Priority Queue Introduction and Concept in DSA Python

Mental Model

A priority queue is like a line where people with higher importance get served first, no matter when they arrive.

Analogy: Imagine a hospital emergency room where patients with more serious conditions are treated before others, even if they arrived later.

Priority Queue:
[10] -> [5] -> [3] -> [1] -> null
↑ front (highest priority)

Dry Run Walkthrough

Input: Insert values 3, 10, 5 into an empty priority queue (higher number means higher priority). Then remove the highest priority element.

Goal: Show how elements are added and removed so that the highest priority is always served first.

Step 1: Insert 3 into empty queue

[3] -> null ↑ front

Why: First element becomes the front as it is the only one

Step 2: Insert 10, which has higher priority than 3

[10] -> [3] -> null ↑ front

Why: 10 goes before 3 because it has higher priority

Step 3: Insert 5, which has priority between 10 and 3

[10] -> [5] -> [3] -> null ↑ front

Why: 5 is placed between 10 and 3 to keep order by priority

Step 4: Remove element from front (highest priority)

[5] -> [3] -> null ↑ front

Why: 10 is removed because it has the highest priority

Result:

[5] -> [3] -> null ↑ front
Removed element: 10

Annotated Code

DSA Python

class Node:
    def __init__(self, value, priority):
        self.value = value
        self.priority = priority
        self.next = None

class PriorityQueue:
    def __init__(self):
        self.front = None

    def insert(self, value, priority):
        new_node = Node(value, priority)
        if self.front is None or priority > self.front.priority:
            new_node.next = self.front
            self.front = new_node
            return
        current = self.front
        while current.next and current.next.priority >= priority:
            current = current.next
        new_node.next = current.next
        current.next = new_node

    def remove(self):
        if self.front is None:
            return None
        removed_value = self.front.value
        self.front = self.front.next
        return removed_value

    def __str__(self):
        result = []
        current = self.front
        while current:
            result.append(str(current.value))
            current = current.next
        return ' -> '.join(result) + ' -> null'

# Driver code
pq = PriorityQueue()
pq.insert(3, 3)
pq.insert(10, 10)
pq.insert(5, 5)
print(pq)
removed = pq.remove()
print(pq)
print(f'Removed element: {removed}')

if self.front is None or priority > self.front.priority:

Check if new node should be front because queue is empty or new priority is highest

while current.next and current.next.priority >= priority:

Traverse to find correct position to insert new node maintaining priority order

removed_value = self.front.value

Store value of front node to return after removal

self.front = self.front.next

Remove front node by moving front pointer to next node

Output

10 -> 5 -> 3 -> null

5 -> 3 -> null

Removed element: 10

Complexity Analysis

Time: O(n) because in worst case we traverse the whole queue to insert an element in correct position

Space: O(n) because we store all elements in linked nodes

vs Alternative: Compared to a simple queue where insertion is O(1) but removal of highest priority is O(n), priority queue keeps removal O(1) but insertion O(n)

Edge Cases

Empty queue when removing

Returns None safely without error

DSA Python

if self.front is None:
            return None

Insert element with priority equal to existing nodes

Inserted after nodes with same priority to maintain stable order

DSA Python

while current.next and current.next.priority >= priority:

Insert into empty queue

New node becomes front

DSA Python

if self.front is None or priority > self.front.priority:

When to Use This Pattern

When you need to always process the most important item first, use a priority queue to keep elements sorted by priority automatically.

Common Mistakes

Mistake: Inserting new element at the end regardless of priority
Fix: Traverse and insert at correct position based on priority

Mistake: Removing from the end instead of front
Fix: Always remove from front to get highest priority element

Summary

A priority queue stores elements so that the highest priority is always at the front.

Use it when you want to process items by importance, not just arrival order.

The key is to insert elements in order so removal is always the highest priority.