Priority Queue Introduction and Concept in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this priority queue insertion and removal?

Consider a priority queue where lower numbers have higher priority. What will be the printed order after inserting 4, 1, 3, and then removing two elements?

DSA C#

using System;
using System.Collections.Generic;

class Program {
    static void Main() {
        var pq = new PriorityQueue<int, int>();
        pq.Enqueue(4, 4);
        pq.Enqueue(1, 1);
        pq.Enqueue(3, 3);
        Console.Write(pq.Dequeue() + " -> ");
        Console.Write(pq.Dequeue() + " -> ");
        Console.WriteLine("null");
    }
}

A 1 -> 3 -> null

B 4 -> 1 -> null

C 3 -> 4 -> null

D 1 -> 4 -> null

💡 Hint

Remember, lower priority value means higher priority in this queue.

The priority queue uses the priority value to decide order. Since 1 has priority 1, it comes out first, then 3 with priority 3.

🧠 Conceptual

intermediate

Which statement best describes a priority queue?

Choose the best description of a priority queue.

A A data structure that only allows insertion at the end and removal from the front.

B A data structure where elements are removed in the order they were added.

C A data structure where each element has a priority and the highest priority element is removed first.

D A data structure that stores elements in sorted order permanently.

💡 Hint

Think about how priority affects removal order.

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

🔧 Debug

advanced

What error does this priority queue code produce?

What error will this C# code produce when run?

DSA C#

using System;
using System.Collections.Generic;

class Program {
    static void Main() {
        var pq = new PriorityQueue<int, int>();
        pq.Enqueue(5, 5);
        pq.Enqueue(2, 2);
        pq.Enqueue(8, 8);
        Console.WriteLine(pq.Dequeue());
        Console.WriteLine(pq.Dequeue());
        Console.WriteLine(pq.Dequeue());
        Console.WriteLine(pq.Dequeue());
    }
}

A NullReferenceException

B No error, prints 2, 5, 8, then 0

C IndexOutOfRangeException

D InvalidOperationException

💡 Hint

Check what happens when you dequeue more elements than present.

Dequeuing from an empty priority queue throws InvalidOperationException.

🚀 Application

advanced

How many elements remain after these operations?

Start with an empty priority queue. Insert elements with priorities: (10, 2), (20, 1), (30, 3). Then remove one element. How many elements remain?

A 1

B 2

C 3

D 0

💡 Hint

One element is removed after inserting three.

After inserting 3 elements and removing 1, 2 remain.

❓ Predict Output

expert

What is the output after mixed enqueue and dequeue operations?

Given a priority queue where lower priority number means higher priority, what is the output of this code?

DSA C#

using System;
using System.Collections.Generic;

class Program {
    static void Main() {
        var pq = new PriorityQueue<string, int>();
        pq.Enqueue("apple", 5);
        pq.Enqueue("banana", 3);
        pq.Enqueue("cherry", 4);
        Console.Write(pq.Dequeue() + " -> ");
        pq.Enqueue("date", 2);
        Console.Write(pq.Dequeue() + " -> ");
        Console.Write(pq.Dequeue() + " -> ");
        Console.WriteLine(pq.Dequeue() + " -> null");
    }
}

A banana -> date -> cherry -> apple -> null

B apple -> banana -> cherry -> date -> null

C banana -> cherry -> date -> apple -> null

D date -> banana -> cherry -> apple -> null

💡 Hint

Track the priority values carefully after each operation.

First dequeue removes banana (priority 3). Then date (priority 2) is added. Next dequeue removes date (priority 2), then cherry (priority 4), then apple (priority 5).

Practice

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

easy

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

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

C. It only stores elements of the same data type

D. It allows random access to elements by index

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 just order.

3. Final Answer:

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

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 allows random access
• Assuming priority queue only stores one data type

2. Which of the following is the correct way to declare a priority queue of integers in C# using System.Collections.Generic.PriorityQueue?

easy

A. var pq = new PriorityQueue();

B. var pq = new PriorityQueue<int>();

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

D. PriorityQueue pq = new PriorityQueue();

Solution

1. Step 1: Recall PriorityQueue syntax in C#

   The generic PriorityQueue requires two types: element type and priority type.

2. Step 2: Check each option

   var pq = new PriorityQueue(); correctly uses PriorityQueue<int, int>. Others have syntax errors or missing types.

3. Final Answer:

   var pq = new PriorityQueue(); -> Option A

4. Quick Check:

   PriorityQueue<TElement, TPriority> syntax [OK]

Hint: PriorityQueue needs element and priority types in angle brackets [OK]

Common Mistakes:

• Omitting priority type in generic declaration
• Using wrong constructor syntax
• Trying to declare without generic types

3. What will be the output of the following C# code?

var pq = new PriorityQueue();
pq.Enqueue("apple", 3);
pq.Enqueue("banana", 1);
pq.Enqueue("cherry", 2);
while (pq.Count > 0) {
    Console.Write(pq.Dequeue() + " ");
}

medium

A. banana cherry apple

B. apple cherry banana

C. cherry banana apple

D. apple banana cherry

Solution

1. Step 1: Understand enqueue priorities

   Elements are enqueued with priorities: apple=3, banana=1, cherry=2.

2. Step 2: Dequeue order based on priority

   PriorityQueue dequeues elements with lowest priority first: banana(1), cherry(2), apple(3).

3. Final Answer:

   banana cherry apple -> Option A

4. Quick Check:

   Lowest priority dequeued first = banana cherry apple [OK]

Hint: PriorityQueue dequeues lowest priority first by default [OK]

Common Mistakes:

• Assuming highest priority dequeued first
• Mixing element order with priority order
• Ignoring priority values

4. Identify the error in the following C# code using PriorityQueue:

var pq = new PriorityQueue();
pq.Enqueue(10, 2);
pq.Enqueue(5);
pq.Enqueue(20, 1);

medium

A. Enqueue method does not exist

B. PriorityQueue cannot store integers

C. PriorityQueue requires three generic types

D. Missing priority argument in second Enqueue call

Solution

1. Step 1: Check Enqueue method parameters

   Enqueue requires two arguments: element and priority.

2. Step 2: Identify incorrect call

   The second Enqueue call pq.Enqueue(5); misses the priority argument.

3. Final Answer:

   Missing priority argument in second Enqueue call -> Option D

4. Quick Check:

   Enqueue needs element and priority [OK]

Hint: Enqueue always needs element and priority arguments [OK]

Common Mistakes:

• Forgetting priority argument in Enqueue
• Thinking PriorityQueue needs three types
• Assuming Enqueue accepts one argument

5. You want to process tasks with priorities where higher numbers mean higher priority. How can you use C#'s PriorityQueue to dequeue tasks in order from highest to lowest priority?

hard

A. Use PriorityQueue as is; it dequeues highest priority first

B. Sort the queue manually after enqueueing

C. Store priorities as negative values when enqueuing

D. Use a Stack instead of PriorityQueue

Solution

1. Step 1: Understand PriorityQueue default behavior

   C# PriorityQueue dequeues elements with lowest priority first by default.

2. Step 2: Adjust priorities to reverse order

   To get highest priority first, store priorities as negative values (e.g., -priority).

3. Final Answer:

   Store priorities as negative values when enqueuing -> Option C

4. Quick Check:

   Invert priorities to reverse dequeue order [OK]

Hint: Invert priorities (negative) to get highest priority first [OK]

Common Mistakes:

• Assuming PriorityQueue dequeues highest priority first by default
• Trying to sort queue manually
• Using Stack which doesn't handle priorities