FIRST EDITION
WAYNE BISHOP
SWIFT ALGORITHMS & DATA STRUCTURES
A practical guide to concepts, theory and code
FOREWORD BY NATASHA MURASHEV
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//array of sorted integers let numberList : Array
= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
(#52'+ %#-2 Our rst approach employs a common “brute force” technique that involves looping through the entire array until we nd a match. In Swift, this can be achieved with the following;
func linearSearch(key: Int) { //check all possible values for number in numberlist { if number == key { print(“value at \(key) found..”) break } } }
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//check bounds if key > sequence[max] || key < sequence[min] { print(“search value \(key) not found..”) return } //evaluate chosen number.. let n = sequence[mid] if n > key { let slice: Array< Int> = Array(sequence[min...mid - 1]) self.binarySearch(slice, key: key) } if n < key { let slice: Array< Int> = Array(sequence[mid + 1...max]) self.binarySearch(slice, key: key) } else { print(“search value \(key) found..”) return } }
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//a simple array of unsorted integers let numberList : Array = [8, 2, 10, 9, 11, 1, 7, 3, 4]
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func insertionSort(numberList: Array< Int>) -> Array { //check for trivial case guard numberList.count > 1 else { return num berList } //mutated copy var output = numberList for primaryindex in 0.. -1 { if key < output[secondaryindex] {
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//move into correct position output.removeAtIndex(secondaryindex + 1) output.insert(key, atIndex: secondaryindex) } secondaryindex -= 1 } } return output }
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func bubbleSort(numberList: Array< Int>) -> Array { guard numberList.count > 1 else { return num berList } //mutated copy var output = numberList for primaryIndex in 0.. output[secondaryIndex + 1]) { swap(&output[secondaryIndex], &output[secondaryIndex + 1]) } } } return output }
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func selectionSort(numberList: Array< Int>) -> Array { guard numberList.count > 1 else { return num berList } //mutated copy var output = numberList for primaryindex in 0.. output[secondaryindex] { minimum = secondaryindex } secondaryindex += 1 } //swap minimum value with array iteration if primaryindex != minimum { swap(&output[primaryindex] , &output[minimum]) } } return output }
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//generic doubly linked list structure class LLNode { var key: T! var next: LLNode? var previous: LLNode? }
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0!#5) *6%#*5'(! 1(43 A%42)&3' 28'"%&)(?6 &)6 '"": #%2A)&A4 )" 64) $"@% A8266 #%"#4%)&46 )" nil 04>"%4 )(4$ 2%4 @64:; a&=4 B&)( 2## :4948"#?43)J nil A23 04 @64: )" :4)4%?&34 ?&66&3' 928@46 "% )" #%4:&A) )(4 43: "> 2 8&6); GB&>) (48#6 43>"%A4 )(&6 046)R#%2A)&A4 2) A"?#&84 )&?4 )(%"@'( 2 #2%2:&'? A2884: "#)&"3286; H"% 4C2?#84J )(4 >@3A)&"3 printAllKeys 4?#8"$6 23 &?#8&A&) @3B%2##4: "#)&"328 X4;';J currentY )" &)4%2)4 )(%"@'( 8&3=4: 8&6) &)4?6;
//print all keys for the class func printAllKeys() { var current: LLNode! = head //assign the next instance while (current != nil) { println(“link item is: \(current.key)”) current = current.next } }
'//#5) (#5=! ^4%4V6 2 >@3A)&"3 )(2) 0@&8:6 2 :"@08$ 8&3=4: 8&6); <(4 ?4)(": addLink A%42)46 2 34B &)4? 23: 2##43:6 &) )" )(4 8&6); <(4 GB&>) '434%&A )$#4 A"36)%2&3) < is also dened to ensure link instances conform to a specic protocol.
class LinkedList { var head: LLNode = LLNode() //append a new item to a linked list func addLink(key: T) {
//establish the head node if (head.key == nil) { head.key = key return } //establish the iteration variables var current: LLNode? = head while (current != nil) {
if current?.next == nil { let childToUse:LLNode = LLNode() childToUse.key = key childToUse.previous = current
"/605"7#.,*894*-
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current!.next = childToUse break } else { current = current?.next }
} //end while }
+2-*B#5) (#5=! !"394%648$J (4%4V6 23 4C2?#84 "> %4?"9&3' &)4?6 >%"? 2 8&6); ]4?"9&3' 8&3=6 3") "38$ &39"8946 %4R A82&?&3' ?4?"%$ X>"% )(4 :484)4: &)4?YJ 0@) 286" %4266&'3&3' 8&3=6 6" )(4 A(2&3 %4?2&36 @30%"=43;
func removeLinkAtIndex(index: Int) { //check for nil conditions if ((index < 0) || (index > (self.count - 1)) || (head.key == nil)) { return } var current: LLNode? = var trailer: LLNode?
head
var listIndex: Int = 0
//determine if the removal is at the head if (index == 0) { current = current?.next head = current! return }
//iterate through the remaining items while (current != nil) { if (listIndex == index) { //redirect the trailer and next pointers trailer!.next = current?.next current = nil break }
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//update assignments trailer = current current = current?.next listIndex += 1 } //end while
} //end function
1*05%#5) (#5=! O) A23 286" 04 A"3943&43) )" count 8&3= &)4?6; O3 GB&>)J )(&6 A23 04 4C#%4664: 26 2 A"?#@)4: #%"#4%)$ ; H"% 4C2?#84J )(4 >"88"B&3' )4A(3&D@4 B&88 288"B 2 8&3=4: 8&6) &36)23A4 )" @64 2 :") 3")2)&"3; X4;';J someList.countY;
var count: Int { if head.key == nil { return 0 } else
{
var current: LLNode = head var x: Int = 1
//cycle through the list of items while current.next != nil { current = current.next! x += 1 } return x } }
2$$#1#2514 a&3=4: 8&6)6 )$#&A288$ #%"9&:4 O(n) >"% 6)"%2'4 23: 8""=@#; 76 B4V88 644J 8&3=4: 8&6)6 2%4 ">)43 @64: B&)( other structures to create new models. Algorithms with an efciency of O(n) 2%4 62&: )" %@3 &3 8&342% )&?4;
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//student linked list structure class StudentNode { var key: Student? var next: StudentNode? }
%,2 1,'((25)2 1(&84 )(&6 6)%@A)@%4 &6 :46A%&#)&94 23: "%'23&P4:J &)V6 3") %4@62084; O3 ")(4% B"%:6J )(4 6)%@A)@%4 &6 928&: >"% 8&6)&3' 6)@:43)6 0@) &6 @32084 )" ?232'4 23$ ")(4% )$#4 "> :2)2 X4;'; )42A(4%6Y; <(4 #%"#R 4%)$ Student is a class that may include specic properties such as nameJ schedule 23: grades; O> $"@ 2))4?#)4: )" %4@64 )(4 62?4 StudentNode A8266 )" ?232'4 TeachersJ )(&6 B"@8: A2@64 2 A"?#8&4% )$#4 ?&6?2)A(;
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//refactored linked list structure class LLNode { var key: T? var next: LLNode? }
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%,2 #-6(2-25%'%#*5 <(4 #"B4% "> '434%&A6 A23 04 3"B 04 6443 )(%"@'( &)6 &?#84?43)2)&"3; 1&)( )(4 A8266 %4>2A)"%4:J LLNode A23 3"B ?232'4 8&6)6 "> StudentsJ TeachersJ "% 23$ ")(4% )$#4 B4 :4A&:4;
//new list of students var studentList = LLNode() //new list of teachers var teacherList = LLNode()
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func insertionSortG(sequence: [T]) -> [T] { guard sequence.count > 1 else { return sequence } //mutated copy var output = Array(sequence) for primaryIndex in 0.. -1; secondaryIndex-- { if key < output[secondaryIndex] { //move into correct positio n output.removeAtIndex(secondaryIndex + 1) output.insert(key, atIndex: secondaryIndex) } } }
return output }
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3#5'+4 !2'+1, %+22! 7 0&32%$ 642%A ( )%44 &6 2 :2)2 6)%@A )@%4 )(2) 6)"%46 &3>" %?2)&"3 &3 2 8" '&A28 (&4%2%A($; 76 :4?"3R 6)%2)4: B&)( 5&' Z [")2)&"3J 28'"%&)(?6 #%"9&:4 )(4 046) %46@8)6 B&)( 6"%)4: :2)2; 5&32%$ G42%A( Trees extend this idea by using specic rules. A binary search tree (BST) should not be mistaken >"% 2 0&32%$ )%44 "% )%&4; <("64 6)%@A)@%46 286" 6)"%4 &3>"%?2)&"3 &3 2 (&4%2%A($J 0@) 4?#8"$ :&>>4%43) %@846;
,*" #% "*+=! 7 0&32% $ 642%A( )%44 &6 A"?#%&6 4: "> 2 =4$ 23: )B" &3:&A 2)"%6; <(4 =4$ %4#%4643)6 )(4 :2)2 $"@ B"@8: 8&=4 )" 6)"%4J 6@A( 26 2 6)%&3' "% 6A282% 928@4; <$#&A288$ %4#%4643)4: B&)( #"&3)4%6 J )(4 &3:&A2R )"%6 6)"%4 )(4 8"A2)&"3 X286" A2884: )(4 2::%466Y "> &)6 )B" A(&8:%43; <(4 left A(&8: A"3)2&36 2 928@4 )(2) &6 6?2884% )(23 &)6 #2%43); !"394%648$J )(4 right A(&8: A"3)2&36 2 928@4 '%42)4% )(23 &)6 #2%43);
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/* An AVL Tree is a kind of self-balancing binary search tree */ public class AVLTree T: < Comparable> { var key: T? var left: AVLTree? var right: AVLTree? }
1(43 A%42)&3' 28'"%&)(?6J &) &6 '"": #%2A)&A4 )" 64) $"@% A8266 #%"#4%)&46 )" nil 04>"%4 )(4$ 2%4 @64:; GB&>) (48#6 )" 43>"%A4 )(&6 046)R#%2A)&A4 2) A"?#&84 )&?4 )(%"@'( 2 34B #2%2:&'? A2884: "#)&"3286; 78"3' B&)( "@% A8266 :4A82%2)&"3J )(4 '434%&A )$#4 A"36)%2&3) f TQ Comparableg &6 286" dened to ensure instances conform to a specic protocol.
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} //end if //check the right side if (key > self.key) { if (self.right != nil) { right?.addNode(key) } else { //create a new right node let rightChild : AVLTree = AVLTree() rightChild.key = key self } .right = rightChild } //end if } //end function
<(4 ?4)(": addNode @646 %4A@%6&"3 )" :4)4%?&34 B(4%4 :2)2 &6 2::4:; 1(&84 3") %4D@&%4:J %4A@%6&"3 &6 2 #"B4%>@8 432084% 26 42A( A(&8: 04A"?46 23")(4% &36)23A4 "> 2 5G<; 76 2 %46@8)J &364%)&3' :2)2 04A"?46 2 6)%2&'()>"%B2%: #%"A466 "> &)4%2)&3' )(%"@'( )(4 2%%2$;
//a simple array of unsorted integers let numberList : Array = [8, 2, 10, 9, 11, 1, 7] //create a new BST instance var root = AVLTree() //sort each item in the list for number in num berList { root.addNode(number) }
2$$#1#2514 5G<6 2%4 #"B4%>@8 :@4 )" )(4&% A"36&6)43) %@846; ^"B494%J )(4&% '%42)46) 2:923)2'4 &6 6#44:; G&3A4 :2)2 &6 "%'23&P4: 2) )(4 )&?4 "> &364%)&"3J 2 A842% #2))4%3 4?4%'46; K28@46 8466 )(23 )(4 root 3":4 X4;'; 8) will naturally lter to the left. Conversely, all values greater than the root B&88 lter to the right.
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//retrieve the height of a node func getNodeHeight(aNode: AVLTree!) -> Int { if (aNode == nil) { return -1 } else { return aNode.height } }
//calculate the height of a node func setNodeHeight() -> Bool { //check for a nil condition if (self.key == nil) { print(“no key provided..”) return false } //initialize leaf variables var nodeHeight: Int = 0 //calculate node height nodeHeight = max( getNodeHeight(self.left),getNodeHeight(self.right)) + 1 self.height = nodeHeight return true }
-2'!0+#5) 3'('512 1&)( )(4 root 3":4 46)208&6(4:J B4 A23 #%"A44: )" 2:: )(4 34C) 928@4; F#"3 &?#84?43)&3' 6)23R :2%: 5G< 8"'&AJ &)4? 26 &6 #"6&)&"34: 26 )(4 left 842> 3":4; 76 2 34B &)4?J &)6 height &6 286" A28R A@82)4: X&;4;J 0Y; ^"B494%J 6&3A4 "@% ?":48 &6 2 (&4%2%A($J B4 )%294%64 @#B2%:6 )" %4A28A@82)4 &)6 #2%43) height 928@4;
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//right rotation sequence let childToUse : AVLTree = AVLTree() childToUse.height = 0 childToUse.key = self.key if (getNodeHeight(self.left) -getNodeHeight(self.right) > 1) { //reset the root node self.key = self.left?.key self.height = getNodeHeight(self.left)
//assign the new right node self.right = childToUse
//adjust the left node self.left = self.left?.left self.left?.height = 0 return true }
I943 )("@'( B4 @3:4%'" 2 64%&46 "> 6)4#6J )(4 #%"A466 "AA@%6 &3 O(1) )&?4; `423&3'J &)6 #4%>"%?23A4 &6 @32>>4A)4: 0$ ")(4% >2A)"%6 6@A( 26 3@?04% "> leaf 3":46J :46A43:23)6 "% )%44 height; O3 2::&)&"3J 4943 )("@'( B4V94 A"?#84)4: 2 right %")2)&"3J 6&?&82% 6)4#6 A"@8: 04 &?#84?43)4: )" %46"894 0")( left 23: right &?02823A46;
%,2 +2!0(%! /"" I5HL #% .")+4 7%+" )<%9# #+)E"+').' )4& M"I#$>N1+'# /")+-$5
1&)( )%44 02823A&3'J &) &6 &?#"%)23) )" 3")4 )(2) )4A(3&D@46 8&=4 %")2)&"36 &?#%"94 #4%>"%?23A4J 0@) :" 3") A(23'4 tree "@)#@); H"% 4C2?#84J 4943 )("@'( 2 right %")2)&"3 A(23'46 )(4 A"334A)&"36 04)B443 nodesJ )(4 "94%288 5G< 6"%) "%:4% &6 #%464%94:; 76 2 )46)J "34 A23 )%294%64 2 02823A4: 23: @302823A4: 5G< XA"?#2%&3' )(4 62?4 928@46Y 23: %4A4&94 )(4 62?4 %46@8)6; O3 "@% A264J 2 6&?#84 depth-rst search will produce the following:
//sorted values from a traversal 23, 26, 29
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//build tree of dictionary content func addWord(keyword: String) { guard keyword.length > 0 else { return } var current: TrieNode = root while(keyword.length != current.level) { var childToUse: TrieNode! let searchKey: String = keyword.substringToIndex(current.level+ 1)
//iterate through the node children for child in current.children { if (child.key == searchKey) { childToUse = child break } }
if
//create a new node (childToUse == nil) { childToUse = TrieNode() childToUse.key = searchKey childToUse.level = current.level + 1 current.children.append(childToUse) } current = childToUse
} //end while
//add final end of word check if (keyword.length == current.level) { current.isFinal = true print(“end of word reached!”) return }
} //end function
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!!++
!"#$% '()*+#%,-. /01 2/%/ !%+34%3+5.
A nal check conrms our keyword after completing the while loop. As part of this nal check, we @#:2)4 )(4 current 3":4 B&)( )(4 isFinal &3:&A2)"%; 76 ?43)&"34:J )(&6 6)4# B&88 288"B @6 )" :&6 )&3'@&6( B"%:6 >%"? #(%2646;
$#5/#5) "*+/! The algorithm for nding words is similar to adding content. Again, we establish a while 8""# )" 329R &'2)4 )(4 )%&4 (&4%2%A($; G&3A4 )(4 '"28 B&88 04 )" %4)@%3 2 8&6) "> #"66&084 B"%:6J )(464 B&88 04 )%2A=4: @6&3' 23 Array;
//finds words based on the prefix func findWord(keyword: String) -> Array! { guard keyword.length > 0 else { return nil } var current: TrieNode = root var wordList: Array< String> = Array() while (keyword.length != current.level) { var childToUse: TrieNode! let searchKey: String = keyword.substringToIndex(current.level + 1) print(“looking for prefix: \(searchKey)..”) //iterate through any children for child in current.children { if (child.key == searchKey) { childToUse = child current = childToUse break } }
if childToUse == nil { return nil }
} //end while
//retrieve the keyword and any decendants if ((current.key == keyword) && (current.isFinal)) { }
"/605"7#.,*894*-
wordList.append(current.key)
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!!+$
//append only children that are words for child in current.children { if (child.isFinal == true) { wordList.append(child.key) } }
return wordList
} //end function
<(4 findWord >@3A)&"3 A(4A=6 )" 436@%4 =4$B"%: #(%264 #4%?@)2)&"36 2%4 >"@3:; Z3A4 )(4 43)&%4 keyword is identied, we start the process of building our word list. In addition to returning keys identied as words (e.g., “ 52)TJ S5288TYJ B4 2AA"@3) >"% )(4 #"66&0&8&)$ "> %4)@%3&3' nil 0$ %4)@%3&3' 23 &?#8&A&) @3B%2##4: "#)&"328;
2N%25/#5) !"#$% I943 )("@'( B4V94 B%&))43 "@% )%&4 &3 GB&> )J B4V94 4C)43:4: 6"?4 823'@2'4 >42)@%46 )" ?2=4 )(&3'6 B"%=; !"??"38$ =3"B3 26 A2)4'"%&46 &3 Z0N4A)&94R!J "@% 28'"%&)(?6 4?#8"$ )B" 2::&)&"328 GB&>) 4C)436&"36; <(4 >"88"B&3' A8266 4C)43:6 )(4 >@3A)&"328&)$ "> )(4 32)&94 String A8266Q
extension String { //compute the length of string var length: Int { return self.characters.count }
//returns characters of a string up to a specified index func substringToIndex( to: Int) -> String { return self.substringToIndex(self .startIndex.advancedBy(to)) }
//return a character at a specific index func stringAtIndex(position: Int) -> String { return String(Array(self.characters)[position]) } }
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Item 1 Item 2 Item 3 Item
4
O3 )(4&% 026&A >"%?J 6)2A=6 23: D@4@46 4?#8"$ )(4 62?4 6)%@A)@%4 23: "38$ 92%$ &3 )(4&% @64; <(4 :2)2 6)%@A)@%4 A"??"3 )" 0")( >"%?6 &6 )(4 8&3=4: 8&6); F6&3' '434%&A6J B4V88 0@&8: 2 D@4@4 )" ("8: 23$ )$#4 "> "0N4A); O3 2::&)&"3J )(4 A8266 B&88 286" 6@##"%) nil 928@46;
//generic queue node class QNode { var key: T? var next: QNode? }
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25@020#5) *3D21%! <(4 #%"A466 "> 2::&3' &)4?6 &6 ">)43 %4>4%%4: )" 26 S43D@4@&3'T. Here, we dene the method used to 43D@4@4 "0N4A)6 23: &:43)&>$ )(4 #%"#4%)$ top )(2) B&88 64%94 26 "@% 6)2%)&3' #"&3);
//enqueue the specified object func enQueue(key: T) { //check for the instance if (top == nil) { top = QNode() } //establish the top node if (top.key == nil) { top.key = key return } let childToUse:QNode = QNode() var current: QNode = top
//cycle through the list of items while (current.next != nil) { current = current.next! } //append a new item childToUse.key = key current.next = childToUse }
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//retrieve items from the top level in O(1) constant time func deQueue() -> T? { //determine if the key or instance exist let topitem: T? = self.top?.key if (topitem == nil) { return nil } //queue the next item let queueitem: T? = top.key! //use optional binding if let nextitem = top.next { top = nextitem } else { top = nil } return queueitem }
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//check queue func isEmpty() -> Bool { //determine if the key or instance exist if let _: T = self.top?.key { return false } else { return true } }
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//retrieve the top most item func peek() -> T? { return top.key! }
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public class Vertex { var key: String? var neighbors: Array< Edge> init() { self.neighbors = Array<
Edge>()
} }
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'/D'12514 (#!%! <(4 neighbors #%"#4%)$ &6 23 2%%2$ )(2) %4#%4643)6 A"334A)&"36 2 vertex ?2$ (294 B&)( ")(4% 94%)&A46; 76 :&6A@664:J 2 vertex A23 04 266"A&2)4: B&)( "34 "% ?"%4 &)4?6; <(&6 8&6) "> 34&'(0"%R &3' &)4?6 &6 6"?4)&?46 A2884: 23 2:N2A43A$ 8&6) 23: A23 04 @64: )" 6"894 2 92%&4)$ "> #%"084?6; ^4%4V6 2 026&A :2)2 6)%@A)@%4 )(2) %4#%4643)6 23 edgeQ
public class Edge { var neighbor: Vertex var weight: Int init() { weight = 0 self.neighbor = }
Vertex()
}
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public class SwiftGraph { //declare graph canvas private var canvas: Array< Vertex> public var isDirected: Bool
* 6+)I$ -)4E)' -%9.& ).'% <" 17I."7"4#"& 01#$ ) /012# D/"#F -%.."-#1%4
init() { canvas = Array< Vertex>() isDirected = true }
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//create a new vertex func addVertex(key key:
String) -> Vertex {
//set the key let childVertex: Vertex = Vertex() childVertex.key = key
//add the vertex to the graph canvas canvas.append(childVertex) return childVertex } }
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//add edge to source vertex func addEdg e(source source: Vertex, neighbor:Vertex, weight: Int) { //create a new edge let newEdge = Edge()
//establish the default properties newEd ge.neighbor = neighbor newEd ge.weight = weight source.neighbors.append(newEdge)
//check condition for an undirected graph if (isDirected == false) {
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//create a new reversed edge let reverseEdge = Edge() //establish the reversed properties reverseEdge.neighbor = source reverseEdge.weight = weight neighbor.neighbors.app end(reverseEdge) } }
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//object initialization init() { destination = Vertex() } }
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//process Dijkstra’s shortest path algorithm func processDijkstra(source: Vertex, destination: Vertex) -> Path? { ... }
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var frontier = Array() var finalPaths = Array< Path>() //use source edges to create the frontier for e in source.neighbors { let newPath: Path = Path() newPath.destination = e.neighbor newPath.previous = nil newPath.total = e.weight //add the new path to the frontier frontier.append(newPath) }
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M%2#( <(4"%$ R ())#Qbb43;B&=:&2;"%'bB&=&bM%2#(c)(4"%$ M%44:$ 7##%"2A( R ())#Qbb43;B&=:&2;"%'bB&=&bM%44:$c28'"%&)(? <%2948&3' G2846?23 R ())#Qbb43;B&=:&2;"%'bB&=&b<%29488&3'c62846?23c#%"084? I:6'4% W&N=6)%2 R ())#Qbb43;B&=:&2;"%'bB&=&bI:6'4%c1;cW&N=6)%2 W&N=6)%2V6 78'"%&)(? R ())#Qbb43;B&=:&2;"%'bB&=&bW&N=6)%2h,i6c28'"%&)(?
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%,2 ,2'6 !%+01%0+2 Let’s create a more efcient frontier; [2?4: PathHeapJ )(4 :2)2 6)%@A)@%4 B&88 4C)43: )(4 >@3AR )&"328&)$ "> 23 array;
public class PathHeap { private var heap: Array init() { heap = Array< }
Path>()
//the number of frontier items var count: Int { return self.heap.count } }
<(4 PathHeap A8266 &3A8@:46 )B" #%"#4%)&46; < " 6@##"%) '"": :46&'3J heap (26 0443 :4A82%4: 2 #%&92)4 #%"#4%)$; <" )%2A= )(4 3@?04% "> &)4?6J count &6 :4A82%4: 26 2 A"?#@)4: #%"#4%)$;
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//sort paths into a min-heap func enQueue(key:
Path) {
heap.append(key) var childIndex: Float = Float(heap.count) - 1 var parentIndex: Int! = 0
//calculate parent index if childIndex != 0 { parentIndex = Int( floorf((childIndex - 1) / 2)) }
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<%294%628 R ())#Qbb43;B&=:&2;"%'bB&=&b<%44c)%294%628 W4#)(RH&%6) G42%A( - http://en.wikipedia.org/wiki/Depth-rst_search 5%42:)(RH&%6) G42%A( - http://en.wikipedia.org/wiki/Breadth-rst_search
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//simple hash table structure class HashNode { var firstname: String! var lastname: String! var next: HashNode! }
%,2 301=2%! Before using our table, we must rst dene a bucket 6)%@A)@%4; O> $"@ %4A288J buckets 2%4 @64: )" '%"@# node items. Since items will be stored in a non-contiguous fashion, we must rst dene our collection 6&P4; O3 GB&>)J )(&6 A23 04 2A(&494: B&)( )(4 >"88"B&3'Q
class HashTable { private var buckets: Array //initialize the buckets with nil values init(capacity:Int) { self.buckets = Array< HashNode!>(count: capacity, repeatedValue:nil) } }
'//#5) "*+/! 1&)( )(4 A"?#"343)6 &3 #82A4J B4 A23 A":4 2 #%"A466 >"% 2::&3' B"%:6; <(4 addWord ?4)(": 6)2%)6 0$ A"3A2)432)&3' &)6 #2%2?4)4%6 26 2 6&3'84 String; <(4 %46@8) &6 )(43 #2664: )" )(4 createHash (26( 28'"%&)(? B(&A(J 6@064D@43)8$J %4)@%36 23 Int; Z3A4 A"?#84)4J B4 A"3:@A) 2 6&?#84 A(4A= >"% 23 4C&6)&3' 43)%$;
//add the key using the specified hash func addWord(firstname:
String, lastname: String) {
var hashindex: Int! var fullname: String! //create a hashvalue using the complete name fullname = firstname + lastname hashindex = self.createHash(fullname)
let childToUse:HashNode = HashNode() var head: HashNode!
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childToUse.firstname = firstname childToUse.lastname = lastname //check for an existing list if (buckets[hashindex] == nil) { buckets[hashindex] = childToUse }
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//compute hash index func createHash(fullname: String) -> Int! { var remainder: Int = 0 var divisor: Int = 0 for key in fullname.unicodeScalars { divisor += Int(key.value) } //calculate the remainder remainder = divisor % buckets.count return remainder - 1 }
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<(4 A%42)&"3 "> (26( 28'"%&)(?6 &6 A "36&:4%4: ?"%4 2%) )(23 6A&43A4; 76 2 %46@8)J )(4%4 2%4 ?23$ )4A(3&D@46 )" (48# %4:@A4 )(4 #")43)&28 "> A"88&6&"36; 54$"3: @6&3' ?":@82% ?2)( )" A"?#@)4 2 hashJ B4V94 2##8&4: 2 )4A(3&D@4 A2884: 64#2%2)4 A(2&3&3'; 5$ 2##8$&3' 2 #%"A466 6&?&82% )" 0@&8:R &3' 2 linked listJ )(&6 B&88 288"B ?@8)T &3#@)6 )" 6(2%4 )(4 62?4 hash;
//add the key using the specified hash func addWord(firstname:
String, lastname: String) {
var hashindex: Int! var fullname: String!
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!!&%
!"#$% '()*+#%,-. /01 2/%/ !%+34%3+5.
//create a hashvalue using the complete name fullname = firstname + lastname hashindex = self.createHash(fullname) let childToUse:HashNode = HashNode() var head: HashNode!
childToUse.firstname = firstname childToUse.lastname = lastname
//check for an existing list if buckets[hashindex] == nil { buckets[hashindex] = childToUse } else { print(“a collision occured. implementing chaining..”) head = buckets[hashindex] //append new item to the head of the list childToUse.next = head head = childToUse //update the chained list buckets[hashindex] = head } }
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^26( <2084 R ())#Qbb43;B&=:&2;"%'bB&=&b^26(c)2084 ^26( 78'"%&)(? R ())#Qbb43;B&=:&2;"%'bB&=&b^26(c>@3A)&"3 `":@82% `2)( R ())#6QbbBBB;=(232A2:4?$;"%' MD5 Algorithm - http://en.wikipedia.org/wiki/MD5
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1(*!0+2! <(%"@'("@) )(&6 64%&46 B4V94 @64: GB&>) )" 0@&8: 92%&"@6 ?":486; 76 3")4:J "34 A23 0@&8: A"?#84C 6)%@A)@%46 @6&3' A"??"3 "0N4A)R"%&43)4: XZZY )4A(3&D@46; 76 6@A(J GB&>) &6 286" =3"B3 26 2 >@3AR )&"328 #%"'%2??&3' 823'@2'4; <(&6 &:42 4C)43:6 )(4 )%2:&)&"328 ZZ #2%2:&'? B&)( )(4 3")&"3 )(2) >@3A)&"36 A23 2A) 26 )$#46; The idea that functions can act as types has numerous benets. As with most functions, the idea "> @6&3' 2 StringJ Int "% Bool )" #266 :2)2 &6 A"??"3; GB&>) 4C)43:6 )(&6 &:42 R 288"B&3' >@3A)&"36 )" 04 @64: B&)( 92%&20846 J #2%2?4)4%6 23: %4)@%3 )$#46; O3 )(&6 A(2#)4%J B4V88 %49&4B ("B A8"6@%46 B"%= 23: B&88 :&6A@66 ("B )" @64 )(4? B&)( 28'"%&)(?6;
%,2 1*5126% <" &3)%":@A4 A8"6@%46J 84)V6 %49&4B )(4 32)&94 Array )$#4; 76 B4V94 6443J GB&>) 2%%2$6 (294 )(4 >@3A)&"328&)$ "34 B"@8: 4C#4A); Z34 A23 2::J ?":&>$ 23: %4?"94 "0N4A)6; H@%)(4%?"%4J Arrays (294 )(%44 2::&)&"328 ?4)(":6 =3"B3 26 mapJ filter 23: reduce; k3"B3 26 (&'(4%R"%:4% >@3A)&"36J )(464 ?4)(":6 2AA4#) >@3A)&"36 26 2 #2%2?4)4%6;
//array of numbers let allNumbers: Array = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
//determine if a number is even func isEven(number: Int) -> Bool { return number % 2 == 0 } //returns 2, 4, 6, 8 10 let evenNumbers: Array = allNumbers.filter(isEven)
'5'(4!#! O3 )(&6 4C2?#84J filter 2AA4#)6 2 >@3A)&"3 )(2) %4)@%36 928@46 :&9&6&084 0$ 2; 1(43 %49&4B&3' isEvenJ )(4%4V6 3")(&3' )" :&6)&3'@&6( &) >%"? 23$ ")(4% >@3A)&"3 R )(@6 ?2=&3' &) %4@62084 >"% ")(4% "0N4A)6; H&3288$J B(43 isEven &6 @64: 26 2 #2%2?4)4%J &)6 6&'32)@%4 &6 %4?"94:;
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%,2 !#)5#$#1'512 This sequence could be have been written as a single function. However, the signicance is that isEven 23: &)6 &?#84?43)2)&"3 2%4 :4A"@#84:; <(&6 288"B6 filter )" @64 23$ >@3A)&"3 )(2) 2AA4#)6 23 Int 23: %4)@%36 2 Bool; 54$"3: GB&>)J )(4 &:42 "> 23"3$?"@6 >@3A)&"36 A23 04 6443 &3 ")(4% 823'@2'46 8&=4 E$)("3J ]@0$ 23: \292; 76 6"?4"34 &3)4%46)4: &3 GB&>)J $"@ ?2$ (294 6443 6&?&82% 6)2)4?43)6 B%&))43 26 A8"6@%4 4C#%466&"36. Now that we understand the signicanc e of anonymous >@3A)&"36J 84)V6 644 ("B )(4$ A23 04 @64: B&)( A @6)"? :2)2 6)%@A)@%46;
-'66#5) (#!%! E%49&"@68$J B4 &3)%":@A4: 8&3=4: 8&6)6 23: 0@&8) 2 3@?04% "> 28'"%&)(?6 )" ?232'4 LLNodes; G&?&82% )" 23 ArrayJ 2 8&3=4: 8&6) A23 286" 04 A"36&:4%4: 2 A"884A)&"3 )$#4; 76 6@A(J )(4 &:42 "> 6@##"%)&3' (&'(4%R"%:4% >@3A)&"36 &6 #"66&084; <" &88@6)%2)4J 84)V6 4C)43: "@% 8&3=4: 8&6) A8266 B&)( 2 map >@3A)&"3;
//map list content - higher order function func map(formula: LLNode -> T) -> LinkedList! { ... }
1(43 B"%=&3' B&)( A8"6@%46J &) A23 6"?4)&?46 04 A(28843'&3' )" @3:4%6)23: )(4&% 6$3)2C; O3 "@% A264J map )2=46 2 6&3'84 #2%2?4)4% Xformula) which is a function. With its syntax rened, formula 2AA4#)6 2 '434%&A LLNode 23: %4)@%36 2 '434%&A )$#4 T; H&3288$J )(4 map >@3A)&"3 %4)@%36 23 "#)&"328;
//map list content - higher order function func map(formula:
LLNode -> T) -> LinkedList! {
if head.key == nil { return nil } var current: LLNode! = head let results: LinkedList! = LinkedList() var newKey: T! while current != nil { //map based on formula newKey = formula(current) //add non-nil entries if newKey != nil { }
"/605"7#.,*894*-
results.addLink(newKey)
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current = current.next } return results } //end function
O3 )(&6 4C2?#84J LinkedList.map?&?&A6 )(4 >@3A)&"328&)$ 6443 B&)( Array.map; 76 )(4 >@3A)&"3 &)4%R 2)46 )(%"@'( '434%&A LLNodesJ 42A( "34 &6 #2664: )" formula )" 04 #%"A 4664:; [")4 )(4 20643A4 "> )(4 formula >@3A)&"3 0":$; <(&6 #"%)&"3 &6 :4)4%?&34: 2) %@3)&?4 B&)( 2 A8"6@%4 4C#%466&"3Q
//map nodes based on closure expression func testLinkMapExpression() {
*' I+"E1%9'., '$%0 4Q 1# 1' 4%# +"U91+"& #$)#
//helper function - builds a linked list let linkedList: LinkedList = self.buildLinkedList() let results = linkedList.map { (node: LLNode) -> Int in return node.key * 2 }
294-#1%4' <" "3"-9#"& )' -.%'9+" "3I+"''1%4'5 However, their concise 2%+7)# 7):"' 1# #$" I+"2"++"& -$% 1-"5
}
%+'B2+!'(! +2B#!#%2/ O3 2::&)&"3 )" 8&3=4: 8&6)6J B4 286" &3)%":@A4: )(4 A"3A4#) "> )%294%6&3' :2)2 6)%@A)@%46; F6&3' depth-r st (DFS) and breadth-rst search (BFS), our goal was to discover new nodes while printing )(4&% key; ^"B494%J B4 A23 43(23A4 )(464 28'"%&)(?6 B&)( A8"6@%46; <" &88@6)%2)4J 84)V6 %4>2A)"% "@% 5HG 28'"%&)(?;
//bfs traversal with inout trailing closure func traverse(startingv: Vertex, formula: (inout node: Vertex) -> ()) { ... }
G&3A4 "@% >@3A)&"3 &6 :46&'34: )" B"%= B&)( '%2#(6J traverse 2AA4#)6 2 6)2%)&3' vertex 23: formula; F#"3 2328$P&3' )(4 formula, B4 644 &) 2AA4#)6 2 vertex 26 23 inout #2%2?4)4% 23: %4)@%36 nil;
V$"4 &"-.)+146 294-#1%4 '164)#9+"'Q 41. E).9"' -)4 <" "3I+"''"& )' ) :",0%+& %+ 01#$ D@ AF5
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//bfs traversal with inout closure function func traverse(startingv:
Vertex, formula: (inout node: Vertex) -> ()) {
//establish a new queue let graphQueue: Queue< Vertex> = Queue()
//queue a starting vertex graphQueue.enQueue(startingv)
while !graphQueue.isEmpty() { //traverse the next queued vertex var vitem: Vertex = graphQueue.deQueue() as Vertex!
//add unvisited vertices to the queue for e in vitem.neighbors { if e.neighbor.visited == false { print(“adding vertex: \(e.neighbor.key!) to queue..”) graphQueue.enQueue(e.neighbor) } }
//invoke formula formula(node: &vitem)
} //end while
print(“graph traversal complete..”) }
G&?&82% )" )(4 map >@3A)&"3J traverse &39"=46 &)6 "B3 formula 26 &) &)4%2)46 )(%"@'( :&6A"94%4: vertices; ^"B494%J 6&3A4 )(4 formula #2%2?4)4% &6 #2664: 0$ %4>4%43A4 J )(4%4V6 3" 344: )" :4A82%4 2 %4)@%3 928@4; <(&6 288"B6 )(4 A8"6@%4 )" >@88$ 43A2#6@82)4 23$ A(23'46;
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//bfs traversal with closure expression func testBFSTraverseExpression() {
/"" #$" -%7I."#" '91#" %2 ).6%+1#$7 941# #"'#' %4
var testGraph:
SwiftGraph = SwiftGraph()
.... testGraph.traverse(vertexA) { inout ( node: Vertex) -> () in node.visited = true print(“traversed vertex: \(node.key!) ..”) } }
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C-LOOP BASICS <(4 !R6)$84 8""# &6 2 A8266&A A"3)%"8 6)%@A)@%4 >"@3: &3 494%$ ! R0264: 823'@2'4; 786" A2884: 2 >"%R 8""#J 4C2?#846 A23 04 4C#%4664: &3 \292J \2926A%&#)J Z0N4A)&94R! 23: !l; !"36&:4% )(4 >"88"B&3'Q
var numberList: Array = [8, 2, 10, 7, 5] //deprecated C-loop syntax for var index = 0; index < numberList.endIndex; index++ { numberList[index] }
76 6("B3J )(4 for-loop consists of three parts. The rst part sets the variable assignment while the second statement provides the terminating condition. The nal statement updates the loop 92%&2084 R 266@?&3' )(4 )4%?&32)&3' A"3:&)&"3 (263V) 0443 ?4); 1(43 2##8&4:J )(&6 A8266&A b A%"66R#82)>"%? )4A(3&D@4 (26 0443 @64: )" 0@&8: A"@3)8466 @64% &3)4%>2A46J 28'"%&)(?6 23: 02A=43: 6$6)4?6;
%,2 ",#(2 (**6 I943 )("@'( )(4 !R8""# >2:46 2B2$ &3 GB&>)J )(4%4 2%4 ")(4% )4A(3&D@46 )(2) ?44) 23:J &3 6"?4 A2646J 4CA44: )(&6 A8266&A )""8; H&%6)J 84)V6 A"36&:4% )(4 while-loopQ
var numberList: Array = [8, 2, 10, 7, 5] var index: Int = 0 //prints 8, 2, 10, 7, 5 while index < numberList.endIndex { numberList[index] index += 1 }
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1(2)V6 3&A4 20"@) )(4 B(&84R8""# &6 )(2) &) &6 2 B&:48$ 2:"#)4: >"%?2); O> $"@ @64: )(&6 )4A(3&D@4 &3 2 )4A(3&A28 &3)4%9&4BJ ")(4%6 B"@8: (294 8&))84 #%"084? >"88"B&3' $"@% 8"'&A; 1&)( ?$ #%"N4A)J O ">)43 @64 )(4 while-loop with other Swift-specic syntax.
$'!% 250-2+'%#*5 54$"3: 026&A 8""#6J 84)V6 A"36&:4% )(4 A"??"3 )26= "> &)4%2)&3' )(%"@'( 2 collection; <(4 &:42 "> >26) 43@?4%2)&"3 &6 A"??"3 0@) )(4 6$3)2C 92%&46J :4#43:43) "3 #%"'%2??&3' 823'@2'4; ^4%4 2%4 some Swift-specic examples:
var numberList: Array = [8, 2, 10, 7, 5]
//for loop with half-open operator for index in 0..
//fast enumeration for item in num berList { print(item) }
//return tuple combination - index & value for (index, value) in numberList.enumerate() { print(“the index \(index) contains value \(value)..”) }
At rst glance, these samples look concise. Using the (28>R"#43 "#4%2)"%J 2 loop 92%&2084 A23 04 &3&)&28&P4: )" zero "% 6"?4 ")(4% 928@4; ^"B494%J B(2)V6 ?&66&3' &6 04&3' 2084 )" A"3)%"8 )(4 loop &)4%2)&"3 64D@43A4; <(&6 B"@8: #4%?&) A$A8&3' )(%"@'( 2 collection &3 %494%64 "% 6=&##&3' A4%)2&3 &3:&A46; 1&)( GB&>)J )(4 0@&8)R&3 reverse >@3A)&"3 A23 04 2##8&4:; 76 6("B3J reverse A23 04 @64: )" %494%64 2 character 64) "% collectionQ
//reversed characters var someArray: String = “Swift” var result = String(someArray.characters. reverse()) print(result) //reversed collection var testArray: Array = [8, 10, 2, 9, 7, 5] var listResult = Array(testArray.reverse()) print(listResult)
"/605"7#.,*894*-
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%'=#5) !%+#/2! For ner control, the Strideable #%")"A"8 A23 04 2##8&4:; 76 )(4 32?4 &?#8&46J 6)%&:4 A23 04 used to produce specic results:
var numberList: Array = [8, 2, 10, 7, 5] //forward stride enumeration for index in 0.stride(through: numberList. endIndex - 1, by: 1) { print(numberList[index]) }
//forward stride enumeration - every two for index in 0.stride(through: numberList. endIndex - 1, by: 2) { print(numberList[index]) numberList[index] }
//reverse stride enumeration for index in (numberList.endIndex - 1). stride(through: 0, by: -1) { print(numberList[index]) }
While more verbose, this syntax provides good exibility. When applied, stride 288"B6 "34 )" 6=&# &)4?6 "% &)4%2)4 )(%"@'( 2 collection &3 %494%64 B&)( 2 A"36&6)43) >"%?2);
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1('!! B!O !%+01% <(4$ 2%4 2 >4B B2$6 %4A@%6&"3 A23 04 4C#%4664: &3 GB&>); O> $"@ 2%4 2AA@6)"?4: )" !R0264: 823R '@2'46J 23 &3)4%46)&3'J 23 &3)4%46)&3' :&>>4%43)&2)"% &6 ("B GB&>) (23:846 types; <" :2)4J ?23$ GB&>) objects are considered rst-class citizens including structs 23: enums; 76 6@A(J ?"6) "#4%2)&"36 3"%?288$ %464%94: >"% 2 class A23 04 %4#82A4: B&)( 2 structQ
//simple struct example - methods & properties struct Car { var color: String var make: String init(color:String, make: String) { self.color = color self.make = make } func buildCar() { print(“a \(color) \(make) has been built..”) } }
GB&>) structs 2%4 8&'()B4&'() A"?#"343)6 )(2) 2A) 26 928@4 )$#46; O3 A"3)%26)J classes &3 GB&>) 2%4 %4>4%43A4 )$#46 ; 54A2@64 struct &36)23A46 2%4 !"#$%& X3") %4>4%43A4:YJ )(4$ A23V) 04 @64: )" 0@&8: %4A@%6&94 :2)2 ?":486Q
//simple usable class class LLNode< T> { var key: T! var previous: LLNode! var next: LLNode! }
//gives compilation error struct Tree< T> { var key: T! var left: Tree! var right: Tree! }
$051%#*5! ]4A@%6&"3 A23 286" 04 6443 B&)( )(4 #"#@82% H&0"32AA& 64D@43A4J )(4 &:42 04(&3: 0@&8:&3' 2 3@R ?4%&A28 64D@43A4 0$ 2::&3' )(4 ) B" #%4A4:&3' 3@?04%6; a4)V6 A"?#2%4 2 )%2:&)&"328 23: %4A@%6&94 )4A(3&D@4Q
"/605"7#.,*894*-
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//fibonacci sequence - traditional approach func fibNormal(n: Int) -> Array! { //check trivial condition guard n > 2 else { return nil } //initialize the sequence var sequence: Array< Int> = [0, 1] var i: Int = sequence.count
while i != n { let results: Int = sequence[i - 1] + sequence[i - 2] sequence.append(results) i += 1 } return sequence }
//fibonacci sequence - recursive approach func fibRecursive(n:Int, sequence: Array = [0, 1]) { //check trivial condition guard n > 2 else { return } //mutated copy var output = sequence let i: Int = output.count //set base condition if i == n { return } let results: Int = output[i - 1] + output[i - 2] output.append(results) //set iteration fibRecursive(n, sequence: output) }
Note the function differences. At rst glance, we see fibRecursive 4?#8"$6 2 '()%*!()% 23: 2 A288 )" "34V6 self; <" A"3)%26)J fibNormal ?2&3)2&36 A"3)%"8 8"'&A &3 2 while-loop; 76 6("B3J %4R A@%6&94 8"'&A ">)43 842:6 )" &3A%4264: A"?#84C&)$J 26 23 43)&%4 A8266J >@3A)&"3 "% ?4)(": &6 ">)43 @64: 26 2 !"+,-". ),-0!,0-% ;
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1('!!2! While recursion tends to add complexity, consider the algorithm for depth-rst search. As discussed &3 2 #%49&"@6 4662$J )(&6 A":4 B"%=6 &3 A"3N@3A)&"3 B&)( )(4 A288 6)2A= )" )%294%64 2 '$+(-1 )%(-!2 ,-%%; 1(&84 &) B"@8: 04 #"66&084 )" %4>2A)"% )(4 28'"%&)(? )" 6@##"%) 23 &)4%2)&94 )4A(3&D@4J %4A@%6&"3 #%"9&:46 23 4>>4A)&94 6"8@)&"3Q
//recursive depth-first search func traverse() { guard self.key !=nil else { return } //process left side if self.left != nil { left?. traverse() } print(“...node \(self.key!) visited..”) //process the right side if self.right != nil { right?. traverse() } }
250-! a&=4 structs, many Swift objects act as rst-class citizens, including %+03%-(,$"+) ; a&=4 enums @64: &3 ")(4% 823'@2'46J )(4 43@? )$#4 Algorithm &6 @64: )" ?":48 04(29&"%; <(4 ?":48 B&88 (48# manage four specic cases. The enum &6 62&: )" 04 -%!0-)$4% 04A2@64 &) A"3)2&36 266"A&2)4: 928@46 )(2) 2%4 286" "> )$#4 AlgorithmQ
//recursive enumeration indirect enum Algorithm { case Empty case Sequence(Array< Int>) case InsertionSort( Algorithm) case BubbleSort( Algorithm) }
"/605"7#.,*894*-
]4A@%6&"3 Z34 '"28 "> enums &6 )" 43(23A4 A":4 %42:20&8&)$; O3 "@% A264J B4 A23 @64 Algorithm )" #%"9&:4 )$#4R62>4)$ 6@##"%) >"% 23 &?#84?43)2)&"3 23: A23 426&8$ 4C)43: &) )" 6@##"% ) 2::&)&"328 6A432%&R "6Q
//build an algorithm model let numberList = Algorithm.Sequence([8, 2, 10, 9, 7, 5]) let result = Algorithm.InsertionSort(numberList) ...
!!("
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