How to Write a Heap Using a Linked List: A Complete Guide

Heaps are one of the most useful data structures in computer science — powering priority queues, scheduling algorithms, and efficient sorting. Most introductions show heaps implemented as arrays, but heaps can also be built using linked lists. Understanding both approaches gives you meaningful flexibility when working with dynamic data and memory constraints.

What Is a Heap, Exactly?

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

• In a max-heap, every parent node holds a value greater than or equal to its children.
• In a min-heap, every parent node holds a value less than or equal to its children.

Heaps are most commonly used to implement priority queues — structures where the highest (or lowest) priority element is always accessible in O(1) time.

The standard implementation stores heap elements in a flat array and uses index math to navigate parent-child relationships. A linked list implementation does the same job differently — using node pointers instead of index arithmetic.

Why Use a Linked List for a Heap?

The array-based heap is compact and cache-friendly, which is why it dominates in practice. But a linked list heap has genuine use cases:

• Dynamic memory allocation — no need to pre-size an array or resize it later
• Educational clarity — the tree structure is visually explicit in the node relationships
• Certain merge-heavy workloads — structures like leftist heaps and skew heaps are natively linked and support efficient merging

If you're building a heap where memory size is unpredictable or where you need frequent heap merges, the linked approach earns its keep.

Core Components of a Linked List Heap

Before writing any logic, define your building blocks.

The Node Structure

Each node needs to store:

In Python, a simple node looks like this:

class HeapNode: def __init__(self, value): self.value = value self.left = None self.right = None self.parent = None 

Your heap class then holds a reference to the root node and tracks the size of the heap (critical for insertion logic).

The Two Core Operations: Insert and Extract

🔼 Inserting a Node

Insertion into a linked heap follows this sequence:

1. Create a new node with the given value
2. Find the correct insertion point — the next available position in level order (breadth-first)
3. Attach the node as a left or right child of that parent
4. Bubble up — compare the new node with its parent and swap values if the heap property is violated; repeat until satisfied

Finding the insertion point is the trickiest part. Since there's no index math, you use the binary representation of the heap size + 1 to navigate from the root to the correct parent. For example, if the heap has 5 nodes, the next node is position 6 — binary 110 — so you go: root → right → left child.

def get_insertion_path(size): path = [] n = size + 1 while n > 1: path.append(n % 2) # 0 = left, 1 = right n //= 2 return path[:-1][::-1] # Remove root bit, reverse for top-down traversal 

🔽 Extracting the Root (Min or Max)

Extraction removes the root — the heap's highest-priority element — and restores order:

1. Replace the root value with the value of the last node (rightmost node at the deepest level)
2. Remove the last node
3. Bubble down (sift down) — compare the root with its children; swap with the appropriate child if the heap property is violated; repeat until satisfied

Finding and removing the last node uses the same binary path technique as insertion, but for the current size rather than size + 1.

Bubble Up and Bubble Down: The Heart of the Heap

Both operations are straightforward once your node structure is in place.

Bubble up (used after insert):

def bubble_up(node): while node.parent and node.value < node.parent.value: # min-heap node.value, node.parent.value = node.parent.value, node.value node = node.parent 

Bubble down (used after extract):

def bubble_down(node): while node.left: smaller = node.left if node.right and node.right.value < node.left.value: smaller = node.right if smaller.value < node.value: node.value, smaller.value = smaller.value, node.value node = smaller else: break 

Swapping values (rather than restructuring pointers) keeps the implementation clean without sacrificing correctness.

Key Variables That Affect Your Implementation

How you build this in practice depends on several factors:

• Language — Python, Java, and C++ all handle pointers and memory differently; C requires explicit malloc/free and struct definitions
• Heap type — min-heap vs. max-heap only changes comparison direction, but advanced variants (Fibonacci heap, binomial heap) require more complex node structures
• Parent pointers — including a parent field simplifies bubble-up but adds memory overhead per node
• Use case — a priority queue for task scheduling has different performance priorities than one used in a graph algorithm like Dijkstra's

Array Heap vs. Linked List Heap at a Glance

Where Your Setup Matters Most

The linked list heap isn't the right tool in every situation — but it's the right tool in some. Whether it fits your needs depends on what you're building: a classroom exercise in tree traversal, a production-grade priority queue, a memory-constrained embedded system, or a merge-heavy data pipeline. The mechanics above are consistent, but the tradeoffs land differently depending on your language, constraints, and how often insertion, extraction, and merging each dominate your workload.