import java.util.Arrays;

import cs125.sorting.quicksort.Partitioner;

String[] array = new String[] {"you", "are", "not", "alone"};

Partitioner.partition(array);

System.out.println(Arrays.toString(array));

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

You knew it was coming…

Create a public class named `BinaryTreeValuesAtLevel`

providing a single static method `valuesAtLevel`

.
`valuesAtLevel`

accepts a `BinaryTree<Comparable>`

(from `cs125.trees`

) and a level as an `int`

.
It should return, as a `List<Comparable>`

, all the values in the passed tree that are at the passed level, sorted
in ascending order.
If the passed tree is `null`

, or the level is negative, you should throw an `IllegalArgumentException`

.

The level corresponds to the depth of the node in the tree. So the root node is at level 0, its children are at level 1, its children's children are at level 2, etc.

To complete this question you probably need a helper method.
Our suggestion is that the main `valuesAtLevel`

create the list, begin the recursion, and sort the result.
(Just use a built-in sort.)
Your recursive method will need to track *both* the current level in the tree *and* the target level.
Once the target level is reached, the current node's value should be added and the recursion can stop.
You will also want to pass the list created by your main method.

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.

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

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

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

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

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.

Sorting Algorithm Review

Let’s review the sorting algorithms we’ve covered together:

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

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

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.

Created By: Geoffrey Challen

/ 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.

Need more practice? Head over to the practice page.