Here you'll find implementations of popular algorithms and data structures in everyone's favorite new language Swift, with detailed explanations of how they work.
If you're a computer science student who needs to learn this stuff for exams -- or if you're a self-taught programmer who wants to brush up on the theory behind your craft -- you've come to the right place!
The goal of this project is to explain how algorithms work. The focus is on clarity and readability of the code, not on making a reusable library that you can drop into your own projects. That said, most of the code should be ready for production use but you may need to tweak it to fit into your own codebase.
All code is compatible with Xcode 7.2 and Swift 2.1. We'll keep this updated with the latest version of Swift.
This is a work in progress. More algorithms will be added soon. :-)
[What are algorithms and data structures?](What are Algorithms.markdown) Pancakes!
[Why learn algorithms?](Why Algorithms.markdown) Worried this isn't your cup of tea? Then read this.
[Big-O notation](Big-O Notation.markdown). We often say things like, "This algorithm is O(n)." If you don't know what that means, read this first.
[Algorithm design techniques](Algorithm Design.markdown). How do you create your own algorithms?
[How to contribute](How to Contribute.markdown). Report an issue to leave feedback, or submit a pull request. Suggestions and contributions are welcome!
If you're new to algorithms and data structures, here are a few good ones to start out with:
- Stack
- Queue
- [Insertion Sort](Insertion Sort/)
- [Binary Search](Binary Search/) and [Binary Search Tree](Binary Search Tree/)
- [Merge Sort](Merge Sort/)
- Boyer-Moore string search
- [Linear Search](Linear Search/). Find an element in an array.
- [Binary Search](Binary Search/). Quickly find elements in a sorted array.
- [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
- [k-th Largest Element](Kth Largest Element/). Find the kth largest element in an array, such as the median.
- [Selection Sampling](Selection Sampling/). Randomly choose a bunch of items from a collection.
- Union-Find. Keeps track of disjoint sets and lets you quickly merge them.
- [Brute-Force String Search](Brute-Force String Search/). A naive method.
- Boyer-Moore. A fast method to search for substrings. It skips ahead based on a look-up table, to avoid looking at every character in the text.
- Rabin-Karp
It's fun to see how sorting algorithms work, but in practice you'll almost never have to provide your own sorting routines. Swift's own sort() is more than up to the job. But if you're curious, read on...
Basic sorts:
- [Insertion Sort](Insertion Sort/)
- [Selection Sort](Selection Sort/)
- [Shell Sort](Shell Sort/)
Fast sorts:
- Quicksort
- [Merge Sort](Merge Sort/)
- [Heap Sort](Heap Sort/)
Special-purpose sorts:
- Bucket Sort
- Counting Sort
- Radix Sort
- Topological Sort
Bad sorting algorithms (don't use these!):
- [Bubble Sort](Bubble Sort/)
- [Run-Length Encoding (RLE)](Run-Length Encoding)
- Huffman Encoding
- Shuffle. Randomly rearranges the contents of an array.
- Greatest Common Divisor (GCD). Special bonus: the least common multiple.
- Permutations and Combinations. Get your combinatorics on!
- Statistics
- k-Nearest Neighbors
- PageRank
The choice of data structure for a particular task depends on a few things.
First, there is the shape of your data and the kinds of operations that you'll need to perform on it. If you want to look up objects by a key you need some kind of dictionary; if your data is hierarchical in nature you want a tree structure of some sort; if your data is sequential you want a stack or queue.
Second, it matters what particular operations you'll be performing most, as certain data structures are optimized for certain actions. For example, if you often need to find the most important object in a queue, then a heap or priority queue is more optimal than a plain array.
Most of the time using just the built-in Array, Dictionary, and Set types is sufficient, but sometimes you may want something more fancy...
- Array2D. A two-dimensional array with fixed dimensions. Useful for board games.
- [Bit Set](Bit Set/). A fixed-size sequence of n bits.
- [Fixed Size Array](Fixed Size Array/). When you know beforehand how large your data will be, it might be more efficient to use an old-fashioned array with a fixed size.
- [Ordered Array](Ordered Array/). An array that is always sorted.
- Stack. Last-in, first-out!
- Queue. First-in, first-out!
- Deque. A double-ended queue.
- [Priority Queue](Priority Queue). A queue where the most important element is always at the front.
- [Ring Buffer](Ring Buffer/). Also known as a circular buffer. An array of a certain size that conceptually wraps around back to the beginning.
- [Linked List](Linked List/). A sequence of data items connected through links. Covers both singly and doubly linked lists.
- Skip List
- Tree. A general-purpose tree structure.
- [Binary Tree](Binary Tree/). A tree where each node has at most two children.
- [Binary Search Tree (BST)](Binary Search Tree/). A binary tree with the special requirement that elements are inserted in a specific way, allowing for faster queries, like when using a [binary search](Binary Search/) algorithm.
- [AVL Tree](AVL Tree/). A binary search tree that balances itself using rotations.
- Red-Black Tree
- Splay Tree
- Threaded Binary Tree
- [Segment Tree](Segment Tree/). Can quickly compute a function over a portion of an array.
- kd-Tree
- Heap. A binary tree stored in an array, so it doesn't use pointers. Makes a great priority queue.
- Fibonacci Heap
- Trie
- [Hash Table](Hash Table/). Allows you to store and retrieve objects by a key. This is how the dictionary type is usually implemented.
- Hash Functions
- Bloom Filter
- [Hash Set](Hash Set/). A set implemented using a hash table.
- Multiset
- Ordered Set
- Graph
- Breadth-First Search (BFS)
- Depth-First Search (DFS)
- Shortest Path
- Minimum Spanning Tree
- All Paths
A lot of software developer interview questions consist of algorithmic puzzles. Here is a small selection of fun ones. For more puzzles (with answers), see here and here.
- [Two-Sum Problem](Two-Sum Problem/)
- [Fizz Buzz](Fizz Buzz/)
- [Monty Hall Problem](Monty Hall Problem/)
For more information, check out these great books:
- Introduction to Algorithms by Cormen, Leiserson, Rivest, Stein
- The Algorithm Design Manual by Skiena
- Elements of Programming Interviews by Aziz, Lee, Prakash
- Algorithms by Sedgewick
The following books are available for free online:
- Algorithms by Dasgupta, Papadimitriou, Vazirani
- Algorithms, Etc. by Erickson
- Algorithms + Data Structures = Programs by Wirth
- Algorithms and Data Structures: The Basic Toolbox by Mehlhorn and Sanders
Other algorithm repositories:
- EKAlgorithms. A great collection of algorithms in Objective-C.
- Rosetta Code. Implementations in pretty much any language you can think of.
All content is licensed under the terms of the MIT open source license.