# Comparing Heap and Quick Sorting Algorithms

Published on Wednesday, March 27, 2024

Imagine you’re building an app and need to sort a massive list of data – maybe product prices, customer names, or high scores. Choosing the right sorting algorithm can make a huge difference in performance. Today, we’ll pit two popular contenders against each other: **heap** and **quick**.

Before we dive into the code, let’s briefly explore the basics of both algorithms. If you’re eager to see the action, feel free to jump straight to the code comparison here.

*Heap* Sort

**Heap Sort** is a powerful sorting algorithm that’s often used in various applications due to its efficiency and in-place nature.

### A Brief History

Heap sort was first described in 1964 by J. W. J. Williams. However, Robert W. Floyd quickly improved upon Williams’ algorithm in the same year, making it possible to sort the array in-place without requiring extra memory.

### How It Works

Heap sort works by first building a max heap from the input array. A max heap is a complete binary tree where the value of each node is greater than or equal to the values of its children. Once the heap is built, the largest element is at the root.

**Build Max Heap:**Create a max heap from the input array.**Extract Maximum:**Swap the root element (largest element) with the last element of the heap.**Heapify:**Restore the max heap property by calling the heapify function on the root node.**Repeat:**Repeat steps 2 and 3 until the entire array is sorted.

### Time Complexity

The time complexity of heap sort is $O(n \log n)$ in both the average and worst-case scenarios. This makes it a very efficient sorting algorithm for large datasets.

### Advantages and Disadvantages

**Advantages:**

- Efficient for large datasets
- In-place sorting, requiring minimal extra memory
- Can be used for priority queues

**Disadvantages:**

- Can be slightly slower than quicksort in the average case
- May not be as stable as other sorting algorithms

### When to Use Heap Sort

Heap sort is a good choice for:

**Large datasets:**Its $O(n \log n)$ time complexity makes it suitable for sorting large arrays.**Priority queues:**Heap sort can be used to implement priority queues efficiently.**Applications where space efficiency is important:**Heap sort is an in-place algorithm, requiring minimal extra memory.

**In conclusion,** heap sort is a powerful and efficient sorting algorithm that’s widely used in various applications. Understanding its principles and advantages can help you make informed decisions when choosing a sorting algorithm for your specific needs.

*Quick* Sort

**Quicksort** is a powerful sorting algorithm that’s a staple in computer science. It’s known for its speed and efficiency, making it a popular choice for various applications.

### A Brief History

Quicksort was first described in 1959 (published in 1961) by the renowned British computer scientist Sir Charles Antony Richard Hoare. His innovative approach to sorting using a divide-and-conquer strategy has had a lasting impact on the field of algorithms.

### How It Works

Quicksort operates on the principle of divide and conquer:

**Partitioning:**Choose a pivot element from the unsorted list.**Rearrangement:**Rearrange the list so that elements smaller than the pivot are on one side, and elements larger than the pivot are on the other.**Recursive Sorting:**Recursively apply quicksort to the sublists on both sides of the pivot.

### Time Complexity

The efficiency of quicksort heavily depends on the choice of pivot elements. With a good choice of pivots, quicksort can achieve an average-case time complexity of $O(n \log n)$, making it one of the fastest sorting algorithms. This means the number of comparisons it takes to sort a list grows proportionally to the logarithm of the number of elements.

However, quicksort’s Achilles’ heel is its worst-case performance. If the pivot element consistently ends up being the largest or smallest element in the list, the algorithm can degenerate to $O(n^2)$ complexity. This can happen with already sorted or reverse-sorted data.

### Advantages and Disadvantages

**Advantages:**

- Efficient for large datasets
- Generally faster than bubble sort and insertion sort
- Can be implemented in-place

**Disadvantages:**

- Worst-case time complexity of $O(n^2)$
- Can be less stable than other sorting algorithms

### When to Use Quicksort

Quicksort is a great choice for:

**Large datasets:**Its average-case efficiency makes it well-suited for sorting large lists.**General-purpose sorting:**It’s a versatile algorithm that can be used in various applications.

**However,** if you’re dealing with already sorted or nearly sorted data, quicksort might not be the best option due to its potential for worst-case performance. In such cases, other algorithms like merge sort or heap sort might be more suitable.

**In conclusion,** quicksort is a powerful and efficient sorting algorithm that’s widely used in computer science. Understanding its principles and limitations can help you make informed decisions when choosing a sorting algorithm for your specific needs.

## The Clash

We put both algorithms to the test with a battlefield of 3500 random numbers. Now, let’s see who emerges victorious!

Now that we have some data to test on, we want to add the algorithm for the **heap sort**. This goes as follows.

And of course the **quick sort** as well, otherwise we won’t have anything to compare against.

Now, let’s test the two against one another.

### Delve deeper:

For even more sorting options, explore our collection of sorting algorithms. Want to get your hands dirty with the code? Head over to **heap sort VS. quick sort Implementation**.

## The Winner

Brace yourselves! The benchmark revealed that the **quick sort** is a staggering **134.63x** faster than its competitor! That translates to running the quick sort almost 135 times in the time it takes the heap sort to complete once!

### The A.I. Nicknames the Winners:

We consulted a top-notch AI to give our champion a superhero nickname. From this day forward, the **quick sort** shall be known as ** The Quickfire Ninja**! The heap sort, while valiant, deserves recognition too. We present to you,

**!**

*The Heap Hero*### The Choice is Yours, Young Padawan

So, does this mean the quick sort is the undisputed king of all sorting algorithms? Not necessarily. Different algorithms have their own strengths and weaknesses. But understanding their efficiency (which you can learn more about in the Big-O Notation post) helps you choose the best tool for the job!

This vast world of sorting algorithms holds countless possibilities. Who knows, maybe you’ll discover the next champion with lightning speed or memory-saving magic!

This showdown hopefully shed light on the contrasting speeds of *heap* and *quick* sorting algorithms. Stay tuned for more algorithm explorations on the blog.