diff --git a/codes/swift/.gitignore b/codes/swift/.gitignore new file mode 100644 index 000000000..6295af4cc --- /dev/null +++ b/codes/swift/.gitignore @@ -0,0 +1,130 @@ +# Created by https://www.toptal.com/developers/gitignore/api/objective-c,swift,swiftpackagemanager +# Edit at https://www.toptal.com/developers/gitignore?templates=objective-c,swift,swiftpackagemanager + +### Objective-C ### +# Xcode +# +# gitignore contributors: remember to update Global/Xcode.gitignore, Objective-C.gitignore & Swift.gitignore + +## User settings +xcuserdata/ + +## compatibility with Xcode 8 and earlier (ignoring not required starting Xcode 9) +*.xcscmblueprint +*.xccheckout + +## compatibility with Xcode 3 and earlier (ignoring not required starting Xcode 4) +build/ +DerivedData/ +*.moved-aside +*.pbxuser +!default.pbxuser +*.mode1v3 +!default.mode1v3 +*.mode2v3 +!default.mode2v3 +*.perspectivev3 +!default.perspectivev3 + +## Obj-C/Swift specific +*.hmap + +## App packaging +*.ipa +*.dSYM.zip +*.dSYM + +# CocoaPods +# We recommend against adding the Pods directory to your .gitignore. However +# you should judge for yourself, the pros and cons are mentioned at: +# https://guides.cocoapods.org/using/using-cocoapods.html#should-i-check-the-pods-directory-into-source-control +# Pods/ +# Add this line if you want to avoid checking in source code from the Xcode workspace +# *.xcworkspace + +# Carthage +# Add this line if you want to avoid checking in source code from Carthage dependencies. +# Carthage/Checkouts + +Carthage/Build/ + +# fastlane +# It is recommended to not store the screenshots in the git repo. +# Instead, use fastlane to re-generate the screenshots whenever they are needed. +# For more information about the recommended setup visit: +# https://docs.fastlane.tools/best-practices/source-control/#source-control + +fastlane/report.xml +fastlane/Preview.html +fastlane/screenshots/**/*.png +fastlane/test_output + +# Code Injection +# After new code Injection tools there's a generated folder /iOSInjectionProject +# https://github.com/johnno1962/injectionforxcode + +iOSInjectionProject/ + +### Objective-C Patch ### + +### Swift ### +# Xcode +# gitignore contributors: remember to update Global/Xcode.gitignore, Objective-C.gitignore & Swift.gitignore + + + + + + +## Playgrounds +timeline.xctimeline +playground.xcworkspace + +# Swift Package Manager +# Add this line if you want to avoid checking in source code from Swift Package Manager dependencies. +# Packages/ +# Package.pins +# Package.resolved +# *.xcodeproj +# Xcode automatically generates this directory with a .xcworkspacedata file and xcuserdata +# hence it is not needed unless you have added a package configuration file to your project +# .swiftpm + +.build/ + +# CocoaPods +# We recommend against adding the Pods directory to your .gitignore. However +# you should judge for yourself, the pros and cons are mentioned at: +# https://guides.cocoapods.org/using/using-cocoapods.html#should-i-check-the-pods-directory-into-source-control +# Pods/ +# Add this line if you want to avoid checking in source code from the Xcode workspace +# *.xcworkspace + +# Carthage +# Add this line if you want to avoid checking in source code from Carthage dependencies. +# Carthage/Checkouts + + +# Accio dependency management +Dependencies/ +.accio/ + +# fastlane +# It is recommended to not store the screenshots in the git repo. +# Instead, use fastlane to re-generate the screenshots whenever they are needed. +# For more information about the recommended setup visit: +# https://docs.fastlane.tools/best-practices/source-control/#source-control + + +# Code Injection +# After new code Injection tools there's a generated folder /iOSInjectionProject +# https://github.com/johnno1962/injectionforxcode + + +### SwiftPackageManager ### +Packages +xcuserdata +*.xcodeproj + + +# End of https://www.toptal.com/developers/gitignore/api/objective-c,swift,swiftpackagemanager diff --git a/codes/swift/Package.swift b/codes/swift/Package.swift new file mode 100644 index 000000000..250c09af1 --- /dev/null +++ b/codes/swift/Package.swift @@ -0,0 +1,18 @@ +// swift-tools-version: 5.7 + +import PackageDescription + +let package = Package( + name: "HelloAlgo", + products: [ + .executable(name: "time_complexity", targets: ["time_complexity"]), + .executable(name: "worst_best_time_complexity", targets: ["worst_best_time_complexity"]), + .executable(name: "space_complexity", targets: ["space_complexity"]), + ], + targets: [ + .target(name: "utils", path: "utils"), + .executableTarget(name: "time_complexity", path: "chapter_computational_complexity", sources: ["time_complexity.swift"]), + .executableTarget(name: "worst_best_time_complexity", path: "chapter_computational_complexity", sources: ["worst_best_time_complexity.swift"]), + .executableTarget(name: "space_complexity", dependencies: ["utils"], path: "chapter_computational_complexity", sources: ["space_complexity.swift"]), + ] +) diff --git a/codes/swift/chapter_computational_complexity/space_complexity.swift b/codes/swift/chapter_computational_complexity/space_complexity.swift new file mode 100644 index 000000000..4931597ca --- /dev/null +++ b/codes/swift/chapter_computational_complexity/space_complexity.swift @@ -0,0 +1,98 @@ +/* + * File: space_complexity.swift + * Created Time: 2023-01-01 + * Author: nuomi1 (nuomi1@qq.com) + */ + +import utils + +// 函数 +@discardableResult +func function() -> Int { + // do something + return 0 +} + +// 常数阶 +func constant(n: Int) { + // 常量、变量、对象占用 O(1) 空间 + let a = 0 + var b = 0 + let nums = Array(repeating: 0, count: 10000) + let node = ListNode(x: 0) + // 循环中的变量占用 O(1) 空间 + for _ in 0 ..< n { + let c = 0 + } + // 循环中的函数占用 O(1) 空间 + for _ in 0 ..< n { + function() + } +} + +// 线性阶 +func linear(n: Int) { + // 长度为 n 的数组占用 O(n) 空间 + let nums = Array(repeating: 0, count: n) + // 长度为 n 的列表占用 O(n) 空间 + let nodes = (0 ..< n).map { ListNode(x: $0) } + // 长度为 n 的哈希表占用 O(n) 空间 + let map = Dictionary(uniqueKeysWithValues: (0 ..< n).map { ($0, "\($0)") }) +} + +// 线性阶（递归实现） +func linearRecur(n: Int) { + print("递归 n = \(n)") + if n == 1 { + return + } + linearRecur(n: n - 1) +} + +// 平方阶 +func quadratic(n: Int) { + // 二维列表占用 O(n^2) 空间 + let numList = Array(repeating: Array(repeating: 0, count: n), count: n) +} + +// 平方阶（递归实现） +@discardableResult +func quadraticRecur(n: Int) -> Int { + if n <= 0 { + return 0 + } + // 数组 nums 长度为 n, n-1, ..., 2, 1 + let nums = Array(repeating: 0, count: n) + print("递归 n = \(n) 中的 nums 长度 = \(nums.count)") + return quadraticRecur(n: n - 1) +} + +// 指数阶（建立满二叉树） +func buildTree(n: Int) -> TreeNode? { + if n == 0 { + return nil + } + let root = TreeNode(x: 0) + root.left = buildTree(n: n - 1) + root.right = buildTree(n: n - 1) + return root +} + +@main +enum SpaceComplexity { + // Driver Code + static func main() { + let n = 5 + // 常数阶 + constant(n: n) + // 线性阶 + linear(n: n) + linearRecur(n: n) + // 平方阶 + quadratic(n: n) + quadraticRecur(n: n) + // 指数阶 + let root = buildTree(n: n) + PrintUtil.printTree(root: root) + } +} diff --git a/codes/swift/chapter_computational_complexity/time_complexity.swift b/codes/swift/chapter_computational_complexity/time_complexity.swift index 38bac4fae..322b4f09d 100644 --- a/codes/swift/chapter_computational_complexity/time_complexity.swift +++ b/codes/swift/chapter_computational_complexity/time_complexity.swift @@ -131,40 +131,41 @@ func factorialRecur(n: Int) -> Int { return count } -func main() { - // 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势 - let n = 8 - print("输入数据大小 n =", n) +@main +enum TimeComplexity { + static func main() { + // 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势 + let n = 8 + print("输入数据大小 n =", n) - var count = constant(n: n) - print("常数阶的计算操作数量 =", count) + var count = constant(n: n) + print("常数阶的计算操作数量 =", count) - count = linear(n: n) - print("线性阶的计算操作数量 =", count) - count = arrayTraversal(nums: Array(repeating: 0, count: n)) - print("线性阶（遍历数组）的计算操作数量 =", count) + count = linear(n: n) + print("线性阶的计算操作数量 =", count) + count = arrayTraversal(nums: Array(repeating: 0, count: n)) + print("线性阶（遍历数组）的计算操作数量 =", count) - count = quadratic(n: n) - print("平方阶的计算操作数量 =", count) - var nums = Array(sequence(first: n, next: { $0 > 0 ? $0 - 1 : nil })) // [n,n-1,...,2,1] - count = bubbleSort(nums: &nums) - print("平方阶（冒泡排序）的计算操作数量 =", count) + count = quadratic(n: n) + print("平方阶的计算操作数量 =", count) + var nums = Array(sequence(first: n, next: { $0 > 0 ? $0 - 1 : nil })) // [n,n-1,...,2,1] + count = bubbleSort(nums: &nums) + print("平方阶（冒泡排序）的计算操作数量 =", count) - count = exponential(n: n) - print("指数阶（循环实现）的计算操作数量 =", count) - count = expRecur(n: n) - print("指数阶（递归实现）的计算操作数量 =", count) + count = exponential(n: n) + print("指数阶（循环实现）的计算操作数量 =", count) + count = expRecur(n: n) + print("指数阶（递归实现）的计算操作数量 =", count) - count = logarithmic(n: n) - print("对数阶（循环实现）的计算操作数量 =", count) - count = logRecur(n: n) - print("对数阶（递归实现）的计算操作数量 =", count) + count = logarithmic(n: n) + print("对数阶（循环实现）的计算操作数量 =", count) + count = logRecur(n: n) + print("对数阶（递归实现）的计算操作数量 =", count) - count = linearLogRecur(n: Double(n)) - print("线性对数阶（递归实现）的计算操作数量 =", count) + count = linearLogRecur(n: Double(n)) + print("线性对数阶（递归实现）的计算操作数量 =", count) - count = factorialRecur(n: n) - print("阶乘阶（递归实现）的计算操作数量 =", count) + count = factorialRecur(n: n) + print("阶乘阶（递归实现）的计算操作数量 =", count) + } } - -main() diff --git a/codes/swift/chapter_computational_complexity/worst_best_time_complexity.swift b/codes/swift/chapter_computational_complexity/worst_best_time_complexity.swift index 73db6954d..4fa2cf2a0 100644 --- a/codes/swift/chapter_computational_complexity/worst_best_time_complexity.swift +++ b/codes/swift/chapter_computational_complexity/worst_best_time_complexity.swift @@ -23,15 +23,16 @@ func findOne(nums: [Int]) -> Int { return -1 } -// Driver Code -func main() { - for _ in 0 ..< 10 { - let n = 100 - let nums = randomNumbers(n: n) - let index = findOne(nums: nums) - print("数组 [ 1, 2, ..., n ] 被打乱后 =", nums) - print("数字 1 的索引为", index) +@main +enum WorstBestTimeComplexity { + // Driver Code + static func main() { + for _ in 0 ..< 10 { + let n = 100 + let nums = randomNumbers(n: n) + let index = findOne(nums: nums) + print("数组 [ 1, 2, ..., n ] 被打乱后 =", nums) + print("数字 1 的索引为", index) + } } } - -main() diff --git a/codes/swift/utils/ListNode.swift b/codes/swift/utils/ListNode.swift new file mode 100644 index 000000000..796ee5125 --- /dev/null +++ b/codes/swift/utils/ListNode.swift @@ -0,0 +1,14 @@ +/* + * File: ListNode.swift + * Created Time: 2023-01-02 + * Author: nuomi1 (nuomi1@qq.com) + */ + +public class ListNode { + public var val: Int // 结点值 + public var next: ListNode? // 后继结点引用 + + public init(x: Int) { + val = x + } +} diff --git a/codes/swift/utils/PrintUtil.swift b/codes/swift/utils/PrintUtil.swift new file mode 100644 index 000000000..3f3fc2688 --- /dev/null +++ b/codes/swift/utils/PrintUtil.swift @@ -0,0 +1,61 @@ +/* + * File: PrintUtil.swift + * Created Time: 2023-01-02 + * Author: nuomi1 (nuomi1@qq.com) + */ + +public enum PrintUtil { + private class Trunk { + var prev: Trunk? + var str: String + + init(prev: Trunk?, str: String) { + self.prev = prev + self.str = str + } + } + + public static func printTree(root: TreeNode?) { + printTree(root: root, prev: nil, isLeft: false) + } + + private static func printTree(root: TreeNode?, prev: Trunk?, isLeft: Bool) { + if root == nil { + return + } + + var prevStr = " " + let trunk = Trunk(prev: prev, str: prevStr) + + printTree(root: root?.right, prev: trunk, isLeft: true) + + if prev == nil { + trunk.str = "———" + } else if isLeft { + trunk.str = "/———" + prevStr = " |" + } else { + trunk.str = "\\———" + prev?.str = prevStr + } + + showTrunks(p: trunk) + print(" \(root!.val)") + + if prev != nil { + prev?.str = prevStr + } + trunk.str = " |" + + printTree(root: root?.left, prev: trunk, isLeft: false) + } + + private static func showTrunks(p: Trunk?) { + if p == nil { + return + } + + showTrunks(p: p?.prev) + print(p!.str, terminator: "") + } +} diff --git a/codes/swift/utils/TreeNode.swift b/codes/swift/utils/TreeNode.swift new file mode 100644 index 000000000..b6ce30575 --- /dev/null +++ b/codes/swift/utils/TreeNode.swift @@ -0,0 +1,17 @@ +/* + * File: TreeNode.swift + * Created Time: 2023-01-02 + * Author: nuomi1 (nuomi1@qq.com) + */ + +public class TreeNode { + public var val: Int // 结点值 + public var height: Int // 结点高度 + public var left: TreeNode? // 左子结点引用 + public var right: TreeNode? // 右子结点引用 + + public init(x: Int) { + val = x + height = 0 + } +} diff --git a/docs/chapter_computational_complexity/space_complexity.md b/docs/chapter_computational_complexity/space_complexity.md index 4c0d2d1bf..1d561792b 100644 --- a/docs/chapter_computational_complexity/space_complexity.md +++ b/docs/chapter_computational_complexity/space_complexity.md @@ -174,6 +174,34 @@ comments: true } ``` +=== "Swift" + + ```swift title="" + // 类 + class Node { + var val: Int + var next: Node? + + init(x: Int) { + val = x + } + } + + // 函数 + func function() -> Int { + // do something... + return 0 + } + + func algorithm(n: Int) -> Int { // 输入数据 + let a = 0 // 暂存数据（常量） + var b = 0 // 暂存数据（变量） + let node = Node(x: 0) // 暂存数据（对象） + let c = function() // 栈帧空间（调用函数） + return a + b + c // 输出数据 + } + ``` + ## 推算方法 空间复杂度的推算方法和时间复杂度总体类似，只是从统计“计算操作数量”变为统计“使用空间大小”。与时间复杂度不同的是，**我们一般只关注「最差空间复杂度」**。这是因为内存空间是一个硬性要求，我们必须保证在所有输入数据下都有足够的内存空间预留。 @@ -261,6 +289,18 @@ comments: true } ``` +=== "Swift" + + ```swift title="" + func algorithm(n: Int) { + let a = 0 // O(1) + let b = Array(repeating: 0, count: 10000) // O(1) + if n > 10 { + let nums = Array(repeating: 0, count: n) // O(n) + } + } + ``` + **在递归函数中，需要注意统计栈帧空间。** 例如函数 `loop()`，在循环中调用了 $n$ 次 `function()` ，每轮中的 `function()` 都返回并释放了栈帧空间，因此空间复杂度仍为 $O(1)$ 。而递归函数 `recur()` 在运行中会同时存在 $n$ 个未返回的 `recur()` ，从而使用 $O(n)$ 的栈帧空间。 === "Java" @@ -387,6 +427,31 @@ comments: true } ``` +=== "Swift" + + ```swift title="" + @discardableResult + func function() -> Int { + // do something + return 0 + } + + // 循环 O(1) + func loop(n: Int) { + for _ in 0 ..< n { + function() + } + } + + // 递归 O(n) + func recur(n: Int) { + if n == 1 { + return + } + recur(n: n - 1) + } + ``` + ## 常见类型 设输入数据大小为 $n$ ，常见的空间复杂度类型有（从低到高排列） @@ -536,6 +601,27 @@ $$ } ``` +=== "Swift" + + ```swift title="space_complexity.swift" + // 常数阶 + func constant(n: Int) { + // 常量、变量、对象占用 O(1) 空间 + let a = 0 + var b = 0 + let nums = Array(repeating: 0, count: 10000) + let node = ListNode(x: 0) + // 循环中的变量占用 O(1) 空间 + for _ in 0 ..< n { + let c = 0 + } + // 循环中的函数占用 O(1) 空间 + for _ in 0 ..< n { + function() + } + } + ``` + ### 线性阶 $O(n)$ 线性阶常见于元素数量与 $n$ 成正比的数组、链表、栈、队列等。 @@ -654,6 +740,20 @@ $$ } ``` +=== "Swift" + + ```swift title="space_complexity.swift" + // 线性阶 + func linear(n: Int) { + // 长度为 n 的数组占用 O(n) 空间 + let nums = Array(repeating: 0, count: n) + // 长度为 n 的列表占用 O(n) 空间 + let nodes = (0 ..< n).map { ListNode(x: $0) } + // 长度为 n 的哈希表占用 O(n) 空间 + let map = Dictionary(uniqueKeysWithValues: (0 ..< n).map { ($0, "\($0)") }) + } + ``` + 以下递归函数会同时存在 $n$ 个未返回的 `algorithm()` 函数，使用 $O(n)$ 大小的栈帧空间。 === "Java" @@ -731,6 +831,19 @@ $$ } ``` +=== "Swift" + + ```swift title="space_complexity.swift" + // 线性阶（递归实现） + func linearRecur(n: Int) { + print("递归 n = \(n)") + if n == 1 { + return + } + linearRecur(n: n - 1) + } + ``` + ![space_complexity_recursive_linear](space_complexity.assets/space_complexity_recursive_linear.png)

Fig. 递归函数产生的线性阶空间复杂度

@@ -838,6 +951,16 @@ $$ ``` +=== "Swift" + + ```swift title="space_complexity.swift" + // 平方阶 + func quadratic(n: Int) { + // 二维列表占用 O(n^2) 空间 + let numList = Array(repeating: Array(repeating: 0, count: n), count: n) + } + ``` + 在以下递归函数中，同时存在 $n$ 个未返回的 `algorithm()` ，并且每个函数中都初始化了一个数组，长度分别为 $n, n-1, n-2, ..., 2, 1$ ，平均长度为 $\frac{n}{2}$ ，因此总体使用 $O(n^2)$ 空间。 === "Java" @@ -921,6 +1044,20 @@ $$ ``` +=== "Swift" + + ```swift title="space_complexity.swift" + // 平方阶（递归实现） + func quadraticRecur(n: Int) -> Int { + if n <= 0 { + return 0 + } + // 数组 nums 长度为 n, n-1, ..., 2, 1 + let nums = Array(repeating: 0, count: n) + return quadraticRecur(n: n - 1) + } + ``` + ![space_complexity_recursive_quadratic](space_complexity.assets/space_complexity_recursive_quadratic.png)

Fig. 递归函数产生的平方阶空间复杂度

@@ -1014,6 +1151,21 @@ $$ } ``` +=== "Swift" + + ```swift title="space_complexity.swift" + // 指数阶（建立满二叉树） + func buildTree(n: Int) -> TreeNode? { + if n == 0 { + return nil + } + let root = TreeNode(x: 0) + root.left = buildTree(n: n - 1) + root.right = buildTree(n: n - 1) + return root + } + ``` + ![space_complexity_exponential](space_complexity.assets/space_complexity_exponential.png)

Fig. 满二叉树下的指数阶空间复杂度