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Explorations Home › Basic › Shortest City Tours Static Preview

Shortest City Tours

In which order should you visit cities so as to travel the shortest distance?

Run the code to get a list of the capitals of Africa. Try other regions, like “northern europe” or “the caribbean”:

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Get a list of capitals of countries in Africa. Type += to get a natural language input box, and type “capitals of africa” into it. Run the code with +:

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\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "capitals of africa", Typeset`boxes$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Africa\"", RowBox[{"EntityClass", "[", RowBox[{"\"Country\"", ",", "\"Africa\""}], "]"}], "\"EntityClass[\\\"Country\\\", \\\"Africa\\\"]\"", "\"countries\""}, "EntityClass"], ",", TemplateBox[{"\"capital city\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Country\"", ",", "\"CapitalCity\""}], "]"}], "\"EntityProperty[\\\"Country\\\", \\\"CapitalCity\\\"]\""}, "EntityProperty"]}], "]"}], Typeset`allassumptions$ = {}, Typeset`assumptions$ = {}, Typeset`open$ = {1}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.287733`5.910534667329372, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{107., {7., 16.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)
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\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "capitals of africa", Typeset`boxes$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Africa\"", RowBox[{"EntityClass", "[", RowBox[{"\"Country\"", ",", "\"Africa\""}], "]"}], "\"EntityClass[\\\"Country\\\", \\\"Africa\\\"]\"", "\"countries\""}, "EntityClass"], ",", TemplateBox[{"\"capital city\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Country\"", ",", "\"CapitalCity\""}], "]"}], "\"EntityProperty[\\\"Country\\\", \\\"CapitalCity\\\"]\""}, "EntityProperty"]}], "]"}], Typeset`allassumptions$ = {}, Typeset`assumptions$ = {}, Typeset`open$ = {1}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.287733`5.910534667329372, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{116., {7., 16.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)
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Get the geographic positions of the capitals. Try getting other properties, like "Population" or "Elevation":

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Get the geographic position of Paris. The result contains {latitude,longitude} coordinates:

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EntityValue[\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "Paris", Typeset`boxes$ = TemplateBox[{"\"Paris\"", RowBox[{"Entity", "[", RowBox[{"\"City\"", ",", RowBox[{"{", RowBox[{"\"Paris\"", ",", "\"IleDeFrance\"", ",", "\"France\""}], "}"}]}], "]"}], "\"Entity[\\\"City\\\", {\\\"Paris\\\", \\\"IleDeFrance\\\", \ \\\"France\\\"}]\"", "\"city\""}, "Entity"], Typeset`allassumptions$ = {{ "type" -> "Clash", "word" -> "Paris", "template" -> "Assuming \"${word}\" is ${desc1}. Use as \ ${desc2} instead", "count" -> "5", "Values" -> {{ "name" -> "City", "desc" -> "a city", "input" -> "*C.Paris-_*City-"}, { "name" -> "AdministrativeDivision", "desc" -> "an administrative division", "input" -> "*C.Paris-_*AdministrativeDivision-"}, { "name" -> "Surname", "desc" -> "a surname", "input" -> "*C.Paris-_*Surname-"}, { "name" -> "GivenName", "desc" -> "a given name", "input" -> "*C.Paris-_*GivenName-"}, { "name" -> "Person", "desc" -> "a person", "input" -> "*C.Paris-_*Person-"}}}, { "type" -> "SubCategory", "word" -> "Paris", "template" -> "Assuming ${desc1}. Use ${desc2} instead", "count" -> "14", "Values" -> {{ "name" -> "{Paris, IleDeFrance, France}", "desc" -> "Paris (France)", "input" -> "*DPClash.CityE.Paris-_**Paris.IleDeFrance.\ France--"}, { "name" -> "{Paris, Illinois, UnitedStates}", "desc" -> "Paris (Illinois, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Illinois.\ UnitedStates--"}, { "name" -> "{Paris, Texas, UnitedStates}", "desc" -> "Paris (Texas, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Texas.\ UnitedStates--"}, { "name" -> "{Paris, Kentucky, UnitedStates}", "desc" -> "Paris (Kentucky, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Kentucky.\ UnitedStates--"}, { "name" -> "{Paris, Tennessee, UnitedStates}", "desc" -> "Paris (Tennessee, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Tennessee.\ UnitedStates--"}, { "name" -> "{Paris, Ontario, Canada}", "desc" -> "Paris (Canada)", "input" -> "*DPClash.CityE.Paris-_**Paris.Ontario.Canada--"}\ , {"name" -> "{Paris, Wisconsin, UnitedStates}", "desc" -> "Paris (Wisconsin, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Wisconsin.\ UnitedStates--"}, { "name" -> "{Paris, Arkansas, UnitedStates}", "desc" -> "Paris (Arkansas, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Arkansas.\ UnitedStates--"}, { "name" -> "{Paris, NewYork, UnitedStates}", "desc" -> "Paris (New York, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.NewYork.\ UnitedStates--"}, { "name" -> "{Paris, Missouri, UnitedStates}", "desc" -> "Paris (Missouri, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Missouri.\ UnitedStates--"}, { "name" -> "{Paris, Maine, UnitedStates}", "desc" -> "Paris (Maine, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Maine.\ UnitedStates--"}, { "name" -> "{ParisGrant, Wisconsin, UnitedStates}", "desc" -> "Paris (Wisconsin, USA)", "input" -> "*DPClash.CityE.Paris-_**ParisGrant.Wisconsin.\ UnitedStates--"}, { "name" -> "{ParisTownship, Michigan, UnitedStates}", "desc" -> "Paris Township (Michigan, USA)", "input" -> "*DPClash.CityE.Paris-_**ParisTownship.Michigan.\ UnitedStates--"}, { "name" -> "{Paris, Idaho, UnitedStates}", "desc" -> "Paris (Idaho, USA)", "input" -> "*DPClash.CityE.Paris-_**Paris.Idaho.\ UnitedStates--"}}}}, Typeset`assumptions$ = {}, Typeset`open$ = {1, 2}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.717032`6.307083531469639, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{83., {7., 15.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), "Position"]
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Get the geographic positions of the capitals of Africa, and give the result the name positions:

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positions = EntityValue[\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "capitals of africa", Typeset`boxes$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Africa\"", RowBox[{"EntityClass", "[", RowBox[{"\"Country\"", ",", "\"Africa\""}], "]"}], "\"EntityClass[\\\"Country\\\", \\\"Africa\\\"]\"", "\"countries\""}, "EntityClass"], ",", TemplateBox[{"\"capital city\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Country\"", ",", "\"CapitalCity\""}], "]"}], "\"EntityProperty[\\\"Country\\\", \ \\\"CapitalCity\\\"]\""}, "EntityProperty"]}], "]"}], Typeset`allassumptions$ = {}, Typeset`assumptions$ = {}, Typeset`open$ = {1}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.287733`5.910534667329372, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{107., {7., 16.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), "Position"]
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positions = EntityValue[\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "capitals of africa", Typeset`boxes$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Africa\"", RowBox[{"EntityClass", "[", RowBox[{"\"Country\"", ",", "\"Africa\""}], "]"}], "\"EntityClass[\\\"Country\\\", \\\"Africa\\\"]\"", "\"countries\""}, "EntityClass"], ",", TemplateBox[{"\"capital city\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Country\"", ",", "\"CapitalCity\""}], "]"}], "\"EntityProperty[\\\"Country\\\", \ \\\"CapitalCity\\\"]\""}, "EntityProperty"]}], "]"}], Typeset`allassumptions$ = {}, Typeset`assumptions$ = {}, Typeset`open$ = {1}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.287733`5.910534667329372, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{116., {7., 16.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), "Position"]
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Find the order of capitals that gives the shortest route:
 

Note: run the code in the previous step first.

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Find the length of the shortest tour through all the capitals, and the order of the capitals along the route:

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FindShortestTour[positions]
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Extract just the order of the capitals on the shortest tour:

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Last[FindShortestTour[positions]]
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tour = Last[FindShortestTour[positions]]
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Show the order of the capitals along the shortest route:
 

Note: run the code in the previous step first.

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Reorder the elements of a list. Put the second element first, then the fourth and so on:

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{"one", "two", "three", "four", "five"}[[{2, 4, 1, 3, 5}]]
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Order the capitals of Africa along the shortest tour route:

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\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "capitals of africa", Typeset`boxes$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Africa\"", RowBox[{"EntityClass", "[", RowBox[{"\"Country\"", ",", "\"Africa\""}], "]"}], "\"EntityClass[\\\"Country\\\", \\\"Africa\\\"]\"", "\"countries\""}, "EntityClass"], ",", TemplateBox[{"\"capital city\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Country\"", ",", "\"CapitalCity\""}], "]"}], "\"EntityProperty[\\\"Country\\\", \ \\\"CapitalCity\\\"]\""}, "EntityProperty"]}], "]"}], Typeset`allassumptions$ = {}, Typeset`assumptions$ = {}, Typeset`open$ = {1}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.287733`5.910534667329372, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{107., {7., 16.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)[[tour]]
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\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$ = "capitals of africa", Typeset`boxes$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Africa\"", RowBox[{"EntityClass", "[", RowBox[{"\"Country\"", ",", "\"Africa\""}], "]"}], "\"EntityClass[\\\"Country\\\", \\\"Africa\\\"]\"", "\"countries\""}, "EntityClass"], ",", TemplateBox[{"\"capital city\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Country\"", ",", "\"CapitalCity\""}], "]"}], "\"EntityProperty[\\\"Country\\\", \ \\\"CapitalCity\\\"]\""}, "EntityProperty"]}], "]"}], Typeset`allassumptions$ = {}, Typeset`assumptions$ = {}, Typeset`open$ = {1}, Typeset`querystate$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.287733`5.910534667329372, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$], Dynamic[Typeset`boxes$], Dynamic[Typeset`allassumptions$], Dynamic[Typeset`assumptions$], Dynamic[Typeset`open$], Dynamic[Typeset`querystate$]], StandardForm], ImageSizeCache->{116., {7., 16.}}, TrackedSymbols:>{ Typeset`query$, Typeset`boxes$, Typeset`allassumptions$, Typeset`assumptions$, Typeset`open$, Typeset`querystate$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)[[tour]]
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Make a map of the shortest tour:

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Get the positions of the capitals in their order along the shortest tour route:

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positions[[tour]]
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Make a map with a thick red line showing the shortest capital tour:

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GeoGraphics[{Thick, Red, Line[positions[[tour]]]}]
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GeoGraphics[{Thick, Red, Line[positions[[tour]]]}]
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Share It—Make a website that shows the shortest route through cities that you specify:

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Deploy a form that asks for a list of cities and makes a map showing the shortest route through them. GeoRangePadding is used to add a margin around the route:

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CloudDeploy[ FormFunction[{{"cities", "cities (city1; city2; ...)"} -> DelimitedSequence["City"]}, Block[{positions, tour}, positions = EntityValue[#cities, "Position"]; tour = Last[FindShortestTour[positions]]; GeoGraphics[{Thick, Red, Line[positions[[tour]]]}, GeoRangePadding -> Scaled[.5]] ] &, "PNG" ], Permissions -> "Public" ]
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Click the link in the output to visit the site. Separate the cities you enter with semicolons (;) rather than spaces or commas, since both of those can occur in city names.

Tell the world about your creation by sharing the link via email, tweet or other message.

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In[1]:=1
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CloudDeploy[ FormFunction[{{"cities", "cities (city1; city2; ...)"} -> DelimitedSequence["City"]}, Block[{positions, tour}, positions = EntityValue[#cities, "Position"]; tour = Last[FindShortestTour[positions]]; GeoGraphics[{Thick, Red, Line[positions[[tour]]]}, GeoRangePadding -> Scaled[.5]] ] &, "PNG" ], Permissions -> "Public" ]
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