Fibonacci Heap in the JavaScript-Algorithms Repository: Implementation Analysis

The trekhleb/javascript-algorithms repository does not contain a Fibonacci heap implementation; it provides only binary heap data structures (MinHeap and MaxHeap) located in src/data-structures/heap/.

The Fibonacci heap is a sophisticated priority queue structure known for its amortized O(1) time complexity for insert and decrease-key operations. Developers exploring the popular trekhleb/javascript-algorithms repository often search for this advanced data structure to optimize graph algorithms like Dijkstra’s or Prim’s. However, a thorough analysis of the source code reveals that the repository deliberately excludes Fibonacci heaps in favor of simpler binary heap implementations.

What Heap Data Structures Are Implemented?

A search of the source tree (src/data-structures/heap/) shows only the binary heap implementation. No file or module named "FibonacciHeap" exists, nor does any reference to the Fibonacci-heap algorithm appear in the codebase.

The repository provides:

• Heap.js – Abstract base class defining core heap operations (insert, extractRoot, heapify, peek).
• MinHeap.js – Concrete min-heap extending Heap; used for priority queues and sorting.
• MaxHeap.js – Concrete max-heap extending Heap.

Core Heap Files and Architecture

The base Heap class in src/data-structures/heap/Heap.js defines the shared logic for maintaining the heap property, while MinHeap.js and MaxHeap.js implement the specific comparison operations. This architecture keeps the code idiomatic and focused on clarity rather than the complex pointer-heavy structure of a Fibonacci heap.

Binary Heap Implementation Details

The binary heap provides O(log n) time for insertions and deletions, which is sufficient for the algorithms showcased in the project. Below is a practical example of using the MinHeap class.

import MinHeap from '../src/data-structures/heap/MinHeap';

// Create a min‑heap.
const heap = new MinHeap();

// Insert values.
heap.insert(10);
heap.insert(5);
heap.insert(30);

// Retrieve the smallest element.
const min = heap.extractRoot(); // → 5

// Peek at the current root without removing it.
console.log(heap.peek()); // → 10

How the Priority Queue Extends MinHeap

The repository’s priority queue implementation in src/data-structures/priority-queue/PriorityQueue.js builds directly upon MinHeap. Elements are ordered by priority, with smaller numbers indicating higher priority.

import PriorityQueue from '../src/data-structures/priority-queue/PriorityQueue';

// Elements are ordered by priority (smaller numbers = higher priority).
const pq = new PriorityQueue();

pq.enqueue('task A', 2);
pq.enqueue('task B', 1);
pq.enqueue('task C', 3);

console.log(pq.dequeue()); // → 'task B' (priority 1)

Heap Sort Integration

The heap sort algorithm in src/algorithms/sorting/heap-sort/HeapSort.js leverages the binary heap structure to achieve O(n log n) sorting.

import HeapSort from '../src/algorithms/sorting/heap-sort/HeapSort';

const sorter = new HeapSort();
const unsorted = [9, 4, 7, 1, 3];
const sorted = sorter.sort(unsorted); // → [1, 3, 4, 7, 9]

Why the Repository Omits Fibonacci Heap

The Fibonacci heap achieves superior amortized time complexity—O(1) for insert and decreaseKey compared to the binary heap’s O(log n)—but requires a complex structure of doubly-linked trees and lazy consolidation. The javascript-algorithms project prioritizes educational clarity and idiomatic JavaScript over advanced asymptotic optimizations. The binary heap implementation is sufficient for demonstrating priority queues, heap sort, and graph algorithms without introducing the pointer-heavy complexity of a Fibonacci heap.

Summary

• The trekhleb/javascript-algorithms repository does not implement a Fibonacci heap.
• The only heap structures provided are binary heaps (MinHeap and MaxHeap) located in src/data-structures/heap/.
• These binary heaps power the PriorityQueue and HeapSort implementations with O(log n) insertion and extraction.
• The absence of a Fibonacci heap reflects the project’s focus on clarity and simplicity over complex amortized optimizations.

Frequently Asked Questions

Does trekhleb/javascript-algorithms include a Fibonacci heap?

No. A thorough search of the codebase confirms that no Fibonacci heap implementation exists. The repository only provides binary heap implementations in the src/data-structures/heap/ directory.

What heap implementation does the repository use instead?

The repository uses a binary heap architecture consisting of an abstract Heap base class and concrete MinHeap and MaxHeap implementations. These provide O(log n) time complexity for insert and extract operations.

Can I use the existing binary heap for Dijkstra's algorithm?

Yes. While a Fibonacci heap offers better theoretical amortized performance for Dijkstra’s algorithm, the provided MinHeap or PriorityQueue (which extends MinHeap) is fully functional and sufficient for most practical use cases, operating with O(log n) per operation.

Where can I find the source code for the heap implementations?

The source files are located in the src/data-structures/heap/ directory. Key files include Heap.js (base class), MinHeap.js, and MaxHeap.js. The priority queue implementation that utilizes these heaps is found at src/data-structures/priority-queue/PriorityQueue.js.

{
  "mcpServers": {
    "instagit": {
      "command": "npx",
      "args": ["-y", "instagit@latest"]
    }
  }
}