Merge pull request #197 from nuomi1/feature/space_complexity-Swift

feat: add Swift codes for space complexity article

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

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"]),
+    ]
+)

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)
+    }
+}

codes/swift/chapter_computational_complexity/time_complexity.swift

@@ -131,7 +131,9 @@ func factorialRecur(n: Int) -> Int {
     return count
 }
 
-func main() {
+@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)
@@ -165,6 +167,5 @@ func main() {
 
         count = factorialRecur(n: n)
         print("阶乘阶（递归实现）的计算操作数量 =", count)
+    }
 }
-
-main()

codes/swift/chapter_computational_complexity/worst_best_time_complexity.swift

@@ -23,8 +23,10 @@ func findOne(nums: [Int]) -> Int {
     return -1
 }
 
-// Driver Code
-func main() {
+@main
+enum WorstBestTimeComplexity {
+    // Driver Code
+    static func main() {
         for _ in 0 ..< 10 {
             let n = 100
             let nums = randomNumbers(n: n)
@@ -32,6 +34,5 @@ func main() {
             print("数组 [ 1, 2, ..., n ] 被打乱后 =", nums)
             print("数字 1 的索引为", index)
         }
+    }
 }
-
-main()

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
+    }
+}

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: "")
+    }
+}

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
+    }
+}

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)
 
 <p align="center"> Fig. 递归函数产生的线性阶空间复杂度 </p>
@@ -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)
 
 <p align="center"> Fig. 递归函数产生的平方阶空间复杂度 </p>
@@ -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)
 
 <p align="center"> Fig. 满二叉树下的指数阶空间复杂度 </p>