[Very Important Coding Interviews : Heap & Priority Queue#05] How To Solve ANY Heap & Priority Queue Programming Question ( Pattern Approach with Shortcuts) : How it Works ( With Implementation Code)

Everything you MUST know to solve any Heap & Priority Queue question...

This is the best hands-on guide you will ever find on Heap & Priority Queue Technique which follows Pattern based Approach to Solve any Heap & Priority Queue question and Shortcuts You MUST READ and Implement.

Objective : Master all Heap & Priority Queue patterns that appear in 100% of coding interview problems.

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Table of Contents

1. Introduction: Understanding Heaps and Priority Queues

2. Pattern 1: Top K Elements - Selection Problems

3. Pattern 2: Two Heaps - Median Finding

4. Pattern 3: Merge K Sorted - K-way Merge

5. Pattern 4: Scheduling with Heaps

6. Pattern 5: Stream Processing - Continuous Data

7. Pattern 6: Frequency-Based Heap

8. Pattern 7: Interval Management with Heaps

9. Advanced Patterns and Techniques

10. Company-Specific Problem Index

11. Interview Strategies and Templates

12. Shortcuts

Note : Each pattern comes with its Python Implementation ( can be found as you scroll) and at the end of thus post along with Heap & Priority Queue Shortcuts and problem examples.

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Introduction: Understanding Heaps and Priority Queues

What is a Heap?

A heap is a specialized tree-based data structure that satisfies the heap property:

Max Heap:

Parent ≥ All Children
       9
      / \
     7   5
    / \
   3   4

Min Heap:

Parent ≤ All Children
       1
      / \
     3   2
    / \
   7   4

Priority Queue Operations

Operation Min Heap Max Heap

Description

peek() O(1) O(1) Get min/max element

push() O(log n) O(log n) Insert element

pop() O(log n) O(log n) Remove min/max

heapify() O(n) O(n) Build heap from array

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Python’s heapq Module

Important: Python’s heapq is a MIN HEAP only!

import heapq

# Min Heap (default)
min_heap = []
heapq.heappush(min_heap, 5)
heapq.heappush(min_heap, 3)
heapq.heappush(min_heap, 7)
print(heapq.heappop(min_heap))  # 3 (smallest)

# Max Heap (negate values)
max_heap = []
heapq.heappush(max_heap, -5)
heapq.heappush(max_heap, -3)
heapq.heappush(max_heap, -7)
print(-heapq.heappop(max_heap))  # 7 (largest)

# Heapify existing list
nums = [3, 1, 4, 1, 5]
heapq.heapify(nums)  # O(n) - better than n insertions

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When to Use Heaps— Deep Dive into Patterns, Implementations and Shortcuts: