@@ -64,5 +64,90 @@ let items = [Item(name: "television", weight: 50, value: 500),
6464 Item ( name: " painting " , weight: 10 , value: 1000 ) ]
6565knapsack ( items: items, maxCapacity: 75 )
6666
67+ /// Travelling Salesman
68+ 69+ let vtCities = [ " Rutland " , " Burlington " , " White River Junction " , " Bennington " , " Brattleboro " ]
70+ 71+ let vtDistances = [
72+ " Rutland " :
73+ [ " Burlington " : 67 , " White River Junction " : 46 , " Bennington " : 55 , " Brattleboro " : 75 ] ,
74+ " Burlington " :
75+ [ " Rutland " : 67 , " White River Junction " : 91 , " Bennington " : 122 , " Brattleboro " : 153 ] ,
76+ " White River Junction " :
77+ [ " Rutland " : 46 , " Burlington " : 91 , " Bennington " : 98 , " Brattleboro " : 65 ] ,
78+ " Bennington " :
79+ [ " Rutland " : 55 , " Burlington " : 122 , " White River Junction " : 98 , " Brattleboro " : 40 ] ,
80+ " Brattleboro " :
81+ [ " Rutland " : 75 , " Burlington " : 153 , " White River Junction " : 65 , " Bennington " : 40 ]
82+ ]
83+ 84+ // backtracking permutations algorithm
85+ func allPermutationsHelper< T> ( contents: [ T ] , permutations: inout [ [ T ] ] , n: Int ) {
86+ guard n > 0 else { permutations. append ( contents) ; return }
87+ var tempContents = contents
88+ for i in 0 ..< n {
89+ tempContents. swapAt ( i, n - 1 ) // move the element at i to the end
90+ // move everything else around, holding the end constant
91+ allPermutationsHelper ( contents: tempContents, permutations: & permutations, n: n - 1 )
92+ tempContents. swapAt ( i, n - 1 ) // backtrack
93+ }
94+ }
95+ 96+ // find all of the permutations of a given array
97+ func allPermutations< T> ( _ original: [ T ] ) -> [ [ T ] ] {
98+ var permutations = [ [ T] ] ( )
99+ allPermutationsHelper ( contents: original, permutations: & permutations, n: original. count)
100+ return permutations
101+ }
102+ 103+ // test allPermutations
104+ let abc = [ " a " , " b " , " c " ]
105+ let testPerms = allPermutations ( abc)
106+ print ( testPerms)
107+ print ( testPerms. count)
108+ 109+ // make complete paths for tsp
110+ func tspPaths< T> ( _ permutations: [ [ T ] ] ) -> [ [ T ] ] {
111+ return permutations. map {
112+ if let first = 0ドル. first {
113+ return ( 0ドル + [ first] ) // append first to end
114+ } else {
115+ return [ ] // empty is just itself
116+ }
117+ }
118+ }
119+ 120+ print ( tspPaths ( testPerms) )
121+ 122+ func solveTSP< T> ( cities: [ T ] , distances: [ T : [ T : Int ] ] ) -> ( solution: [ T ] , distance: Int ) {
123+ let possiblePaths = tspPaths ( allPermutations ( cities) )
124+ var bestPath : [ T ] = [ ]
125+ var minDistance : Int = Int . max
126+ for path in possiblePaths {
127+ if path. count < 2 { continue }
128+ var distance = 0
129+ var last = path. first! // we know there is one becuase of above line
130+ for next in path [ 1 ..< path. count] {
131+ distance += distances [ last] ![ next] !
132+ last = next
133+ }
134+ if distance < minDistance {
135+ minDistance = distance
136+ bestPath = path
137+ }
138+ }
139+ return ( solution: bestPath, distance: minDistance)
140+ }
141+ 142+ let vtTSP = solveTSP ( cities: vtCities, distances: vtDistances)
143+ print ( " The shortest path is \( vtTSP. solution) in \( vtTSP. distance) miles. " )
144+ 145+ //func dog(test: inout [String]) {
146+ // test.append("hello")
147+ //
148+ //}
149+ 150+ // City 0
151+ 67152//: [Next](@next)
68153
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