Max Heap

Definition

A Max Heap is a specific type of heap where the value of every “parent” node is greater than or equal to the values of its “children.” This means the largest number is always sitting at the top (the root).

How it Works

1. The Rule: If you look at any node in the tree, it must be larger than the nodes below it.
2. Insertion: When you add a new number, you add it to the bottom-leftmost open spot. Then you “bubble it up” (swap it with its parent) until the rule is satisfied.
3. Extraction: When you remove the max element (the root), you replace it with the last element in the tree and “bubble it down” (swap with the largest child) to restore the order.

Example

Input Numbers: [10, 20, 15, 30, 40]

Max Heap Structure:

      40
    /  \
  30    15
  /  \
10    20

Notice that 40 is bigger than its children (30 and 15), and 30 is bigger than its children (10 and 20).

Code Example (Python)

Python

import heapq

# Python’s heapq module implements a Min Heap by default.
# To create a Max Heap, we invert the values (multiply by -1).

numbers = [10, 20, 15, 30, 40]
max_heap = []

# Insert into Max Heap
for num in numbers:
    heapq.heappush(max_heap, -num) # Invert value

# Print Max Element (remember to invert back)
print(“Max value:”, -max_heap[0]) # Output: 40

# Pop Max Element
largest = -heapq.heappop(max_heap)
print(“Removed:”, largest) # Output: 40

Use Cases & Interview Relevance

• Finding the Kth Smallest Element: Often used to efficiently manage sets of data where you need quick access to the largest item.
• Memory Management: The Java Garbage Collector often uses similar structures to manage memory blocks.