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!
You knew it was coming…
Let's continue exploring recursion on binary trees. However, this problem takes a significant step forward in difficulty, so be prepared!
We've provided a method
pathToValue that accepts a
BinaryTree<Any> as its first parameter
Any as its second.
It returns a
List<Any> containing all the values in the tree on the way to the first node with a
value equal to the passed
null if the tree does not contain the passed
Any. We've handled this
case already for you in the starter code.
Our wrapper method initializes the list properly and then calls a private helper method which performs the
recursion. The helper should return
true if the tree contains the value, and if it does also manipulate the list
properly. If the tree does not contain the value it should return
false. You will want to use
Any value) to add values to the front of the list as you work your way through the tree.
This problem is hard! Here's an outline of a solution to help get you started:
false, since an empty tree does not contain the value
Good luck and have fun!
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:
Next, first we’ll implement Quicksort. Then we’ll analyze its performance!
Next, let’s build a recursive sorting algorithm based on
Once we have a partition method, completing the implementation is quite straightforward!
Next, let’s use the Quicksort implementation we completed above to experiment with its performance. Surprises are in store!
What’s going on here? Let’s consider things visually.
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 algorithms represent a fascinating set of tradeoffs between different performance attributes. For example:
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.
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.
Create a method
fun partition(value: IntArray?) 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.