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 sequence?

Consider a min-priority queue where smaller numbers have higher priority. Insert the numbers 5, 3, 8, 1 in this order. What is the state of the queue after all insertions?

DSA C

Insert 5
Insert 3
Insert 8
Insert 1
Print queue

A 8 -> 5 -> 3 -> 1 -> null

B 5 -> 3 -> 8 -> 1 -> null

C 3 -> 1 -> 5 -> 8 -> null

D 1 -> 3 -> 5 -> 8 -> null

💡 Hint

Remember, in a min-priority queue, the smallest element is always at the front.

In a min-priority queue, elements are arranged so that the smallest element is always at the front. After inserting 5, 3, 8, and 1, the queue orders them as 1 -> 3 -> 5 -> 8 -> null.

❓ Predict Output

intermediate

What is the output after removing the highest priority element?

Given a max-priority queue with elements 10, 20, 15, 30 inserted in that order, what is the state of the queue after one removal of the highest priority element?

DSA C

Insert 10
Insert 20
Insert 15
Insert 30
Remove highest priority
Print queue

A 20 -> 15 -> 10 -> null

B 30 -> 20 -> 15 -> 10 -> null

C 15 -> 10 -> null

D 10 -> 15 -> 20 -> null

💡 Hint

In a max-priority queue, the largest element is removed first.

The largest element 30 is removed first. The remaining elements are 20, 15, and 10 arranged to keep max priority order: 20 -> 15 -> 10 -> null.

🧠 Conceptual

advanced

Which data structure is best suited to implement a priority queue efficiently?

Choose the data structure that allows efficient insertion and removal of the highest priority element in a priority queue.

A Linked List

B Binary Heap

C Array

D Stack

💡 Hint

Think about which structure supports fast access to the highest priority element and efficient reordering.

Binary Heap is the best choice because it allows insertion and removal in O(log n) time, maintaining the heap property for priority queue operations.

🔧 Debug

advanced

What error occurs in this priority queue code snippet?

This code tries to remove an element from an empty priority queue. What error will it cause?

DSA C

PriorityQueue pq = new PriorityQueue();
pq.remove();

A UnderflowError

B No error, returns null

C IndexOutOfBoundsException

D NullPointerException

💡 Hint

Removing from an empty queue usually causes an underflow condition.

Removing from an empty priority queue causes an UnderflowError because there are no elements to remove.

🚀 Application

expert

How many elements remain after these operations on a min-priority queue?

Start with an empty min-priority queue. Insert 7, 2, 9, 4, then remove two elements. How many elements remain in the queue?

DSA C

Insert 7
Insert 2
Insert 9
Insert 4
Remove
Remove
Count elements

A 4

B 3

C 2

D 1

💡 Hint

Each removal deletes one element. Count carefully after all operations.

Four elements inserted, two removed, so 2 elements remain in the queue.

Practice

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

easy

A. It does not allow insertion of new elements after creation

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

C. It only stores elements of the same value

D. Elements are dequeued based on their priority, not just arrival order

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 priority, not arrival order.

3. Final Answer:

   Elements are dequeued based on their priority, not just arrival order -> Option D

4. Quick Check:

   Priority queue = priority-based removal [OK]

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

Common Mistakes:

• Thinking priority queue is same as FIFO queue
• Assuming elements must be unique
• Believing insertion order is always preserved

2. Which of the following is the correct way to declare a priority queue in C using the standard library?

easy

A. There is no built-in priority queue in standard C

B. struct priority_queue pq;

C. PriorityQueue pq = new PriorityQueue();

D. priority_queue<int> pq;

Solution

1. Step 1: Recall C standard library features

   The C standard library does not include a built-in priority queue type.

2. Step 2: Analyze options

   The other options show declaration syntax resembling C++ (priority_queue or struct) or Java (PriorityQueue class), none of which are standard in C.

3. Final Answer:

   There is no built-in priority queue in standard C -> Option A

4. Quick Check:

   C standard library lacks priority queue [OK]

Hint: C standard library lacks priority queue type [OK]

Common Mistakes:

• Confusing C with C++ STL syntax
• Assuming priority queue is built-in in C
• Using Java or C++ syntax in C code

3. Consider the following pseudocode for a max-priority queue operations:

insert(5)
insert(3)
insert(10)
extract_max()
insert(1)
extract_max()

What is the sequence of extracted elements?

medium

A. [10, 3]

B. [5, 3]

C. [10, 5]

D. [3, 1]

Solution

1. Step 1: Insert elements into max-priority queue

   Insert 5, 3, 10. The max element is 10.

2. Step 2: Extract max elements in order

   First extract_max() returns 10. Then insert 1. Next extract_max() returns 5 (next highest).

3. Final Answer:

   [10, 5] -> Option C

4. Quick Check:

   Extracted max elements = [10, 5] [OK]

Hint: Extract max returns highest inserted so far [OK]

Common Mistakes:

• Extracting elements in insertion order
• Confusing min and max priority
• Ignoring new insertions before extraction

4. The following C-like pseudocode tries to implement a priority queue insertion but has a bug:

void insert(int pq[], int *size, int value) {
  pq[*size] = value;
  (*size)++;
  int i = *size - 1;
  while (i > 0 && pq[i] < pq[(i - 1) / 2]) {
    int temp = pq[i];
    pq[i] = pq[(i - 1) / 2];
    pq[(i - 1) / 2] = temp;
    i = (i - 1) / 2;
  }
}

What is the bug in this insertion logic?

medium

A. It uses < instead of > for max-heap property

B. It increments size before inserting value

C. It swaps with wrong parent index

D. It does not update the heap after insertion

Solution

1. Step 1: Understand heap property for max-heap

   Max-heap requires parent >= children, so swap if child > parent.

2. Step 2: Analyze condition in while loop

   Condition uses pq[i] < pq[parent], which is correct for min-heap, not max-heap.

3. Final Answer:

   It uses < instead of > for max-heap property -> Option A

4. Quick Check:

   Max-heap needs child > parent to swap [OK]

Hint: Max-heap swaps when child > parent, not < [OK]

Common Mistakes:

• Using min-heap condition for max-heap
• Incorrect parent index calculation
• Not incrementing size correctly

5. You have a priority queue that stores tasks with integer priorities. You want to process tasks in order of highest priority but also keep track of the order tasks with the same priority were added. Which data structure modification best supports this?

hard

A. Use a simple array sorted by priority only

B. Use a max-heap with a timestamp to break ties

C. Use a queue ignoring priorities

D. Use a stack to process tasks in reverse order

Solution

1. Step 1: Understand requirement for priority and insertion order

   We want highest priority first, but for equal priority, process by insertion order.

2. Step 2: Choose data structure supporting priority and tie-break

   A max-heap with timestamps can break ties by earlier insertion time, preserving order among equals.

3. Final Answer:

   Use a max-heap with a timestamp to break ties -> Option B

4. Quick Check:

   Max-heap + timestamp = priority + insertion order [OK]

Hint: Add timestamp to priority for tie-breaking [OK]

Common Mistakes:

• Ignoring insertion order for equal priorities
• Using simple array without tie-break
• Using stack or queue ignoring priority