# 10 Priority Queue Interview Questions and Answers

Prepare for your technical interview with our guide on priority queues, featuring common questions and in-depth explanations to enhance your understanding.

Prepare for your technical interview with our guide on priority queues, featuring common questions and in-depth explanations to enhance your understanding.

Priority queues are a fundamental data structure in computer science, essential for efficiently managing tasks that need to be processed in a specific order. They are widely used in various applications, including operating systems for task scheduling, network routing algorithms, and simulation systems. Understanding how priority queues work and their implementation can significantly enhance your problem-solving skills and algorithmic thinking.

This article provides a curated selection of priority queue interview questions designed to test and improve your understanding of this critical data structure. By working through these questions, you will gain deeper insights into priority queue operations, their complexities, and practical applications, preparing you to tackle related challenges in technical interviews.

A Priority Queue is an abstract data type that processes elements based on their priority rather than their order in the queue. Elements with higher priority are processed before those with lower priority. Common use cases include task scheduling, graph algorithms like Dijkstra’s and A*, and event simulation. Here’s a simple Python implementation using the `heapq`

module:

import heapq class PriorityQueue: def __init__(self): self._queue = [] self._index = 0 def push(self, item, priority): heapq.heappush(self._queue, (-priority, self._index, item)) self._index += 1 def pop(self): return heapq.heappop(self._queue)[-1] pq = PriorityQueue() pq.push("task1", 1) pq.push("task2", 5) pq.push("task3", 3) print(pq.pop()) # Output: task2 print(pq.pop()) # Output: task3 print(pq.pop()) # Output: task1

In a binary heap implementation of a priority queue, the time complexities are as follows:

**Insertion:**O(log n) – The element is added to the end and “bubbled up” to maintain the heap property.**Deletion:**O(log n) – The root is removed, replaced with the last element, and “bubbled down” to restore the heap property.**Access:**O(1) – The highest priority element is at the root, allowing constant time access.

To merge two Min-Heaps, extract all elements from both heaps and insert them into a new Min-Heap. Here’s a Python example:

import heapq def merge_priority_queues(heap1, heap2): merged_heap = [] for element in heap1: heapq.heappush(merged_heap, element) for element in heap2: heapq.heappush(merged_heap, element) return merged_heap heap1 = [1, 3, 5] heap2 = [2, 4, 6] merged_heap = merge_priority_queues(heap1, heap2) print(merged_heap) # Output: [1, 2, 3, 4, 5, 6]

A Fibonacci Heap is a collection of trees satisfying the minimum-heap property, offering efficient amortized time complexities for various operations. Key operations include:

- Insertion:
**O(1)**amortized time - Find minimum:
**O(1)**time - Union:
**O(1)**amortized time - Decrease key:
**O(1)**amortized time - Delete minimum:
**O(log n)**amortized time

Advantages include efficient decrease-key operations and low amortized time complexities, making Fibonacci Heaps suitable for algorithms like Dijkstra’s and Prim’s.

To decrease the key of an element in a Min-Heap, update the key and move the element up the tree until the Min-Heap property is satisfied. Here’s an example:

def decrease_key(heap, index, new_key): if new_key > heap[index]: raise ValueError("New key is greater than the current key") heap[index] = new_key while index > 0 and heap[(index - 1) // 2] > heap[index]: parent = (index - 1) // 2 heap[index], heap[parent] = heap[parent], heap[index] index = parent # Example usage heap = [1, 3, 6, 5, 9, 8] decrease_key(heap, 4, 2) print(heap) # Output: [1, 3, 6, 5, 2, 8]

Dijkstra’s algorithm uses a priority queue to manage and retrieve the next node with the smallest tentative distance, ensuring the shortest path is extended first. Here’s a Python example using the `heapq`

module:

import heapq def dijkstra(graph, start): priority_queue = [] heapq.heappush(priority_queue, (0, start)) distances = {node: float('inf') for node in graph} distances[start] = 0 while priority_queue: current_distance, current_node = heapq.heappop(priority_queue) if current_distance > distances[current_node]: continue for neighbor, weight in graph[current_node].items(): distance = current_distance + weight if distance < distances[neighbor]: distances[neighbor] = distance heapq.heappush(priority_queue, (distance, neighbor)) return distances graph = { 'A': {'B': 1, 'C': 4}, 'B': {'A': 1, 'C': 2, 'D': 5}, 'C': {'A': 4, 'B': 2, 'D': 1}, 'D': {'B': 5, 'C': 1} } print(dijkstra(graph, 'A')) # {'A': 0, 'B': 1, 'C': 3, 'D': 4}

A concurrent priority queue allows multiple threads to perform operations in a thread-safe manner. One approach is to use a heap-based priority queue with a lock. Here’s a high-level overview and pseudocode:

- Use a heap to maintain priority queue properties.
- Use a lock to synchronize access to the heap.
- Implement thread-safe methods for insertion and deletion.

Pseudocode:

class ConcurrentPriorityQueue: def __init__(self): self.heap = [] self.lock = Lock() def insert(self, item): with self.lock: heapq.heappush(self.heap, item) def delete_min(self): with self.lock: if self.heap: return heapq.heappop(self.heap) else: return None

A priority queue can be implemented using a linked list by maintaining the list in a sorted order based on priority. Here’s an example in Python:

class Node: def __init__(self, data, priority): self.data = data self.priority = priority self.next = None class PriorityQueue: def __init__(self): self.head = None def insert(self, data, priority): new_node = Node(data, priority) if not self.head or self.head.priority < priority: new_node.next = self.head self.head = new_node else: current = self.head while current.next and current.next.priority >= priority: current = current.next new_node.next = current.next current.next = new_node def delete(self): if self.head: self.head = self.head.next # Example usage pq = PriorityQueue() pq.insert('task1', 1) pq.insert('task2', 3) pq.insert('task3', 2) while pq.head: print(pq.head.data) pq.delete()

The amortized time complexity of operations in a Fibonacci Heap is:

**Insert:**O(1) – Adding a new element is done in constant time.**Find Minimum:**O(1) – The minimum element is always at the root.**Union (Meld):**O(1) – Merging two heaps is done by concatenating their root lists.**Extract Minimum:**O(log n) – Involves removing the root and consolidating the trees.**Decrease Key:**O(1) – Done in constant time, with potential cascading cuts.**Delete:**O(log n) – Decreasing the key to negative infinity and extracting the minimum.

These complexities are achieved through lazy operations and potential functions, ensuring low average costs over a sequence of operations.

To find the k-th largest element in a stream of numbers using a priority queue, use a min-heap of size k. Here’s a Python implementation:

import heapq class KthLargest: def __init__(self, k, nums): self.k = k self.min_heap = nums heapq.heapify(self.min_heap) while len(self.min_heap) > k: heapq.heappop(self.min_heap) def add(self, val): if len(self.min_heap) < self.k: heapq.heappush(self.min_heap, val) elif val > self.min_heap[0]: heapq.heapreplace(self.min_heap, val) return self.min_heap[0] # Example usage: kth_largest = KthLargest(3, [4, 5, 8, 2]) print(kth_largest.add(3)) # returns 4 print(kth_largest.add(5)) # returns 5 print(kth_largest.add(10)) # returns 5 print(kth_largest.add(9)) # returns 8 print(kth_largest.add(4)) # returns 8