Priority Queue Introduction and Concept in DSA Javascript - Time & Space Complexity

Time Complexity: Priority Queue Introduction and Concept

O(n^2)

Understanding Time Complexity

We want to understand how the time needed to use a priority queue changes as we add or remove items.

How does the work grow when the queue gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class PriorityQueue {
  constructor() {
    this.items = [];
  }

  enqueue(element) {
    this.items.push(element);
    this.items.sort((a, b) => b.priority - a.priority);
  }

  dequeue() {
    return this.items.pop();
  }
}
    

This code adds elements with priorities and keeps the queue sorted so the highest priority is last.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Sorting the array after each insertion.
• How many times: Sorting happens every time we add an element.

How Execution Grows With Input

Sorting takes more time as the queue grows because it compares many elements.

Input Size (n)	Approx. Operations
10	About 30 to 40 comparisons
100	About 700 to 800 comparisons
1000	About 10,000 to 12,000 comparisons

Pattern observation: The work grows faster than the number of items, roughly multiplying by a bit more than the size each time.

Final Time Complexity

Time Complexity: O(n^2)

This means adding an item takes longer as the queue grows, roughly proportional to the square of the number of items.

Common Mistake

[X] Wrong: "Adding an item is always quick because we just push it to the array."

[OK] Correct: After adding, sorting the whole array takes time that grows with the number of items, so adding is not just a simple push.

Interview Connect

Knowing how priority queues work and their time costs helps you explain your choices clearly and shows you understand how data grows in real problems.

Self-Check

"What if we used a heap instead of sorting the array every time? How would the time complexity change?"

Practice

1. What is the main difference between a Priority Queue and a regular queue?

easy

A. Elements are always dequeued in the order they were enqueued

B. Elements are dequeued based on priority, not just order of arrival

C. It only stores numbers, not other data types

D. It uses a stack internally to manage elements

Solution

1. Step 1: Understand queue behavior

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

2. Step 2: Understand priority queue behavior

   A priority queue removes elements based on their priority, not just arrival order.

3. Final Answer:

   Elements are dequeued based on priority, not just order of arrival -> Option B

4. Quick Check:

   Priority Queue = priority-based removal [OK]

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

Common Mistakes:

• Thinking priority queue works like a normal queue
• Assuming priority queue only stores numbers
• Confusing priority queue with stack

2. Which of the following is the correct way to declare a priority queue class in JavaScript?

easy

A. let PriorityQueue = () => { this.items = []; }

B. function PriorityQueue() { this.items = {}; }

C. class PriorityQueue { constructor() { this.items = []; } }

D. var PriorityQueue = new Array();

Solution

1. Step 1: Check class syntax

   class PriorityQueue { constructor() { this.items = []; } } uses correct ES6 class syntax with constructor initializing an array.

2. Step 2: Check other options

   function PriorityQueue() { this.items = {}; } uses function but initializes an object, not array; let PriorityQueue = () => { this.items = []; } uses arrow function incorrectly for class; var PriorityQueue = new Array(); assigns array directly, not a class.

3. Final Answer:

   class PriorityQueue { constructor() { this.items = []; } } -> Option C

4. Quick Check:

   Correct class syntax = class PriorityQueue { constructor() { this.items = []; } } [OK]

Hint: Use ES6 class with constructor for priority queue [OK]

Common Mistakes:

• Using arrow functions as classes
• Initializing items as object instead of array
• Assigning array directly without class

3. Consider this JavaScript code using a simple priority queue implementation:

class PriorityQueue {
  constructor() {
    this.items = [];
  }
  enqueue(element, priority) {
    this.items.push({element, priority});
    this.items.sort((a, b) => a.priority - b.priority);
  }
  dequeue() {
    return this.items.shift().element;
  }
}

const pq = new PriorityQueue();
pq.enqueue('A', 2);
pq.enqueue('B', 1);
pq.enqueue('C', 3);
console.log(pq.dequeue());

What will be printed?

medium

A. 'B'

B. 'A'

C. 'C'

D. undefined

Solution

1. Step 1: Analyze enqueue operations

   Elements are added with priorities: A(2), B(1), C(3). After each enqueue, array is sorted by priority ascending.

2. Step 2: Analyze dequeue operation

   Dequeue removes first element (lowest priority number). After sorting, order is B(1), A(2), C(3). So dequeue returns 'B'.

3. Final Answer:

   'B' -> Option A

4. Quick Check:

   Lowest priority dequeued first = 'B' [OK]

Hint: Lowest priority number dequeued first [OK]

Common Mistakes:

• Assuming FIFO order instead of priority
• Confusing priority sorting order
• Forgetting to return element, not object

4. The following code is intended to implement a priority queue, but it has a bug:

class PriorityQueue {
  constructor() {
    this.items = [];
  }
  enqueue(element, priority) {
    this.items.push({element, priority});
  }
  dequeue() {
    return this.items.shift().element;
  }
}

What is the main problem with this code?

medium

A. It stores elements as objects instead of arrays

B. It uses shift() instead of pop() to remove elements

C. It does not initialize items array in constructor

D. It does not sort items by priority before dequeue

Solution

1. Step 1: Check enqueue method

   Enqueue adds elements but does not sort by priority.

2. Step 2: Check dequeue method

   Dequeue removes first element, but without sorting, priority order is not guaranteed.

3. Final Answer:

   It does not sort items by priority before dequeue -> Option D

4. Quick Check:

   Missing sorting causes wrong dequeue order [OK]

Hint: Sort items by priority before dequeue [OK]

Common Mistakes:

• Assuming shift() removes highest priority
• Ignoring sorting requirement
• Confusing object vs array storage

5. You want to implement a priority queue that supports fast insertion and removal of the highest priority element. Which data structure is best suited for this, and why?

hard

A. Binary heap, because it provides efficient insert and remove operations

B. Linked list, because it maintains insertion order

C. Stack, because it removes the last inserted element quickly

D. Array, because it allows easy sorting after each insertion

Solution

1. Step 1: Understand operation needs

   Priority queue needs fast insertion and removal of highest priority element.

2. Step 2: Compare data structures

   Array requires sorting after insertion (slow). Linked list maintains order but slow for priority. Stack removes last inserted only. Binary heap supports insert and remove in O(log n) time efficiently.

3. Final Answer:

   Binary heap, because it provides efficient insert and remove operations -> Option A

4. Quick Check:

   Binary heap = efficient priority queue [OK]

Hint: Use binary heap for efficient priority queue operations [OK]

Common Mistakes:

• Choosing array and ignoring sorting cost
• Confusing stack with priority queue
• Ignoring time complexity of operations