This section tells you a few things you need to know before you get started, such as what you’ll need for hardware and software, where to find the project files for this book, and more.
The chapters in this short but important section will motivate the study of data structures and algorithms as well as give you a quick rundown of what is built into the Swift standard library that you can build from.
Data structures are a well-studied area, and the concepts are language agnostic; a data structure from C is functionally and conceptually identical to the same data structure in any other language, such as Swift. At the same time, the high-level expressiveness of Swift make it an ideal choice for learning these core concepts without sacrificing too much performance.
Answering the question, "Does it scale?" is all about understanding the complexity of an algorithm. Big-O notation is the primary tool you use to think about algorithmic performance in the abstract, independent of hardware or language. This chapter will prepare you to think in these terms.
Before you dive into the rest of this book, you’ll first look at a few data structures that are baked into the Swift language. The Swift standard library refers to the framework that defines the core components of the Swift language. Inside, you’ll find a variety of tools and types to help build your Swift apps.
This section looks at a few important data structures that are not found in the Swift standard library but form the basis of more advanced algorithms covered in future sections. All of them are collections optimized for (and enforce) a particular access pattern. You will also get a glimpse of how protocols in Swift can be used to build up these useful primitives.
Each concept chapter is followed by a Challenge chapter where you will be asked to answer something about the data structure, write a utility function, or use it directly to solve a common problem. Worked solutions to the Challenge chapters are located at the end of the book. We encourage you not to peek at our solution until you have given the challenge a shot yourself.
The stack data structure is identical in concept to a physical stack of objects. When you add an item to a stack, you place it on top of the stack. When you remove an item from a stack, you always remove the top-most item. Stacks are useful, and also exceedingly simple. The main goal of building a stack is to enforce how you access your data.
Practise your new-found Stack knowledge with these challenges.
A linked list is a collection of values arranged in a linear unidirectional sequence. A linked list has several theoretical advantages over contiguous storage options such as the Swift Array, including constant time insertion and removal from the front of the list, and other reliable performance characteristics
Practise your new-found linked list knowledge with these challenges.
Lines are everywhere, whether you are lining up to buy tickets to your favorite movie, or waiting for a printer machine to print out your documents. These real-life scenarios mimic the queue data structure. Queues use first-in-first-out ordering, meaning the first element that was enqueued will be the first to get dequeued. Queues are handy when you need to maintain the order of your elements to process later.
In this chapter, you will explore five different problems related to queues.
Trees are another way to organize information, introducing the concept of children and parents. You‘ll take a look of the most common tree types and see how they can be used to solve specific computational problems. Just like the last section, this section will introduce you to a concept with a chapter, followed by a Challenge chapter to help you hone the skills you are learning.
Trees are a very useful way to organize information when performance is critical. Adding them as a tool to your toolbelt will undoubtedly prove to be useful throughout your career.
The tree is a data structure of profound importance. It is used to tackle many recurring challenges in software development, such as representing hierarchical relationships, managing sorted data, and facilitating fast lookup operations. There are many types of trees, and they come in various shapes and sizes.
Test your understanding of the previous chapter with these challenges.
In the previous chapter, you looked at a basic tree where each node can have many children. A binary tree is a tree where each node has at most two children, often referred to as the left and right children. Binary trees serve as the basis for many tree structures and algorithms. In this chapter, you’ll build a binary tree and learn about the three most important tree traversal algorithms.
Binary trees are a surprisingly popular topic in algorithm interviews. Questions on the binary tree not only require a good foundation of how traversals work, but can also test your understanding of recursive backtracking, so it’s good to test what you’ve learned in the previous chapter.
A binary search tree facilitates fast lookup, addition, and removal operations. Each operation has an average time complexity of O(log n), which is considerably faster than linear data structures such as arrays and linked lists.
Try out these three challenges to lock the concepts of binary search trees down.
In the previous chapter, you learned about the O(log n) performance characteristics of the binary search tree. However, you also learned that unbalanced trees can deteriorate the performance of the tree, all the way down to O(n). In 1962, Georgy Adelson-Velsky and Evgenii Landis came up with the first self-balancing binary search tree: the AVL Tree.
Here are three challenges that revolve around AVL trees. Solve these to make sure you have the concepts down.
The trie (pronounced as “try”) is a tree that specializes in storing data that can be represented as a collection, such as English words. The benefits of a trie are best illustrated by looking at it in the context of prefix matching, which is what you’ll do in this chapter.
Here are two challenges to test your understanding of the previous chapter.
Binary search is one of the most efficient searching algorithms with a time complexity
of O(log n). This is comparable with searching for an element inside a balanced binary search tree. To perform a binary search, the collection must be able to perform index manipulation in constant time, and must be sorted.
Here are three challenges about implementing binary search. Solve these to make sure you have the concepts down.
A heap is a complete binary tree, also known as a binary heap, that can be constructed using an array. Heaps come in two flavors: Max heaps and Min heaps. Have you seen the movie Toy Story, with the claw machine and the squeaky little green aliens? Imagine that the claw machine is operating on your heap structure, and will always pick the minimum or maximum value, depending on the flavor of heap.
Think you have a handle on heaps? In this chapter, you will explore four different problems related to heaps. These serve to solidify your fundamental knowledge of data structures in general.
Queues are simply lists that maintain the order of elements using first-in-first-out (FIFO) ordering. A priority queue is another version of a queue that, instead of using FIFO ordering, dequeues elements in priority order. A priority queue is especially useful when you need to identify the maximum or minimum value given a list of elements.
Check your understanding of the previous chapter with these challenges.
Putting lists in order is a classical computational problem. Sorting has been studied since the days of vacuum tubes and perhaps even before that. Although you may never need to write your own sorting algorithm when you can use the highly optimized standard library, studying sorting has many benefits. You will be introduced, for example, to the all important technique of divide and conquer, stability, and best and worst case timings.
This section will follow the same structure of introducing you to a concept with a chapter, followed by a Challenge chapter so that you can practice the skills you are acquiring.
Studying sorting may seem a bit academic and disconnected to the “real world” of app development, but understanding the tradeoffs for these simple cases will lead you to a better understanding and let you analyze any algorithm.
O(n²) time complexity is not great performance, but the sorting algorithms in this category are easy to understand and useful in some scenarios. These algorithms are space efficient; they only require constant O(1) additional memory space. In this chapter, you'll be looking at the bubble sort, selection sort, and insertion sort algorithms.
In the previous chapter, you looked at the bubble sort, selection sort, and insertion sort algorithms. Solve these challenges to solidify your understanding.
Merge sort is one of the most efficient sorting algorithms. With a time complexity of O(log n), it’s one of the fastest of all general-purpose sorting algorithms. The idea behind merge sort is divide and conquer: to break up a big problem into several smaller, easier to solve problems and then combine those solutions into a final result. The merge sort mantra is to split first, and merge after.
Test your understanding of the merge sort with these challenges.
In this chapter, you’ll look at a completely different model of sorting. So far, you’ve been relying on comparisons to determine the sorting order. Radix sort is a non-comparative algorithm for sorting integers in linear time. There are multiple implementations of radix sort that focus on different problems. To keep things simple, in this chapter you’ll focus on sorting base 10 integers while investigating the least significant digit (LSD) variant of radix sort.
Solve this challenge to further explore the radix sort.
Heapsort is another comparison-based algorithm that sorts an array in ascending order using a heap. This chapter builds on the heap concepts presented in Chapter 12, “The Heap Data Structure”.Heapsort takes advantage of a heap being, by definition, a partially sorted binary tree.
Solving these heapsort related challenges will make sure you have full understanding of the concepts learned in the previous chapter.
In the preceding chapters, you’ve learned to sort an array using comparison-based sorting algorithms, merge sort, and heap sort. Quicksort is another comparison-based sorting algorithm. Much like merge sort, it uses the same strategy of divide and conquer. In this chapter, you will implement Quicksort and look at various partitioning strategies to get the most out of this sorting algorithm.
Here are a couple of quicksort challenges to make sure you have the topic down.
Graphs are an extremely useful data structure that can be used to model a wide range of things: webpages on the internet, the migration patterns of birds, protons in the nucleus of an atom. This section gets you thinking deeply (and broadly) about how to use graphs and graph algorithms to solve real world problems.
The chapters that follow will give the foundation you need to understand graph data structures. Like previous sections, every other chapter will serve as a Challenge chapter so you can practice what you’ve learned.
After completing this section, you will have powerful tools at your disposal to model and solve important real-life problems using graphs. Let’s get started!
What do social networks have in common with booking cheap flights around the world? You can represent both of these real-world models as graphs! A graph is a data structure that captures relationships between objects. It is made up of vertices connected by edges. In a weighted graph, every edge has a weight associated with it that represents the cost of using this edge. This lets you choose the cheapest or shortest path between two vertices.
Test your understanding of graphs with these two challenges.
In the previous chapter, you explored how graphs can be used to capture relationships between objects. Several algorithms exist to traverse or search through a graph's vertices. One such algorithm is the breadth-first search algorithm, which can be used to solve a wide variety of problems, including generating a minimum spanning tree, finding potential paths between vertices, and finding the shortest path between two vertices.
Solve these challenges by implementing what you learned in the previous chapter.
In the previous chapter, you looked at breadth-first search where you had to explore every neighbor of a vertex before going to the next level. In this chapter, you will look at depth-first search, which has applications for topological sorting, detecting cycles, path finding in maze puzzles, and finding connected components in a sparse graph.
Try to solve these challenges that use what you have learned about the depth-first search.
Have you ever used the Google or Apple Maps app to find the shortest or fastest from one place to another? Dijkstra’s algorithm is particularly useful in GPS networks to help find the shortest path between two places. Dijkstra’s algorithm is a greedy algorithm, which constructs a solution step-by-step, and picks the most optimal path at every step.
Solve these challenges to make sure you've understood the previous chapter.
In previous chapters, you’ve looked at depth-first and breadth-first search algorithms. These algorithms form spanning trees. In this chapter, you will look at Prim’s algorithm, a greedy algorithm used to construct a minimum spanning tree. A minimum spanning tree is a spanning tree with weighted edges where the total weight of all edges is minimized. You’ll learn how to implement a greedy algorithm to construct a solution step-by-step, and pick the most optimal path at every step.
Test your understanding of Prim's Algorithm with these challenges.
