|
| 1 | + |
| 2 | + |
| 3 | +## Welcome to Algorithm |
| 4 | + |
| 5 | +Explore a world of data structures in Swift. Learn how to use data structures to organize, analyze, and manipulate data. |
| 6 | + |
| 7 | +## A Tour |
| 8 | + |
| 9 | +* [Probability](#probability) |
| 10 | +* [DoublyLinkedList](#doublylinkedlist) |
| 11 | +* [Stack](#stack) |
| 12 | +* [Queue](#queue) |
| 13 | +* [Deque](#deque) |
| 14 | +* [RedBlackTree](#redblacktree) |
| 15 | +* [SortedSet](#sortedset) |
| 16 | +* [SortedMultiSet](#sortedmultiset) |
| 17 | +* [SortedDictionary](#sorteddictionary) |
| 18 | +* [SortedMultiDictionary](#sortedmultidictionary) |
| 19 | + |
| 20 | +<a name="probability"></a> |
| 21 | +## Probability |
| 22 | + |
| 23 | +Probability is a core feature. Your application may be completely catered to your users' habits and usage. To demonstrate this wonderful feature, let's look at some examples: |
| 24 | + |
| 25 | +Determining the probability of rolling a 3 using a die of 6 numbers. |
| 26 | + |
| 27 | +```swift |
| 28 | +let die: Array<Int> = Array<Int>(arrayLiteral: 1, 2, 3, 4, 5, 6) |
| 29 | +print(die.probabilityOf(3)) // Output: 0.166666666666667 |
| 30 | +``` |
| 31 | + |
| 32 | +The expected value of rolling a 3 or 6 with 100 trials using a die of 6 numbers. |
| 33 | + |
| 34 | +```swift |
| 35 | +let die: Array<Int> = Array<Int>(arrayLiteral: 1, 2, 3, 4, 5, 6) |
| 36 | +print(die.expectedValueOf(100, elements: 3, 6)) // Output: 33.3333333333333 |
| 37 | +``` |
| 38 | + |
| 39 | +The above examples are quite simple. They use basic calculations to determine the probability of an outcome (X). What if you have a complicated condition? To solve this problem, it is possible to pass in blocks that return a boolean value. Each block may execute any operations it pleases, so long as it returns a "true" or "false". The "true" values contribute to the likelihood of an outcome, "false" results do not. Below is an example to demonstrate this feature. |
| 40 | + |
| 41 | +```swift |
| 42 | +let die: Array<Int> = Array<Int>(arrayLiteral: 1, 2, 3, 4, 5, 6) |
| 43 | + |
| 44 | +let probabilityOfX: Double = purchased.probabilityOf { (number: Int) in |
| 45 | + if 1 < number && 0 == number % 3 { |
| 46 | + // Do more. |
| 47 | + return true |
| 48 | + } |
| 49 | + return false |
| 50 | +} |
| 51 | + |
| 52 | +if 33.33 < probabilityOfX { |
| 53 | + // Do something. |
| 54 | +} |
| 55 | +``` |
| 56 | + |
| 57 | +<a name="doublylinkedlist"></a> |
| 58 | +## DoublyLinkedList |
| 59 | + |
| 60 | +The DoublyLinkedList data structure is excellent for large growing collections of data. Below is an example of its usage. |
| 61 | + |
| 62 | +```swift |
| 63 | +let listA: DoublyLinkedList<Int> = DoublyLinkedList<Int>() |
| 64 | +listA.insertAtFront(3) |
| 65 | +listA.insertAtFront(2) |
| 66 | +listA.insertAtFront(1) |
| 67 | + |
| 68 | +let listB: DoublyLinkedList<Int> = DoublyLinkedList<Int>() |
| 69 | +listB.insertAtBack(4) |
| 70 | +listB.insertAtBack(5) |
| 71 | +listB.insertAtBack(6) |
| 72 | + |
| 73 | +let listC: DoublyLinkedList<Int> = listA + listB |
| 74 | + |
| 75 | +listC.cursorToFront() |
| 76 | +repeat { |
| 77 | + print(listC.cursor) |
| 78 | +} while nil != listC.next |
| 79 | +// Output: |
| 80 | +// 1 |
| 81 | +// 2 |
| 82 | +// 3 |
| 83 | +// 4 |
| 84 | +// 5 |
| 85 | +// 6 |
| 86 | +``` |
| 87 | + |
| 88 | +<a name="stack"></a> |
| 89 | +## Stack |
| 90 | + |
| 91 | +The Stack data structure is a container of objects that are inserted and removed according to the last-in-first-out (LIFO) principle. Below is an example of its usage. |
| 92 | + |
| 93 | +```swift |
| 94 | +let stack: Stack<Int> = Stack<Int>() |
| 95 | +stack.push(1) |
| 96 | +stack.push(2) |
| 97 | +stack.push(3) |
| 98 | + |
| 99 | +while !stack.isEmpty { |
| 100 | + print(stack.pop()) |
| 101 | +} |
| 102 | +// Output: |
| 103 | +// 3 |
| 104 | +// 2 |
| 105 | +// 1 |
| 106 | +``` |
| 107 | + |
| 108 | +<a name="queue"></a> |
| 109 | +## Queue |
| 110 | + |
| 111 | +The Queue data structure is a container of objects that are inserted and removed according to the first-in-first-out (FIFO) principle. Below is an example of its usage. |
| 112 | + |
| 113 | +```swift |
| 114 | +let queue: Queue<Int> = Queue<Int>() |
| 115 | +queue.enqueue(1) |
| 116 | +queue.enqueue(2) |
| 117 | +queue.enqueue(3) |
| 118 | + |
| 119 | +while !queue.isEmpty { |
| 120 | + print(queue.dequeue()) |
| 121 | +} |
| 122 | +// Output: |
| 123 | +// 1 |
| 124 | +// 2 |
| 125 | +// 3 |
| 126 | +``` |
| 127 | + |
| 128 | +<a name="deque"></a> |
| 129 | +## Deque |
| 130 | + |
| 131 | +The Deque data structure is a container of objects that are inserted and removed according to the first-in-first-out (FIFO) and last-in-first-out (LIFO) principle. Essentially, a Deque is a Stack and Queue combined. Below are examples of its usage. |
| 132 | + |
| 133 | +```swift |
| 134 | +let dequeA: Deque<Int> = Deque<Int>() |
| 135 | +dequeA.insertAtBack(1) |
| 136 | +dequeA.insertAtBack(2) |
| 137 | +dequeA.insertAtBack(3) |
| 138 | + |
| 139 | +while !dequeA.isEmpty { |
| 140 | + print(dequeA.removeAtFront()) |
| 141 | +} |
| 142 | +// Output: |
| 143 | +// 1 |
| 144 | +// 2 |
| 145 | +// 3 |
| 146 | + |
| 147 | +let dequeB: Deque<Int> = Deque<Int>() |
| 148 | +dequeB.insertAtBack(4) |
| 149 | +dequeB.insertAtBack(5) |
| 150 | +dequeB.insertAtBack(6) |
| 151 | + |
| 152 | +while !dequeB.isEmpty { |
| 153 | + print(dequeB.removeAtBack()) |
| 154 | +} |
| 155 | +// Output: |
| 156 | +// 6 |
| 157 | +// 5 |
| 158 | +// 4 |
| 159 | +``` |
| 160 | + |
| 161 | +<a name="redblacktree"></a> |
| 162 | +## RedBlackTree |
| 163 | + |
| 164 | +A RedBlackTree is a Balanced Binary Search Tree that maintains insert, remove, update, and search operations in a complexity of O(logn). The following implementation of a RedBlackTree also includes an order-statistic, which allows the data structure to be accessed using subscripts like an array or dictionary. RedBlackTrees may store unique keys or non-unique key values. Below is an example of its usage. |
| 165 | + |
| 166 | +```swift |
| 167 | +let rbA: RedBlackTree<Int, Int> = RedBlackTree<Int, Int>(uniqueKeys: true) |
| 168 | + |
| 169 | +for var i: Int = 1000; 0 < i; --i { |
| 170 | + rbA.insert(1, value: 1) |
| 171 | + rbA.insert(2, value: 2) |
| 172 | + rbA.insert(3, value: 3) |
| 173 | +} |
| 174 | +print(rbA.count) // Output: 3 |
| 175 | +``` |
| 176 | + |
| 177 | +<a name="sortedset"></a> |
| 178 | +## SortedSet |
| 179 | + |
| 180 | +SortedSets are a powerful data structure for algorithm and analysis design. Elements within a SortedSet are unique and insert, remove, and search operations have a complexity of O(logn). The following implementation of a SortedSet also includes an order-statistic, which allows the data structure to be accessed using an index subscript like an array. Below are examples of its usage. |
| 181 | + |
| 182 | +```swift |
| 183 | +let setA: SortedSet<Int> = SortedSet<Int>(elements: 1, 2, 3) // Sorted: [1, 2, 3] |
| 184 | +let setB: SortedSet<Int> = SortedSet<Int>(elements: 4, 3, 6) // Sorted: [3, 4, 6] |
| 185 | + |
| 186 | +let setC: SortedSet<Int> = SortedSet<Int>(elements: 7, 1, 2) // Sorted: [1, 2, 7] |
| 187 | +let setD: SortedSet<Int> = SortedSet<Int>(elements: 1, 7) // Sorted: [1, 7] |
| 188 | + |
| 189 | +let setE: SortedSet<Int> = SortedSet<Int>(elements: 1, 6, 7) // Sorted: [1, 6, 7] |
| 190 | + |
| 191 | +// Union. |
| 192 | +print((setA + setB).count) // Output: 5 |
| 193 | +print(setA.union(setB).count) // Output: 5 |
| 194 | + |
| 195 | +// Intersect. |
| 196 | +print(setC.intersect(setD).count) // Output: 2 |
| 197 | + |
| 198 | +// Subset. |
| 199 | +print(setD < setC) // true |
| 200 | +print(setD.isSubsetOf(setC)) // true |
| 201 | + |
| 202 | +// Superset. |
| 203 | +print(setD > setC) // false |
| 204 | +print(setD.isSupersetOf(setC)) // false |
| 205 | + |
| 206 | +// Contains. |
| 207 | +print(setE.contains(setA.first!)) // true |
| 208 | + |
| 209 | +// Probability. |
| 210 | +print(setE.probabilityOf(setA.first!, setA.last!)) // 0.333333333333333 |
| 211 | +``` |
| 212 | + |
| 213 | +<a name="sortedmultiset"></a> |
| 214 | +## SortedMultiSet |
| 215 | + |
| 216 | +A SortedMultiSet is identical to a SortedSet, except that a SortedMultiSet allows non-unique elements. Look at [SortedSet](#sortedset) for examples of its usage. |
| 217 | + |
| 218 | +<a name="sorteddictionary"></a> |
| 219 | +## SortedDictionary |
| 220 | + |
| 221 | +A SortedDictionary is a powerful data structure that maintains a sorted set of keys with value pairs. Keys within a SortedDictionary are unique and insert, remove, update, and search operations have a complexity of O(logn). |
| 222 | + |
| 223 | +<a name="sortedmultidictionary"></a> |
| 224 | +## SortedMultiDictionary |
| 225 | + |
| 226 | +A SortedMultiDictionary is identical to a SortedDictionary, except that a SortedMultiDictionary allows non-unique keys. Below is an example of its usage. |
| 227 | + |
| 228 | +```swift |
| 229 | +struct Student { |
| 230 | + var name: String |
| 231 | +} |
| 232 | + |
| 233 | +let dict: SortedMultiDictionary<String, Student> = SortedMultiDictionary<String, Student>() |
| 234 | + |
| 235 | +// Do something with an alphabetically SortedMultiDictionary of Student structs. |
| 236 | +for student in students { |
| 237 | + dict.insert(student.name, value: student) |
| 238 | +} |
| 239 | +``` |
| 240 | + |
| 241 | +## License |
| 242 | + |
| 243 | +Copyright (C) 2015 - 2016, Daniel Dahan and CosmicMind, Inc. <http://cosmicmind.io>. All rights reserved. |
| 244 | + |
| 245 | +Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: |
| 246 | + |
| 247 | +* Redistributions of source code must retain the above copyright notice, this |
| 248 | + list of conditions and the following disclaimer. |
| 249 | + |
| 250 | +* Redistributions in binary form must reproduce the above copyright notice, |
| 251 | + this list of conditions and the following disclaimer in the documentation |
| 252 | + and/or other materials provided with the distribution. |
| 253 | + |
| 254 | +* Neither the name of Algorithm nor the names of its |
| 255 | + contributors may be used to endorse or promote products derived from |
| 256 | + this software without specific prior written permission. |
| 257 | + |
| 258 | +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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