Priority Queue Introduction and Concept in DSA C++ - Execution Trace

Concept Flow - Priority Queue Introduction and Concept

Create empty priority queue

↓

Insert element with priority

↓

Place element based on priority

↓

Peek or remove highest priority element

↓

Rearrange queue to maintain priority order

↓

Repeat insert/remove as needed

Shows how elements enter the priority queue, are placed by priority, and how highest priority elements are accessed or removed.

Execution Sample

DSA C++

pq.push(30);
pq.push(10);
pq.push(20);
int top = pq.top();
pq.pop();

Insert elements 30, 10, 20 into priority queue, then get and remove the highest priority element.

Execution Table

Step	Operation	Nodes in Queue	Pointer Changes	Visual State
1	Create empty priority queue	[]	head=nullptr	null
2	Insert 30	[30]	head -> 30	30
3	Insert 10	[30, 10]	head -> 30	30 -> 10
4	Insert 20	[30, 20, 10]	head -> 30	30 -> 20 -> 10
5	Peek top element	[30, 20, 10]	head -> 30	30 -> 20 -> 10
6	Remove top element (30)	[20, 10]	head -> 20	20 -> 10
7	Final state	[20, 10]	head -> 20	20 -> 10

💡 No more operations; priority queue maintains order with highest priority element at head.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 6	Final
head	nullptr	30	30	30	20	20
size	0	1	2	3	2	2
top element	N/A	30	30	30	20	20

Key Moments - 3 Insights

Why does the highest priority element stay at the front after insertions?

Because after each insertion (see steps 2-4 in execution_table), the queue rearranges to keep the highest priority element at the head, so peek (step 5) always shows it.

What happens to the queue when we remove the top element?

At step 6, removing the top element (30) causes the queue to rearrange so the next highest priority (20) moves to the front, maintaining priority order.

Is the priority queue the same as a normal queue?

No, unlike a normal queue that follows first-in-first-out, the priority queue always keeps the highest priority element at the front regardless of insertion order, as shown in the visual state.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the order of elements in the queue?

A [30, 10, 20]

B [10, 20, 30]

C [20, 10, 30]

D [10, 30, 20]

💡 Hint

Check the 'Nodes in Queue' and 'Visual State' columns at step 4 in execution_table.

At which step does the top element change from 30 to 20?

A Step 4

B Step 5

C Step 6

D Step 7

💡 Hint

Look at the 'top element' variable in variable_tracker after each step.

If we insert 40 after step 6, what would be the new top element?

A 20

B 40

C 30

D 10

💡 Hint

Priority queue always keeps the highest priority element at the front; 40 is higher than current top 20.

Concept Snapshot

Priority Queue stores elements with priorities.
Highest priority element is always accessed first.
Insertion rearranges queue to maintain order.
Supports push (insert), top (peek), pop (remove).
Used when order depends on priority, not arrival.

Full Transcript

A priority queue is a special data structure where each element has a priority. Elements are stored so that the one with the highest priority is always at the front. When we insert elements, the queue rearranges to keep this order. We can peek at the top element or remove it, and the queue updates accordingly. This example shows inserting 30, 10, and 20, then removing the top element 30, leaving 20 as the new top. This helps in tasks where priority matters more than order of arrival.

Practice

1. What is the main property of a priority queue in data structures?

easy

A. Elements are always served in the order they were inserted

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

C. It stores elements in sorted order permanently

D. It only allows insertion of unique elements

Solution

1. Step 1: Understand priority queue behavior

   A priority queue serves elements based on priority, not just the order they arrive. Options A, C, and D describe other data structures or incorrect properties.

2. Final Answer:

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

3. Quick Check:

   Priority queue = priority-based serving [OK]

Hint: Remember: priority queue serves highest priority first [OK]

Common Mistakes:

• Confusing priority queue with regular queue
• Thinking elements are always sorted inside
• Assuming only unique elements allowed

2. Which of the following is the correct way to declare a max priority queue of integers in C++ STL?

easy

A. std::priority_queue<int> pq;

B. std::priority_queue pq;

C. std::priority_queue pq;

D. std::priority_queue pq;

Solution

1. Step 1: Recall default priority queue type

   By default, std::priority_queue is a max heap using std::vector and std::less. std::priority_queue<int> pq; uses default syntax. B creates min priority queue. C and D use invalid container type std::list.

2. Final Answer:

   std::priority_queue<int> pq; -> Option A

3. Quick Check:

   Default priority queue is max heap [OK]

Hint: Default priority_queue<int> is max heap in C++ STL [OK]

Common Mistakes:

• Using std::greater<int> for max heap (it's for min heap)
• Using unsupported container types like std::list
• Overcomplicating declaration when default works

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

std::priority_queue<int> pq;
pq.push(10);
pq.push(5);
pq.push(20);
std::cout << pq.top() << std::endl;
pq.pop();
std::cout << pq.top() << std::endl;

medium

A. 20\n10

B. 10\n5

C. 5\n10

D. 20\n5

Solution

1. Step 1: Insert elements into max priority queue

   Elements 10, 5, 20 pushed; max 20 at top, print 20. After pop, 20 removed, next max 10, print 10.

2. Final Answer:

   20\n10 -> Option A

3. Quick Check:

   Max heap top changes from 20 to 10 after pop [OK]

Hint: Top always shows current max in max priority queue [OK]

Common Mistakes:

• Confusing priority queue with FIFO queue
• Assuming pop removes smallest element
• Mixing up order of outputs

4. Identify the error in the following C++ code using priority queue:

std::priority_queue<int> pq;
pq.push(15);
pq.push(30);
pq.pop();
std::cout << pq.top() << std::endl;
pq.pop();
pq.pop();

medium

A. Missing semicolon after pq.push(30)

B. Using std::cout without including <iostream>

C. Calling pop() on empty priority queue causes runtime error

D. Priority queue cannot store integers

Solution

1. Step 1: Trace push and pop operations

   Push 15, 30; first pop removes 30, top now 15 printed; second pop removes 15; third pop on empty queue causes runtime error.

2. Final Answer:

   Calling pop() on empty priority queue causes runtime error -> Option C

3. Quick Check:

   Pop on empty queue = error [OK]

Hint: Never pop from empty priority queue [OK]

Common Mistakes:

• Ignoring empty check before pop
• Assuming pop returns value
• Confusing syntax errors with runtime errors

5. You want to maintain a priority queue that always gives the smallest element first (a min priority queue). Which of the following is the correct way to declare it in C++ STL?

hard

A. std::priority_queue pq;

B. std::priority_queue<int> pq;

C. std::priority_queue pq;

D. std::priority_queue pq;

Solution

1. Step 1: Understand default and min heap declaration

   Default std::priority_queue is max heap (std::less). For min heap (smallest first), use std::greater with std::vector. A and B are max heaps; D uses unsupported std::list.

2. Final Answer:

   std::priority_queue<int, std::vector<int>, std::greater<int>> pq; -> Option D

3. Quick Check:

   Min heap = priority_queue with std::greater [OK]

Hint: Use std::greater for min priority queue in C++ STL [OK]

Common Mistakes:

• Using std::less for min heap
• Using unsupported containers like std::list
• Forgetting to specify comparator