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Merge pull request kodecocodes#63 from paulot/master
Adding simple example for Depth-First Search
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‎Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/Contents.swift

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func depthFirstSearch(graph: Graph, source: Node) -> [String] {
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var nodesExplored: [String] = [source.label]
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source.visited = true
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// Iterate through all neighbors, and for each one visit all of its neighbors
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for edge in source.neighbors {
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let neighbor: Node = edge.neighbor
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if (!neighbor.visited) {
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nodesExplored += depthFirstSearch(graph, source: neighbor)
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}
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}
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return nodesExplored
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}
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let graph = Graph()
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let nodeA = graph.addNode("a")
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let nodeB = graph.addNode("b")
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let nodeC = graph.addNode("c")
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let nodeD = graph.addNode("d")
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let nodeE = graph.addNode("e")
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let nodeF = graph.addNode("f")
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let nodeG = graph.addNode("g")
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let nodeH = graph.addNode("h")
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graph.addEdge(nodeA, neighbor: nodeB)
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graph.addEdge(nodeA, neighbor: nodeC)
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graph.addEdge(nodeB, neighbor: nodeD)
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graph.addEdge(nodeB, neighbor: nodeE)
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graph.addEdge(nodeC, neighbor: nodeF)
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graph.addEdge(nodeC, neighbor: nodeG)
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graph.addEdge(nodeE, neighbor: nodeH)
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let nodesExplored = depthFirstSearch(graph, source: nodeA)
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print(nodesExplored)

‎Depth-First Search/DepthFirstSearch.playground/Pages/Simple Example.xcplaygroundpage/timeline.xctimeline

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<?xml version="1.0" encoding="UTF-8"?>
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<Timeline
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version = "3.0">
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<TimelineItems>
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</TimelineItems>
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</Timeline>

‎Depth-First Search/DepthFirstSearch.playground/Sources/Edge.swift

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public class Edge : Equatable {
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public var neighbor: Node
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public init(neighbor: Node) {
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self.neighbor = neighbor
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}
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}
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public func ==(lhs: Edge, rhs: Edge) -> Bool {
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return lhs.neighbor == rhs.neighbor
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}

‎Depth-First Search/DepthFirstSearch.playground/Sources/Graph.swift

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public class Graph : CustomStringConvertible, Equatable {
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public private(set) var nodes: [Node]
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public init() {
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self.nodes = []
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}
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public func addNode(label: String) -> Node {
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let node = Node(label: label)
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nodes.append(node)
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return node
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}
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public func addEdge(source: Node, neighbor: Node) {
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let edge = Edge(neighbor: neighbor)
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edge.neighbor = neighbor
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source.neighbors.append(edge)
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}
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public var description: String {
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var description = ""
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for node in nodes {
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if !node.neighbors.isEmpty {
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description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
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}
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}
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return description
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}
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public func findNodeWithLabel(label: String) -> Node {
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return nodes.filter{ $0.label == label }.first!
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}
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public func duplicate() -> Graph {
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let duplicated = Graph()
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for node in nodes {
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duplicated.addNode(node.label)
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}
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for node in nodes {
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for edge in node.neighbors {
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let source = duplicated.findNodeWithLabel(node.label)
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let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
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duplicated.addEdge(source, neighbor: neighbour)
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}
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}
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return duplicated
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}
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}
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public func ==(lhs: Graph, rhs: Graph) -> Bool {
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return lhs.nodes == rhs.nodes
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}

‎Depth-First Search/DepthFirstSearch.playground/Sources/Node.swift

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public class Node : CustomStringConvertible, Equatable {
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public var neighbors: [Edge]
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public private(set) var label: String
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public var distance: Int?
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public var visited: Bool
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public init(label: String) {
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self.label = label
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neighbors = []
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visited = false
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}
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public var description: String {
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if let distance = distance {
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return "Node(label: \(label), distance: \(distance))"
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}
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return "Node(label: \(label), distance: infinity)"
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}
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public var hasDistance: Bool {
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return distance != nil
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}
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public func remove(edge: Edge) {
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neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
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}
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}
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public func ==(lhs: Node, rhs: Node) -> Bool {
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return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
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}

‎Depth-First Search/DepthFirstSearch.playground/contents.xcplayground

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<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
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<playground version='6.0' target-platform='ios' display-mode='rendered'/>

‎Depth-First Search/DepthFirstSearch.swift

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func depthFirstSearch(graph: Graph, source: Node) -> [String] {
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var nodesExplored: [String] = [source.label]
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source.visited = true
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// Iterate through all neighbors, and for each one visit all of its neighbors
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for edge in source.neighbors {
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let neighbor: Node = edge.neighbor
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if (!neighbor.visited) {
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nodesExplored += depthFirstSearch(graph, source: neighbor)
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}
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}
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return nodesExplored
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}

‎Depth-First Search/Edge.swift

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public class Edge : Equatable {
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public var neighbor: Node
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public init(neighbor: Node) {
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self.neighbor = neighbor
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}
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}
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public func ==(lhs: Edge, rhs: Edge) -> Bool {
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return lhs.neighbor == rhs.neighbor
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}

‎Depth-First Search/Graph.swift

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public class Graph : CustomStringConvertible, Equatable {
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public private(set) var nodes: [Node]
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public init() {
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self.nodes = []
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}
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public func addNode(label: String) -> Node {
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let node = Node(label: label)
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nodes.append(node)
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return node
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}
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public func addEdge(source: Node, neighbor: Node) {
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let edge = Edge(neighbor: neighbor)
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edge.neighbor = neighbor
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source.neighbors.append(edge)
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}
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public var description: String {
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var description = ""
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for node in nodes {
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if !node.neighbors.isEmpty {
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description += "[node: \(node.label) edges: \(node.neighbors.map{ $0.neighbor.label})]"
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}
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}
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return description
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}
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public func findNodeWithLabel(label: String) -> Node {
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return nodes.filter{ $0.label == label }.first!
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}
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public func duplicate() -> Graph {
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let duplicated = Graph()
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for node in nodes {
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duplicated.addNode(node.label)
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}
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for node in nodes {
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for edge in node.neighbors {
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let source = duplicated.findNodeWithLabel(node.label)
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let neighbour = duplicated.findNodeWithLabel(edge.neighbor.label)
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duplicated.addEdge(source, neighbor: neighbour)
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}
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}
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return duplicated
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}
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}
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public func ==(lhs: Graph, rhs: Graph) -> Bool {
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return lhs.nodes == rhs.nodes
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}

‎Depth-First Search/Node.swift

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public class Node : CustomStringConvertible, Equatable {
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public var neighbors: [Edge]
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public private(set) var label: String
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public var distance: Int?
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public var visited: Bool
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public init(label: String) {
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self.label = label
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neighbors = []
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visited = false
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}
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public var description: String {
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if let distance = distance {
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return "Node(label: \(label), distance: \(distance))"
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}
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return "Node(label: \(label), distance: infinity)"
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}
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public var hasDistance: Bool {
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return distance != nil
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}
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public func remove(edge: Edge) {
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neighbors.removeAtIndex(neighbors.indexOf{ $0 === edge }!)
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}
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}
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public func ==(lhs: Node, rhs: Node) -> Bool {
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return lhs.label == rhs.label && lhs.neighbors == rhs.neighbors
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}

‎Depth-First Search/README.markdown

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# Depth-First Search
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Depth-first search (DFS) is an algorithm for traversing or searching [tree](../Tree/) or [graph](../Graph/) data structures. It starts at the tree source and explores as far as possible along each branch before backtracking.
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## The code
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Simple implementation of breadth-first search using a queue:
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```swift
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func depthFirstSearch(graph: Graph, source: Node) -> [String] {
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var nodesExplored: [String] = [source.label]
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source.visited = true
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// Iterate through all neighbors, and for each one visit all of its neighbors
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for edge in source.neighbors {
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let neighbor: Node = edge.neighbor
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if (!neighbor.visited) {
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nodesExplored += depthFirstSearch(graph, source: neighbor)
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}
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}
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return nodesExplored
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}
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```
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Put this code in a playground and test it like so:
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```swift
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let graph = Graph() // Representing the graph from the animated example
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let nodeA = graph.addNode("a")
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let nodeB = graph.addNode("b")
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let nodeC = graph.addNode("c")
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let nodeD = graph.addNode("d")
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let nodeE = graph.addNode("e")
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let nodeF = graph.addNode("f")
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let nodeG = graph.addNode("g")
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let nodeH = graph.addNode("h")
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graph.addEdge(nodeA, neighbor: nodeB)
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graph.addEdge(nodeA, neighbor: nodeC)
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graph.addEdge(nodeB, neighbor: nodeD)
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graph.addEdge(nodeB, neighbor: nodeE)
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graph.addEdge(nodeC, neighbor: nodeF)
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graph.addEdge(nodeC, neighbor: nodeG)
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graph.addEdge(nodeE, neighbor: nodeH)
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let nodesExplored = depthFirstSearch(graph, source: nodeA)
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print(nodesExplored)
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```
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This will output: `["a", "b", "d", "e", "h", "c", "f", "g"]`
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## Applications
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Depth-first search can be used to solve many problems, for example:
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* Finding connected components of a sparse graph
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* Topological sorting of nodes in a graph
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* Finding bridges of a graph (see: [Bridges](https://en.wikipedia.org/wiki/Bridge_(graph_theory)#Bridge-finding_algorithm))
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* Among others

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