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armcknightarmcknight
committedJun 5, 2016
add project for SSSP with Bellman-Ford implementation
1 parent 495303b commit dd3ba8d

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‎.travis.yml

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@@ -3,25 +3,26 @@ osx_image: xcode7.3
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script:
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- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
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- xcodebuild test -project ./Array2D/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./AVL\ Tree/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Binary\ Search/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Binary\ Search\ Tree/Solution\ 1/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Bloom\ Filter/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Breadth-First\ Search/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Heap/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Heap\ Sort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Insertion\ Sort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./K-Means/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Linked\ List/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Priority\ Queue/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Queue/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Quicksort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Run-Length\ Encoding/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Select\ Minimum\ Maximum/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Selection\ Sort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Shell\ Sort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Longest\ Common\ Subsequence/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./Bucket\ Sort/Tests/Tests.xcodeproj -scheme Tests
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- xcodebuild test -project ./All-Pairs\ Shortest\ Paths/APSP/APSP.xcodeproj -scheme APSPTests
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- xcodebuild test -project ./Single-Source\ Shortest\ Paths\ \(Weighted\)/SSSP.xcodeproj -scheme SSSPTests
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- xcodebuild test -project ./Stack/Tests/Tests.xcodeproj -scheme Tests

‎Single-Source Shortest Paths (Weighted)/SSSP.playground/Contents.swift

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import Graph
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import SSSP
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let graph = AdjacencyMatrixGraph<String>()
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let s = graph.createVertex("s")
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let t = graph.createVertex("t")
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let x = graph.createVertex("x")
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let y = graph.createVertex("y")
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let z = graph.createVertex("z")
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graph.addDirectedEdge(s, to: t, withWeight: 6)
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graph.addDirectedEdge(s, to: y, withWeight: 7)
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graph.addDirectedEdge(t, to: x, withWeight: 5)
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graph.addDirectedEdge(t, to: y, withWeight: 8)
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graph.addDirectedEdge(t, to: z, withWeight: -4)
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graph.addDirectedEdge(x, to: t, withWeight: -2)
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graph.addDirectedEdge(y, to: x, withWeight: -3)
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graph.addDirectedEdge(y, to: z, withWeight: 9)
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graph.addDirectedEdge(z, to: s, withWeight: 2)
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graph.addDirectedEdge(z, to: x, withWeight: 7)
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let result = BellmanFord<String>.apply(graph, source: s)!
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let path = result.path(z, inGraph: graph)

‎Single-Source Shortest Paths (Weighted)/SSSP.playground/contents.xcplayground

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<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
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<playground version='5.0' target-platform='osx'>
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<timeline fileName='timeline.xctimeline'/>
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</playground>

‎Single-Source Shortest Paths (Weighted)/SSSP.playground/playground.xcworkspace/contents.xcworkspacedata

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‎Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/project.pbxproj

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‎Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSP.xcscheme

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<Scheme
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LastUpgradeVersion = "0730"
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version = "1.3">
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parallelizeBuildables = "YES"
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buildImplicitDependencies = "YES">
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<BuildActionEntries>
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<BuildActionEntry
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buildForTesting = "YES"
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buildForRunning = "YES"
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buildForProfiling = "YES"
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buildForArchiving = "YES"
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buildForAnalyzing = "YES">
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<BuildableReference
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BuildableIdentifier = "primary"
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BlueprintIdentifier = "49BFA2921CDF86E100522D66"
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BuildableName = "SSSP.framework"
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BlueprintName = "SSSP"
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ReferencedContainer = "container:SSSP.xcodeproj">
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</BuildableReference>
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</BuildActionEntry>
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</BuildActionEntries>
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</BuildAction>
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<TestAction
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buildConfiguration = "Debug"
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selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
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selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
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shouldUseLaunchSchemeArgsEnv = "YES">
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<Testables>
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skipped = "NO">
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BuildableIdentifier = "primary"
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BuildableName = "SSSPTests.xctest"
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BlueprintName = "SSSPTests"
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ReferencedContainer = "container:SSSP.xcodeproj">
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<MacroExpansion>
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<BuildableReference
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BuildableIdentifier = "primary"
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BlueprintIdentifier = "49BFA2921CDF86E100522D66"
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BuildableName = "SSSP.framework"
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BlueprintName = "SSSP"
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ReferencedContainer = "container:SSSP.xcodeproj">
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<AdditionalOptions>
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<LaunchAction
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buildConfiguration = "Debug"
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selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
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selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
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launchStyle = "0"
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useCustomWorkingDirectory = "NO"
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ignoresPersistentStateOnLaunch = "NO"
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debugDocumentVersioning = "YES"
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debugServiceExtension = "internal"
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allowLocationSimulation = "YES">
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<MacroExpansion>
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BuildableIdentifier = "primary"
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BlueprintIdentifier = "49BFA2921CDF86E100522D66"
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BuildableName = "SSSP.framework"
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BlueprintName = "SSSP"
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ReferencedContainer = "container:SSSP.xcodeproj">
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</BuildableReference>
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</MacroExpansion>
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<AdditionalOptions>
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</AdditionalOptions>
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</LaunchAction>
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<ProfileAction
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buildConfiguration = "Release"
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shouldUseLaunchSchemeArgsEnv = "YES"
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savedToolIdentifier = ""
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useCustomWorkingDirectory = "NO"
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debugDocumentVersioning = "YES">
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<BuildableReference
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BuildableIdentifier = "primary"
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BlueprintIdentifier = "49BFA2921CDF86E100522D66"
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BuildableName = "SSSP.framework"
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BlueprintName = "SSSP"
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ReferencedContainer = "container:SSSP.xcodeproj">
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</BuildableReference>
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</MacroExpansion>
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</ProfileAction>
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<AnalyzeAction
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buildConfiguration = "Debug">
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</AnalyzeAction>
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<ArchiveAction
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buildConfiguration = "Release"
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revealArchiveInOrganizer = "YES">
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</ArchiveAction>
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</Scheme>

‎Single-Source Shortest Paths (Weighted)/SSSP.xcodeproj/xcshareddata/xcschemes/SSSPTests.xcscheme

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LastUpgradeVersion = "0730"
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parallelizeBuildables = "YES"
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buildImplicitDependencies = "YES">
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selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
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selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
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shouldUseLaunchSchemeArgsEnv = "YES">
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skipped = "NO">
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BuildableName = "SSSPTests.xctest"
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BlueprintName = "SSSPTests"
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ReferencedContainer = "container:SSSP.xcodeproj">
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</BuildableReference>
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</TestableReference>
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</Testables>
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<AdditionalOptions>
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</AdditionalOptions>
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</TestAction>
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<LaunchAction
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buildConfiguration = "Debug"
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selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
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selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
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launchStyle = "0"
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useCustomWorkingDirectory = "NO"
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ignoresPersistentStateOnLaunch = "NO"
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debugDocumentVersioning = "YES"
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debugServiceExtension = "internal"
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allowLocationSimulation = "YES">
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<AdditionalOptions>
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</AdditionalOptions>
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</LaunchAction>
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<ProfileAction
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buildConfiguration = "Release"
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shouldUseLaunchSchemeArgsEnv = "YES"
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savedToolIdentifier = ""
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useCustomWorkingDirectory = "NO"
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debugDocumentVersioning = "YES">
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</ProfileAction>
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buildConfiguration = "Debug">
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<ArchiveAction
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buildConfiguration = "Release"
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revealArchiveInOrganizer = "YES">
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</ArchiveAction>
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</Scheme>

‎Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/contents.xcworkspacedata

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‎Single-Source Shortest Paths (Weighted)/SSSP.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

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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>IDEWorkspaceSharedSettings_AutocreateContextsIfNeeded</key>
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<false/>
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</dict>
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</plist>

‎Single-Source Shortest Paths (Weighted)/SSSP/BellmanFord.swift

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//
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// BellmanFord.swift
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// SSSP
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//
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// Created by Andrew McKnight on 5/8/16.
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//
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import Foundation
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import Graph
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public struct BellmanFord<T where T: Hashable> {
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public typealias Q = T
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}
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/**
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Encapsulation of the Bellman-Ford Single-Source Shortest Paths algorithm, which operates on a general directed graph that may contain negative edge weights.
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- note: In all complexity bounds, `V` is the number of vertices in the graph, and `E` is the number of edges.
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*/
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extension BellmanFord: SSSPAlgorithm {
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/**
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Compute the shortest path from `source` to each other vertex in `graph`, if such paths exist. Also report negative weight cycles reachable from `source`, which are cycles whose sum of edge weights is negative.
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- precondition: `graph` must have no negative weight cycles
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- complexity: `O(VE)` time, `Θ(V)` space
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- returns a `BellmanFordResult` struct which can be queried for shortest paths and their total weights, or `nil` if a negative weight cycle exists
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*/
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public static func apply(graph: AbstractGraph<T>, source: Vertex<Q>) -> BellmanFordResult<T>? {
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let vertices = graph.vertices
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let edges = graph.edges
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var predecessors = Array<Int?>(count: vertices.count, repeatedValue: nil)
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var weights = Array(count: vertices.count, repeatedValue: Double.infinity)
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predecessors[source.index] = source.index
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weights[source.index] = 0
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for _ in 0 ..< vertices.count - 1 {
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var weightsUpdated = false
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edges.forEach() { edge in
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let weight = edge.weight!
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let relaxedDistance = weights[edge.from.index] + weight
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let nextVertexIdx = edge.to.index
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if relaxedDistance < weights[nextVertexIdx] {
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predecessors[nextVertexIdx] = edge.from.index
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weights[nextVertexIdx] = relaxedDistance
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weightsUpdated = true
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}
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}
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if !weightsUpdated {
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break
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}
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}
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// check for negative weight cycles reachable from the source vertex
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// TODO: modify to incorporate solution to 24.1-4, pg 654, to set the weight of a path containing a negative weight cycle to -∞, instead of returning nil for the entire result
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for edge in edges {
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if weights[edge.to.index] > weights[edge.from.index] + edge.weight! {
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return nil
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}
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}
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return BellmanFordResult(predecessors: predecessors, weights: weights)
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}
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}
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/**
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`BellmanFordResult` encapsulates the result of the computation, namely the minimized distances, and the predecessor indices.
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It conforms to the `SSSPResult` procotol which provides methods to retrieve distances and paths between given pairs of start and end nodes.
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*/
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public struct BellmanFordResult<T where T: Hashable> {
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private var predecessors: [Int?]
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private var weights: [Double]
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}
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extension BellmanFordResult: SSSPResult {
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/**
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- returns: the total weight of the path from the source vertex to a destination. This value is the minimal connected weight between the two vertices, or `nil` if no path exists
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- complexity: `Θ(1)` time/space
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*/
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public func distance(to: Vertex<T>) -> Double? {
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let distance = weights[to.index]
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guard distance != Double.infinity else {
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return nil
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}
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return distance
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}
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/**
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- returns: the reconstructed path from the source vertex to a destination, as an array containing the data property of each vertex, or `nil` if no path exists
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- complexity: `Θ(V)` time, `Θ(V^2)` space
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*/
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public func path(to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]? {
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guard weights[to.index] != Double.infinity else {
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return nil
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}
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guard let path = recursePath(to, inGraph: graph, path: [to]) else {
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return nil
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}
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return path.map() { vertex in
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return vertex.data
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}
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}
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/**
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The recursive component to rebuilding the shortest path between two vertices using predecessors.
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- returns: the list of predecessors discovered so far, or `nil` if the next vertex has no predecessor
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*/
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private func recursePath(to: Vertex<T>, inGraph graph: AbstractGraph<T>, path: [Vertex<T>]) -> [Vertex<T>]? {
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guard let predecessorIdx = predecessors[to.index] else {
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return nil
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}
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let predecessor = graph.vertices[predecessorIdx]
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if predecessor.index == to.index {
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return [ to ]
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}
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guard let buildPath = recursePath(predecessor, inGraph: graph, path: path) else {
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return nil
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}
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return buildPath + [ to ]
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}
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}

‎Single-Source Shortest Paths (Weighted)/SSSP/Info.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>CFBundleDevelopmentRegion</key>
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<string>en</string>
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<key>CFBundleExecutable</key>
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<string>$(EXECUTABLE_NAME)</string>
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<key>CFBundleIdentifier</key>
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<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
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<key>CFBundleInfoDictionaryVersion</key>
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<string>6.0</string>
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<key>CFBundleName</key>
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<string>$(PRODUCT_NAME)</string>
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<key>CFBundlePackageType</key>
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<string>FMWK</string>
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<key>CFBundleShortVersionString</key>
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<string>1.0</string>
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<key>CFBundleSignature</key>
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<string>????</string>
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<key>CFBundleVersion</key>
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<string>$(CURRENT_PROJECT_VERSION)</string>
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<key>NSPrincipalClass</key>
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<string></string>
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</dict>
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</plist>

‎Single-Source Shortest Paths (Weighted)/SSSP/SSSP.h

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//
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// SSSP.h
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// SSSP
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//
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// Created by Andrew McKnight on 5/8/16.
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//
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#import <Cocoa/Cocoa.h>
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//! Project version number for SSSP.
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FOUNDATION_EXPORT double SSSPVersionNumber;
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//! Project version string for SSSP.
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FOUNDATION_EXPORT const unsigned char SSSPVersionString[];
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// In this header, you should import all the public headers of your framework using statements like #import <SSSP/PublicHeader.h>
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‎Single-Source Shortest Paths (Weighted)/SSSP/SSSP.swift

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//
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// SSSP.swift
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// SSSP
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//
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// Created by Andrew McKnight on 5/8/16.
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//
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import Foundation
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import Graph
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/**
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`SSSPAlgorithm` is a protocol for encapsulating a Single-Source Shortest Path algorithm. It provides a single function `apply` that accepts a subclass of `AbstractGraph` and returns an object conforming to `SSSPResult`.
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*/
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protocol SSSPAlgorithm {
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associatedtype Q: Equatable, Hashable
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associatedtype P: SSSPResult
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static func apply(graph: AbstractGraph<Q>, source: Vertex<Q>) -> P?
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}
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/**
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`SSSPResult` is a protocol defining functions `distance` and `path`, allowing for opaque queries into the actual data structures that represent the SSSP solution according to the algorithm used.
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*/
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protocol SSSPResult {
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associatedtype T: Equatable, Hashable
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func distance(to: Vertex<T>) -> Double?
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func path(to: Vertex<T>, inGraph graph: AbstractGraph<T>) -> [T]?
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}

‎Single-Source Shortest Paths (Weighted)/SSSPTests/Info.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>CFBundleDevelopmentRegion</key>
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<string>en</string>
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<key>CFBundleExecutable</key>
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<string>$(EXECUTABLE_NAME)</string>
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<key>CFBundleIdentifier</key>
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<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
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<key>CFBundleInfoDictionaryVersion</key>
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<string>6.0</string>
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<key>CFBundleName</key>
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<string>$(PRODUCT_NAME)</string>
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<key>CFBundlePackageType</key>
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<string>BNDL</string>
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<key>CFBundleShortVersionString</key>
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<string>1.0</string>
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<key>CFBundleSignature</key>
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<string>????</string>
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<key>CFBundleVersion</key>
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<string>1</string>
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</dict>
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</plist>

‎Single-Source Shortest Paths (Weighted)/SSSPTests/SSSPTests.swift

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//
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// SSSPTests.swift
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// SSSPTests
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//
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// Created by Andrew McKnight on 5/8/16.
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//
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import Graph
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import XCTest
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@testable import SSSP
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class SSSPTests: XCTestCase {
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/**
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See Figure 24.4 of “Introduction to Algorithms” by Cormen et al, 3rd ed., pg 652
16+
*/
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func testExampleFromBook() {
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let graph = AdjacencyMatrixGraph<String>()
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let s = graph.createVertex("s")
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let t = graph.createVertex("t")
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let x = graph.createVertex("x")
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let y = graph.createVertex("y")
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let z = graph.createVertex("z")
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graph.addDirectedEdge(s, to: t, withWeight: 6)
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graph.addDirectedEdge(s, to: y, withWeight: 7)
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graph.addDirectedEdge(t, to: x, withWeight: 5)
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graph.addDirectedEdge(t, to: y, withWeight: 8)
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graph.addDirectedEdge(t, to: z, withWeight: -4)
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graph.addDirectedEdge(x, to: t, withWeight: -2)
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graph.addDirectedEdge(y, to: x, withWeight: -3)
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graph.addDirectedEdge(y, to: z, withWeight: 9)
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graph.addDirectedEdge(z, to: s, withWeight: 2)
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graph.addDirectedEdge(z, to: x, withWeight: 7)
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let result = BellmanFord<String>.apply(graph, source: s)!
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let expectedPath = ["s", "y", "x", "t", "z"]
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let computedPath = result.path(z, inGraph: graph)!
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XCTAssertEqual(expectedPath, computedPath, "expected path of \(expectedPath) but got \(computedPath)")
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let expectedWeight = -2.0
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let computedWeight = result.distance(z)
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XCTAssertEqual(expectedWeight, computedWeight, "expected weight of \(expectedWeight) but got \(computedWeight)")
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}
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func testSimpleExample() {
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let graph = AdjacencyMatrixGraph<String>()
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let a = graph.createVertex("a")
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let b = graph.createVertex("b")
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let c = graph.createVertex("c")
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let d = graph.createVertex("d")
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let e = graph.createVertex("e")
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graph.addDirectedEdge(a, to: b, withWeight: 4)
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graph.addDirectedEdge(a, to: c, withWeight: 5)
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graph.addDirectedEdge(a, to: d, withWeight: 8)
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graph.addDirectedEdge(b, to: c, withWeight: -2)
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graph.addDirectedEdge(c, to: e, withWeight: 4)
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graph.addDirectedEdge(d, to: e, withWeight: 2)
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graph.addDirectedEdge(e, to: d, withWeight: 1)
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let result = BellmanFord<String>.apply(graph, source: a)!
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let expectedPath = ["a", "b", "c", "e", "d"]
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let computedPath = result.path(d, inGraph: graph)!
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XCTAssertEqual(expectedPath, computedPath, "expected path of \(expectedPath) but got \(computedPath)")
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let expectedWeight = 7.0
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let computedWeight = result.distance(d)
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XCTAssertEqual(expectedWeight, computedWeight, "expected weight of \(expectedWeight) but got \(computedWeight)")
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}
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/**
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Construct a nearly bipartite graph, except one vertex only has out-edges. Then no path should exist from the source to that vertex.
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*/
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func testGraphWithUnreachableVertex() {
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let graph = AdjacencyMatrixGraph<String>()
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let a = graph.createVertex("a")
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let b = graph.createVertex("b")
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let s = graph.createVertex("s")
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let t = graph.createVertex("t")
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graph.addDirectedEdge(a, to: s, withWeight: 9)
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graph.addDirectedEdge(a, to: t, withWeight: 2)
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graph.addDirectedEdge(b, to: a, withWeight: 1)
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graph.addDirectedEdge(b, to: s, withWeight: 2)
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graph.addDirectedEdge(b, to: t, withWeight: 3)
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graph.addDirectedEdge(s, to: a, withWeight: 4)
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graph.addDirectedEdge(s, to: t, withWeight: 1)
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graph.addDirectedEdge(t, to: a, withWeight: 7)
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graph.addDirectedEdge(t, to: s, withWeight: 5)
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let result = BellmanFord<String>.apply(graph, source: a)!
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XCTAssertNil(result.path(b, inGraph: graph), "a path should not be defined from a ~> b")
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XCTAssertNil(result.distance(b), "a path should not be defined from a ~> b")
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XCTAssertNotNil(result.path(s, inGraph: graph), "a path should be defined from a ~> s")
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XCTAssertNotNil(result.distance(s), "a path should be defined from a ~> s")
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XCTAssertNotNil(result.path(t, inGraph: graph), "a path should be defined from a ~> t")
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XCTAssertNotNil(result.distance(t), "a path should be defined from a ~> t")
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}
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func testNegativeWeightCycle() {
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let graph = AdjacencyMatrixGraph<String>()
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let a = graph.createVertex("a")
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let b = graph.createVertex("b")
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let s = graph.createVertex("s")
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let t = graph.createVertex("t")
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graph.addDirectedEdge(a, to: t, withWeight: 2)
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graph.addDirectedEdge(b, to: t, withWeight: 5)
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graph.addDirectedEdge(s, to: a, withWeight: 4)
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graph.addDirectedEdge(s, to: b, withWeight: 4)
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graph.addDirectedEdge(t, to: s, withWeight: -15)
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XCTAssertNil(BellmanFord<String>.apply(graph, source: s), "negative weight cycle not reported")
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}
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}

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