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Based on the "Data Structures / Algorithms" category.
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README
SwiftGraph
SwiftGraph is a pure Swift (no Cocoa) implementation of a graph data structure, appropriate for use on all platforms Swift supports (iOS, macOS, Linux, etc.). It includes support for weighted, unweighted, directed, and undirected graphs. It uses generics to abstract away both the type of the vertices, and the type of the weights.
It includes copious insource documentation, unit tests, as well as search functions for doing things like breadthfirst search, depthfirst search, and Dijkstra's algorithm. Further, it includes utility functions for topological sort, Jarnik's algorithm to find a minimumspanning tree, detecting a DAG (directedacyclicgraph), and enumerating all cycles.
Installation
SwiftGraph 3.0 requires Swift 5 (Xcode 10.2). Use SwiftGraph 2.0 for Swift 4.2 (Xcode 10.1) support, SwiftGraph 1.5.1 for Swift 4.1 (Xcode 9), SwiftGraph 1.4.1 for Swift 3 (Xcode 8), SwiftGraph 1.0.6 for Swift 2 (Xcode 7), and SwiftGraph 1.0.0 for Swift 1.2 (Xcode 6.3) support. SwiftGraph supports GNU/Linux and is tested on it.
CocoaPods
Use the CocoaPod SwiftGraph
.
Carthage
Add the following to your Cartfile
:
github "davecom/SwiftGraph" ~> 3.0.0
Swift Package Manager (SPM)
Use this repository as your dependency.
Manual
Copy all of the sources in the Sources
folder into your project.
Tips and Tricks
 To get a sense of how to use SwiftGraph, checkout the unit tests
 Inserting an edge by vertex indices is much faster than inserting an edge by vertex objects that need to have their indices looked up
 Generally, looking for the index of a vertex is O(n) time, with n being the number of vertices in the graph
 SwiftGraph includes the functions
bfs()
anddfs()
for finding a route between one vertex and another in a graph anddijkstra()
for finding shortest paths in a weighted graph  A sample Mac app that implements the Nine Tails problem is included  just change the target of the project to
SwiftGraphSampleApp
to build it
Example
For more detail, checkout the Documentation section, but this example building up a weighted graph of American cities and doing some operations on it, should get you started.
let cityGraph: WeightedGraph<String, Int> = WeightedGraph<String, Int>(vertices: ["Seattle", "San Francisco", "Los Angeles", "Denver", "Kansas City", "Chicago", "Boston", "New York", "Atlanta", "Miami", "Dallas", "Houston"])
cityGraph
is a WeightedGraph
with String
vertices and Int
weights on its edges.
cityGraph.addEdge(from: "Seattle", to:"Chicago", weight:2097)
cityGraph.addEdge(from: "Seattle", to:"Chicago", weight:2097)
cityGraph.addEdge(from: "Seattle", to: "Denver", weight:1331)
cityGraph.addEdge(from: "Seattle", to: "San Francisco", weight:807)
cityGraph.addEdge(from: "San Francisco", to: "Denver", weight:1267)
cityGraph.addEdge(from: "San Francisco", to: "Los Angeles", weight:381)
cityGraph.addEdge(from: "Los Angeles", to: "Denver", weight:1015)
cityGraph.addEdge(from: "Los Angeles", to: "Kansas City", weight:1663)
cityGraph.addEdge(from: "Los Angeles", to: "Dallas", weight:1435)
cityGraph.addEdge(from: "Denver", to: "Chicago", weight:1003)
cityGraph.addEdge(from: "Denver", to: "Kansas City", weight:599)
cityGraph.addEdge(from: "Kansas City", to: "Chicago", weight:533)
cityGraph.addEdge(from: "Kansas City", to: "New York", weight:1260)
cityGraph.addEdge(from: "Kansas City", to: "Atlanta", weight:864)
cityGraph.addEdge(from: "Kansas City", to: "Dallas", weight:496)
cityGraph.addEdge(from: "Chicago", to: "Boston", weight:983)
cityGraph.addEdge(from: "Chicago", to: "New York", weight:787)
cityGraph.addEdge(from: "Boston", to: "New York", weight:214)
cityGraph.addEdge(from: "Atlanta", to: "New York", weight:888)
cityGraph.addEdge(from: "Atlanta", to: "Dallas", weight:781)
cityGraph.addEdge(from: "Atlanta", to: "Houston", weight:810)
cityGraph.addEdge(from: "Atlanta", to: "Miami", weight:661)
cityGraph.addEdge(from: "Houston", to: "Miami", weight:1187)
cityGraph.addEdge(from: "Houston", to: "Dallas", weight:239)
Convenience methods are used to add WeightedEdge
connections between various vertices.
let (distances, pathDict) = cityGraph.dijkstra(root: "New York", startDistance: 0)
var nameDistance: [String: Int?] = distanceArrayToVertexDict(distances: distances, graph: cityGraph)
// shortest distance from New York to San Francisco
let temp = nameDistance["San Francisco"]
// path between New York and San Francisco
let path: [WeightedEdge<Int>] = pathDictToPath(from: cityGraph.indexOfVertex("New York")!, to: cityGraph.indexOfVertex("San Francisco")!, pathDict: pathDict)
let stops: [String] = cityGraph.edgesToVertices(edges: path)
The shortest paths are found between various vertices in the graph using Dijkstra's algorithm.
let mst = cityGraph.mst()
The minimum spanning tree is found connecting all of the vertices in the graph.
let cycles = cityGraph.detectCycles()
All of the cycles in cityGraph
are found.
let isADAG = cityGraph.isDAG
isADAG
is false
because cityGraph
is not found to be a Directed Acyclic Graph.
let result = cityGraph.findAll(from: "New York") { v in
return v.characters.first == "S"
}
A breadthfirst search is performed, starting from New York, for all cities in cityGraph
that start with the letter "S."
SwiftGraph contains many more useful features, but hopefully this example was a nice quickstart.
Documentation
There is a large amount of documentation in the source code using the latest Apple documentation technique—so you should be able to just altclick a method name to get a lot of great information about it in Xcode. We also use Jazzy to produce HTML Docs. In addition, here's an overview of each of SwiftGraph's components:
Edges
Edges connect the vertices in your graph to one another.
Edge
(Protocol)  A protocol that all edges in a graph must conform to. An edge is a connection between two vertices in the graph. The vertices are specified by their index in the graph which is an integer. AllEdge
s must beCodable
.UnweightedEdge
 This is a concrete implementation ofEdge
for unweighted graphs.WeightedEdge
 This is a concrete implementation ofEdge
for weighted graphs. Weights are a generic type  they can be anything that implementsComparable
,Numeric
andCodable
. Typical weight types areInt
andFloat
.
Graphs
Graphs are the data structures at the heart of SwiftGraph. All vertices are assigned an integer index when they are inserted into a graph and it's generally faster to refer to them by their index than by the vertex's actual object.
Graphs implement the standard Swift protocols Collection
(for iterating through all vertices and for grabbing a vertex by its index through a subscript) and Codable
. For instance, the following example prints all vertices in a Graph on separate lines:
for v in g { // g is a Graph<String>
print(v)
}
And we can grab a specific vertex by its index using a subscript
print(g[23]) // g is a Graph<String>
Note: At this time, graphs are not threadsafe. However, once a graph is constructed, if you will only be doing lookups and searches through it (no removals of vertices/edges and no additions of vertices/edges) then you should be able to do that from multiple threads. A fully threadsafe graph implementation is a possible future direction.
Graph
(Protocol)  This is the base protocol for all graphs. Generally, you should use one of its canonical class implementations,UnweightedGraph
orWeightedGraph
, instead of rolling your own adopter, because they offer significant builtin functionality. The vertices in aGraph
(defined as a generic at graph creation time) can be of any type that conforms toEquatable
andCodable
. AllGraph
s areCodable
.Graph
has methods for: Adding a vertex
 Getting the index of a vertex
 Finding the neighbors of an index/vertex
 Finding the edges of an index/vertex
 Checking if an edge from one index/vertex to another index/vertex exists
 Checking if a vertex is in the graph
 Adding an edge
 Removing all edges between two indexes/vertices
 Removing a particular vertex (all other edge relationships are automatically updated at the same time (because the indices of their connections changes) so this is slow  O(v + e) where v is the number of vertices and e is the number of edges)
UnweightedGraph
 A generic class implementation ofGraph
that adds convenience methods for adding and removing edges of typeUnweightedEdge
.UnweightedGraph
is generic over the type of the vertices.WeightedGraph
 A generic class implementation ofGraph
that adds convenience methods for adding and removing edges of typeWeightedEdge
.WeightedGraph
also adds a method for returning a list of tuples containing all of the neighbor vertices of an index along with their respective weights.WeightedGraph
is generic over the types of the vertices and its weights.UniqueElementsGraph
 aGraph
implementation with support for union operations that ensures all vertices and edges in a graph are unique.
Search
Search methods are defined in extensions of Graph
and WeightedGraph
in Search.swift
.
bfs()
(method onGraph
)  Finds a path from one vertex to another in aGraph
using a breadthfirst search. Returns an array ofEdge
s going from the source vertex to the destination vertex or an empty array if no path could be found. A version of this method takes a function,goalTest()
, that operates on a vertex and returns a boolean to indicate whether it is a goal for the search. It returns a path to the first vertex that returns true fromgoalTest()
.dfs()
(method onGraph
)  Finds a path from one vertex to another in aGraph
using a depthfirst search. Returns an array ofEdge
s going from the source vertex to the destination vertex or an empty array if no path could be found. A version of this method takes a function,goalTest()
, that operates on a vertex and returns a boolean to indicate whether it is a goal for the search. It returns a path to the first vertex that returns true fromgoalTest()
.findAll()
Uses a breadthfirst search to find all connected vertices from the starting vertex that return true when run through agoalTest()
function. Paths to the connected vertices are returned in an array, which is empty if no vertices are found.dijkstra()
(method onWeightedGraph
)  Finds the shortest path from a starting vertex to every other vertex in aWeightedGraph
. Returns a tuple who's first element is an array of the distances to each vertex in the graph arranged by index. The second element of the tuple is a dictionary mapping graph indices to the previousEdge
that gets them there in the shortest time from the staring vertex. Using this dictionary and the functionpathDictToPath()
, you can find the shortest path from the starting vertex to any other connected vertex. See thedijkstra()
unit tests inDijkstraGraphTests.swift
for a demo of this. Graph traversal versions of
bfs()
anddfs()
that allow a visit function to execute at each stop
Sort & Miscellaneous
An extension to Graph
in Sort.swift
provides facilities for topological sort and detecting a DAG.
topologicalSort()
 Does a topological sort of the vertices in a given graph if possible (returns nil if it finds a cycle). Returns a sorted list of the vertices. Runs in O(n) time.isDAG
 A property that usestopologicalSort()
to determine whether a graph is a DAG (directedacyclic graph). Runs in O(n) time.
An extension to WeightedGraph
in MST.swift
can find a minimumspanning tree from a weighted graph.
mst()
 Uses Jarnik's Algorithm (aka Prim's Algorithm) to find the tree made of minimum cumulative weight that connects all vertices in a weighted graph. This assumes the graph is completely undirected and connected. If the graph has directed edges, it may not return the right answer. Also, if the graph is not fully connected it will create the tree for the connected component that the starting vertex is a part of. Returns an array ofWeightedEdge
s that compose the tree. Use utility functionstotalWeight()
andprintMST()
to examine the returned MST. Runs in O(n lg n) time.
An extension to Graph
in Cycles.swift
finds all of the cycles in a graph.
detectCycles()
 Uses an algorithm developed by Liu/Wang to find all of the cycles in a graph. Optionally, this method can take one parameter,upToLength
, that specifies a length at which to stop searching for cycles. For instance, ifupToLength
is 3,detectCycles()
will find all of the 1 vertex cycles (selfcycles, vertices with edges to themselves), and 3 vertex cycles (connection to another vertex and back again, present in all undirected graphs with more than 1 vertex). There is no such thing as a 2 vertex cycle.
Authorship, License, & Contributors
SwiftGraph is written by David Kopec and other contributors (see CONTRIBUTORS.md
). It is released under the Apache License (see LICENSE
). You can find my email address on my GitHub profile page. I encourage you to submit pull requests and open issues here on GitHub.
I would like to thank all of the contributors who have helped improve SwiftGraph over the years, and have kept me motivated. Contributing to SwiftGraph, inline with the Apache license, means also releasing your contribution under the same license as the original project. However, the Apache license is permissive, and you are free to include SwiftGraph in a commercial, closed source product as long as you give it & its author credit (in fact SwiftGraph has already found its way into several products). See LICENSE
for details.
Future Direction
Future directions for this project to take could include:
 More utility functions
 A thread safe implementation of
Graph
 More extensive performance testing
 GraphML and Other Format Support
*Note that all licence references and agreements mentioned in the SwiftGraph README section above
are relevant to that project's source code only.