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data cost <"1">, distance <"1">
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data vertex <'[a-f]'>, to <vertex>, from <vertex>, path <[<vertex>* VOID]>
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templates shortestPaths&{graph:}
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@: {||};
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{| {to: $, distance: 0"1", path:[]} |} -> #
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when <?($::count <=0>)> do $@ !
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otherwise
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def closest: $ ... -> ..=Min&{by: :(distance:), select: :()};
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@: ($@ union {|$closest|});
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def path: [ $closest.path..., $closest.to ];
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{| ($ notMatching {| $closest({to:}) |})...,
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(($graph matching {| $closest({from: §.to}) |}) notMatching $@({to:}))...
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-> { to: $.to, distance: $.cost + $closest.distance, path: $path}
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|} -> #
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end shortestPaths
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def edges: {|
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{ from: vertex´'a', to: vertex´'b', cost: 7"1" },
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{ from: vertex´'a', to: vertex´'c', cost: 9"1" },
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{ from: vertex´'a', to: vertex´'f', cost: 14"1" },
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{ from: vertex´'b', to: vertex´'c', cost: 10"1" },
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{ from: vertex´'b', to: vertex´'d', cost: 15"1" },
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{ from: vertex´'c', to: vertex´'d', cost: 11"1" },
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{ from: vertex´'c', to: vertex´'f', cost: 2"1" },
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{ from: vertex´'d', to: vertex´'e', cost: 6"1" },
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{ from: vertex´'e', to: vertex´'f', cost: 9"1" }
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|};
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def fromA: vertex´'a' -> shortestPaths&{graph: $edges};
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($fromA matching {|{to:vertex´'e'}|})... -> 'Shortest path from $.path(1); to $.to; is distance $.distance; via $.path(2..last);
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' -> !OUT::write
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($fromA matching {|{to:vertex´'f'}|})... -> 'Shortest path from $.path(1); to $.to; is distance $.distance; via $.path(2..last);
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' -> !OUT::write
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