Quicksort

We continue our discussion of sorting algorithms by introducing the wild child: Quicksort. Quicksort can achieve best-case sorting behavior while using less space than Mergesort. But, Quicksort also has some pathological cases we need to understand. Let’s get started!

Warm Up Debugging Challenge

Warm Up Debugging Challenge

You knew it was coming…

Partitioning

Partitioning

Mergesort was our first recursive sorting algorithm. It employed a bottom-up approach—first breaking the array into individual chunks, and then merging them back together.

Quicksort is another recursive approach, but it works differently. Let’s first examine its operation at a high level, and then break it down further.

https://www.youtube.com/watch?v=lrOyOL71-l8

Like Mergesort, Quicksort is also based on another building block: partitioning. Let’s see how that works:

https://www.youtube.com/watch?v=jO9W8Y-PVS0

You’ll get to complete partition on our next homework! But we can at least experiment with it using the method built-in to our playground:

// Experiment with partition

Quicksort

Quicksort

Next, first we’ll implement Quicksort. Then we’ll analyze its performance!

Implementation

Implementation

Next, let’s build a recursive sorting algorithm based on Partitioner.partition! Once we have a partition method, completing the implementation is quite straightforward!

// Quicksort

Performance Analysis

Performance Analysis

Next, let’s use the Quicksort implementation we completed above to experiment with its performance. Surprises are in store!

// Quicksort Performance Analysis

import java.util.Random;

import java.util.Arrays;

Integer[] randomIntArray(int length) {

Random random = new Random();

Integer[] results = new Integer[length];

for (int i = 0; i < results.length; i++) {

results[i] = random.nextInt(128);

}

return results;

}

System.out.println(Arrays.toString(randomIntArray(8)));

What’s going on here? Let’s consider things visually.

https://www.youtube.com/watch?v=nTmObzFNhqU

Sorting Algorithm Review

Sorting Algorithm Review

Our next quiz will focus on sorting algorithms, and particularly the ones that we’ve covered together:

• Bubblesort
• Insertion Sort
• Mergesort
• Quicksort

Let’s review salient aspects of sorting performance. Specifically: best and worst case inputs and runtime, and memory usage.

https://www.youtube.com/watch?v=csMVUXnBeBA

Sorting Tradeoffs

Sorting Tradeoffs

Sorting algorithms represent a fascinating set of tradeoffs between different performance attributes. For example:

• Have a very small array to sort? Insertion sort can actually outperform other algorithms on small arrays, because the recursive calls needed by Mergesort and Quicksort have some overhead associated with them.
• Want predictable performance? Mergesort has your back. O(n log n), O(n log n), O(n log n). Sometimes it’s actually more important that a sort take a predictable amount of time than that it be completely optimal.
• Short on space? Quicksort’s space utilization is substantially smaller than Mergesort, and with good pivot selection it can achieve similar performance.

Timsort, the default sorting algorithm used by several languages including Python and Java, actually combines elements of both insertion sort and Mergesort, in addition to some other tricks.

Sorting Stability

Sorting Stability

As a final note, let’s discuss sort algorithm stability. Stability is a desirable property of sorting algorithms. It means that items with equal values will not change positions while the array is sorted.

Why is stability desirable? Because it allows us to run a sorting algorithm multiple times on complex data and produce meaningful results.

For example, imagine that want a list of restaurants sorted first by cuisine and then by name. Assuming our sorting algorithm is stable, we can accomplish this by first sorting the list by name and then by cuisine. However, if the sorting algorithm in unstable that second sort by cuisine will destroy the results of the sort by name, and render the combination meaningless.

Homework: Quicksort Partition (First Value)

Created By: CS 124 Staff

/ Version: 2020.6.0

Create a public, non-final class named Partitioner. Implement a public static method int partition(int[] values) that returns the input array partitioned using the first array value as the pivot. All values smaller than the pivot should precede it in the array, and all values larger than or equal to the pivot should follow it. Your method should return the index of the pivot value. If the array is null or empty you should return -1.

This problem deadline has passed, but you can continue to practice. Experiment! You will not lose credit.

Homework Restricted to Current CS 124 Students

A publicly-accessible version of this content is available at learncs.online.

More Practice

Need more practice? Head over to the practice page.