixing types
• Wrong import statement
• Assuming add() method is unsupported

5. You want to create a Priority Queue in Java that always returns the largest element first. Which of the following is the best way to achieve this?

hard

A. Use PriorityQueue<Integer> pq = new PriorityQueue<>(); and add elements normally

B. Use PriorityQueue<Integer> pq = new PriorityQueue<>(null);

C. Use PriorityQueue<Integer> pq = new PriorityQueue<>(Comparator.naturalOrder());

D. Use PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder());

Solution

1. Step 1: Understand default PriorityQueue order

   By default, PriorityQueue is a min-heap, so smallest element is returned first.

2. Step 2: Use reverse order comparator for max-heap behavior

   Passing Collections.reverseOrder() makes it return largest element first.

3. Final Answer:

   PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder()); -> Option D

4. Quick Check:

   Reverse order comparator = max-heap PriorityQueue [OK]

Hint: Use Collections.reverseOrder() to get max element first [OK]

Common Mistakes:

• Assuming default PriorityQueue is max-heap
• Passing null comparator causes NullPointerException
• Using naturalOrder() returns min element first