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Merge branch 'master' into rbtree-improve
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‎.github/CONTRIBUTING.md

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@@ -6,7 +6,7 @@ Want to help out with the Swift Algorithm Club? Great! While we don't have stric
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Our repo is all about learning. The `README` file is the cake, and the sample code is the cherry on top. A good contribution has succinct explanations supported by diagrams. Code is best introduced in chunks, weaved into the explanations where relevant.
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> When choosing between brievity and performance, err to the side of brievity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things.
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> When choosing between brevity and performance, err to the side of brevity as long as the time complexity of the particular implementation is the same. You can make a note afterwards suggesting a more performant way of doing things.
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**API Design Guidelines**
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@@ -22,7 +22,7 @@ We follow the following Swift [style guide](https://github.com/raywenderlich/swi
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Unit tests. Fixes for typos. No contribution is too small. :-)
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The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library is most welcomed.
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The repository has over 100 different data structures and algorithms. We're always interested in improvements to existing implementations and better explanations. Suggestions for making the code more Swift-like or to make it fit better with the standard library are most welcome.
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### New Contributions
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‎.travis.yml

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This file was deleted.

‎3Sum and 4Sum/3Sum.playground/Contents.swift

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// last checked with Xcode 10.1
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#if swift(>=4.2)
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print("Hello, Swift 4.2!")
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#endif
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extension Collection where Element: Equatable {
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‎Binary Search/BinarySearch.playground/playground.xcworkspace/contents.xcworkspacedata renamed to ‎3Sum and 4Sum/3Sum.playground/playground.xcworkspace/contents.xcworkspacedata

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‎3Sum and 4Sum/3Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
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<plist version="1.0">
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<dict>
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<key>IDEDidComputeMac32BitWarning</key>
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<true/>
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</dict>
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</plist>

‎3Sum and 4Sum/4Sum.playground/Contents.swift

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// last checked with Xcode 10.1
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#if swift(>=4.2)
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print("Hello, Swift 4.2!")
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#endif
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extension Collection where Element: Equatable {
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/// In a sorted collection, replaces the given index with a successor mapping to a unique element.

‎Fizz Buzz/FizzBuzz.playground/playground.xcworkspace/contents.xcworkspacedata renamed to ‎3Sum and 4Sum/4Sum.playground/playground.xcworkspace/contents.xcworkspacedata

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‎3Sum and 4Sum/4Sum.playground/playground.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
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<plist version="1.0">
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<dict>
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<key>IDEDidComputeMac32BitWarning</key>
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<true/>
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</dict>
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</plist>

‎A-Star/AStar.swift

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// Written by Alejandro Isaza.
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import Foundation
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public protocol Graph {
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associatedtype Vertex: Hashable
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associatedtype Edge: WeightedEdge where Edge.Vertex == Vertex
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/// Lists all edges going out from a vertex.
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func edgesOutgoing(from vertex: Vertex) -> [Edge]
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}
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public protocol WeightedEdge {
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associatedtype Vertex
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/// The edge's cost.
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var cost: Double { get }
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/// The target vertex.
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var target: Vertex { get }
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}
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public final class AStar<G: Graph> {
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/// The graph to search on.
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public let graph: G
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/// The heuristic cost function that estimates the cost between two vertices.
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///
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/// - Note: The heuristic function needs to always return a value that is lower-than or equal to the actual
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/// cost for the resulting path of the A* search to be optimal.
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public let heuristic: (G.Vertex, G.Vertex) -> Double
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/// Open list of nodes to expand.
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private var open: HashedHeap<Node<G.Vertex>>
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/// Closed list of vertices already expanded.
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private var closed = Set<G.Vertex>()
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/// Actual vertex cost for vertices we already encountered (refered to as `g` on the literature).
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private var costs = Dictionary<G.Vertex, Double>()
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/// Store the previous node for each expanded node to recreate the path.
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private var parents = Dictionary<G.Vertex, G.Vertex>()
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/// Initializes `AStar` with a graph and a heuristic cost function.
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public init(graph: G, heuristic: @escaping (G.Vertex, G.Vertex) -> Double) {
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self.graph = graph
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self.heuristic = heuristic
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open = HashedHeap(sort: <)
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}
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/// Finds an optimal path between `source` and `target`.
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///
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/// - Precondition: both `source` and `target` belong to `graph`.
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public func path(start: G.Vertex, target: G.Vertex) -> [G.Vertex] {
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open.insert(Node<G.Vertex>(vertex: start, cost: 0, estimate: heuristic(start, target)))
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while !open.isEmpty {
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guard let node = open.remove() else {
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break
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}
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costs[node.vertex] = node.cost
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if (node.vertex == target) {
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let path = buildPath(start: start, target: target)
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cleanup()
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return path
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}
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if !closed.contains(node.vertex) {
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expand(node: node, target: target)
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closed.insert(node.vertex)
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}
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}
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// No path found
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return []
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}
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private func expand(node: Node<G.Vertex>, target: G.Vertex) {
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let edges = graph.edgesOutgoing(from: node.vertex)
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for edge in edges {
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let g = cost(node.vertex) + edge.cost
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if g < cost(edge.target) {
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open.insert(Node<G.Vertex>(vertex: edge.target, cost: g, estimate: heuristic(edge.target, target)))
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parents[edge.target] = node.vertex
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}
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}
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}
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private func cost(_ vertex: G.Edge.Vertex) -> Double {
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if let c = costs[vertex] {
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return c
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}
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let node = Node(vertex: vertex, cost: Double.greatestFiniteMagnitude, estimate: 0)
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if let index = open.index(of: node) {
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return open[index].cost
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}
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return Double.greatestFiniteMagnitude
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}
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private func buildPath(start: G.Vertex, target: G.Vertex) -> [G.Vertex] {
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var path = Array<G.Vertex>()
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path.append(target)
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var current = target
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while current != start {
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guard let parent = parents[current] else {
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return [] // no path found
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}
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current = parent
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path.append(current)
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}
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return path.reversed()
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}
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private func cleanup() {
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open.removeAll()
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closed.removeAll()
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parents.removeAll()
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}
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}
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private struct Node<V: Hashable>: Hashable, Comparable {
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/// The graph vertex.
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var vertex: V
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/// The actual cost between the start vertex and this vertex.
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var cost: Double
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/// Estimated (heuristic) cost betweent this vertex and the target vertex.
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var estimate: Double
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public init(vertex: V, cost: Double, estimate: Double) {
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self.vertex = vertex
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self.cost = cost
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self.estimate = estimate
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}
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static func < (lhs: Node<V>, rhs: Node<V>) -> Bool {
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return lhs.cost + lhs.estimate < rhs.cost + rhs.estimate
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}
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static func == (lhs: Node<V>, rhs: Node<V>) -> Bool {
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return lhs.vertex == rhs.vertex
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}
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var hashValue: Int {
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return vertex.hashValue
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}
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}

‎A-Star/Images/graph.dot

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digraph G {
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rankdir=LR;
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{ A [ label = "h = 3" ] }
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{ rank = same; B [ label = "h = 2" ]; C [ label = "h = 2" ]; D [ label = "h = 2" ] }
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{ rank = same; E [ label = "h = 1" ]; F [ label = "h = 1" ]; G [ label = "h = 1" ] }
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{ H [ label = "h = 0", style = filled, color = green ] }
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A -> { B C D }
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B -> E
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E -> F
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D -> G
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G -> H
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}

‎A-Star/Images/graph.png

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‎A-Star/Images/step1.dot

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digraph G {
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rankdir=LR;
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{ A [ label = "g = 0\nh = 3", style = filled, color = deepskyblue1 ] }
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{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; C [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
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{ rank = same; E [ label = "g = \?\nh = 1" ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
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{ H [ label = "g = \?\nh = 0" ] }
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A -> { B C D }
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B -> E
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E -> F
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D -> G
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G -> H
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}

‎A-Star/Images/step1.png

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‎A-Star/Images/step2.dot

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digraph G {
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rankdir=LR;
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{ A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
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{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ]; C [ label = "g = 1\nh = 2", style = filled, color = lightgrey ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
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{ rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
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{ H [ label = "g = \?\nh = 0" ] }
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A -> { B C D }
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B -> E
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E -> F
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D -> G
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G -> H
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}

‎A-Star/Images/step2.png

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‎A-Star/Images/step3.dot

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@@ -0,0 +1,12 @@
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digraph G {
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rankdir=LR;
3+
{ A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
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{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ]; D [ label = "g = 1\nh = 2", style = filled, color = lightgrey ] }
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{ rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = \?\nh = 1" ] }
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{ H [ label = "g = \?\nh = 0" ] }
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A -> { B C D }
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B -> E
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E -> F
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D -> G
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G -> H
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}

‎A-Star/Images/step3.png

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‎A-Star/Images/step4.dot

+12
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@@ -0,0 +1,12 @@
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digraph G {
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rankdir=LR;
3+
{ A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
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{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = deepskyblue1 ] }
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{ rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightgrey ]; F [ label = "g = \?\nh = 1" ]; G [ label = "g = 2\nh = 1", style = filled, color = lightgrey ] }
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{ H [ label = "g = \?\nh = 0" ] }
7+
A -> { B C D }
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B -> E
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E -> F
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D -> G
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G -> H
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}

‎A-Star/Images/step4.png

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‎A-Star/Images/step5.dot

+12
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@@ -0,0 +1,12 @@
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digraph G {
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rankdir=LR;
3+
{ A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
4+
{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
5+
{ rank = same; E [ label = "g = 2\nh = 1", style = filled, color = deepskyblue1 ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = lightgrey ] }
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{ H [ label = "g = \?\nh = 0" ] }
7+
A -> { B C D }
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B -> E
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E -> F
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D -> G
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G -> H
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}

‎A-Star/Images/step5.png

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‎A-Star/Images/step6.dot

+12
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@@ -0,0 +1,12 @@
1+
digraph G {
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rankdir=LR;
3+
{ A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
4+
{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
5+
{ rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightblue ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = deepskyblue1 ] }
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{ H [ label = "g = 3\nh = 0", style = filled, color = lightgrey ] }
7+
A -> { B C D }
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B -> E
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E -> F
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D -> G
11+
G -> H
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}

‎A-Star/Images/step6.png

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‎A-Star/Images/step7.dot

+12
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,12 @@
1+
digraph G {
2+
rankdir=LR;
3+
{ A [ label = "g = 0\nh = 3", style = filled, color = lightblue ] }
4+
{ rank = same; B [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; C [ label = "g = 1\nh = 2", style = filled, color = lightblue ]; D [ label = "g = 1\nh = 2", style = filled, color = lightblue ] }
5+
{ rank = same; E [ label = "g = 2\nh = 1", style = filled, color = lightblue ]; F [ label = "g = 3\nh = 1", style = filled, color = lightgrey ]; G [ label = "g = 2\nh = 1", style = filled, color = lightblue ] }
6+
{ H [ label = "g = 3\nh = 0", style = filled, color = deepskyblue1 ] }
7+
A -> { B C D }
8+
B -> E
9+
E -> F
10+
D -> G
11+
G -> H
12+
}

‎A-Star/Images/step7.png

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