From 306dc019ef3d2fd0b51af57c58cc337040adde3b Mon Sep 17 00:00:00 2001
From: curtishd <131777542+curtishd@users.noreply.github.com>
Date: Tue, 27 Feb 2024 17:04:57 +0800
Subject: [PATCH] Add Kotlin code for computational complexity (#1090)

* feat(kotlin):new kotlin support files

* fix(kotlin):

    reviewed the formatting, comments and so on.

* fix(kotlin): fix the indentation and format

* feat(kotlin): Add kotlin code for the backtraking chapter.

* fix(kotlin): fix incorrect output of preorder_traversal_iii_template.kt file

* fix(kotlin): simplify kotlin codes

* fix(kotlin): modify n_queens.kt for consistency.

* feat(kotlin): add kotlin code for computational complexity.

* fix(kotlin): remove iteration folder.

* fix(kotlin): remove n_queens.kt file out of folder.

* fix(kotlin): remove some folders.

* style(kotlin): modified two chapters.
---
 .../{n_queens => }/n_queens.kt                |   0
 .../{permutations_i => }/permutations_i.kt    |   0
 .../{permutations_ii => }/permutations_ii.kt  |   0
 .../preorder_traversal_i_compact.kt           |   0
 .../preorder_traversal_ii_compact.kt          |   0
 .../preorder_traversal_iii_compact.kt         |   0
 .../preorder_traversal_iii_template.kt        |   0
 .../{subset_sum_i => }/subset_sum_i.kt        |   0
 .../subset_sum_i_naive.kt                     |   0
 .../{subset_sum_ii => }/subset_sum_ii.kt      |   0
 .../iteration.kt                              |  74 ++++++++
 .../recursion.kt                              |  76 ++++++++
 .../space_complexity.kt                       | 109 ++++++++++++
 .../time_complexity.kt                        | 166 ++++++++++++++++++
 .../worst_best_time_complexity.kt             |  47 +++++
 15 files changed, 472 insertions(+)
 rename codes/kotlin/chapter_backtracking/{n_queens => }/n_queens.kt (100%)
 rename codes/kotlin/chapter_backtracking/{permutations_i => }/permutations_i.kt (100%)
 rename codes/kotlin/chapter_backtracking/{permutations_ii => }/permutations_ii.kt (100%)
 rename codes/kotlin/chapter_backtracking/{preorder_traversal_i_compact => }/preorder_traversal_i_compact.kt (100%)
 rename codes/kotlin/chapter_backtracking/{preorder_traversal_ii_compact => }/preorder_traversal_ii_compact.kt (100%)
 rename codes/kotlin/chapter_backtracking/{preorder_traversal_iii_compact => }/preorder_traversal_iii_compact.kt (100%)
 rename codes/kotlin/chapter_backtracking/{preorder_traversal_iii_template => }/preorder_traversal_iii_template.kt (100%)
 rename codes/kotlin/chapter_backtracking/{subset_sum_i => }/subset_sum_i.kt (100%)
 rename codes/kotlin/chapter_backtracking/{subset_sum_i_naive => }/subset_sum_i_naive.kt (100%)
 rename codes/kotlin/chapter_backtracking/{subset_sum_ii => }/subset_sum_ii.kt (100%)
 create mode 100644 codes/kotlin/chapter_computational_complexity/iteration.kt
 create mode 100644 codes/kotlin/chapter_computational_complexity/recursion.kt
 create mode 100644 codes/kotlin/chapter_computational_complexity/space_complexity.kt
 create mode 100644 codes/kotlin/chapter_computational_complexity/time_complexity.kt
 create mode 100644 codes/kotlin/chapter_computational_complexity/worst_best_time_complexity.kt

diff --git a/codes/kotlin/chapter_backtracking/n_queens/n_queens.kt b/codes/kotlin/chapter_backtracking/n_queens.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/n_queens/n_queens.kt
rename to codes/kotlin/chapter_backtracking/n_queens.kt
diff --git a/codes/kotlin/chapter_backtracking/permutations_i/permutations_i.kt b/codes/kotlin/chapter_backtracking/permutations_i.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/permutations_i/permutations_i.kt
rename to codes/kotlin/chapter_backtracking/permutations_i.kt
diff --git a/codes/kotlin/chapter_backtracking/permutations_ii/permutations_ii.kt b/codes/kotlin/chapter_backtracking/permutations_ii.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/permutations_ii/permutations_ii.kt
rename to codes/kotlin/chapter_backtracking/permutations_ii.kt
diff --git a/codes/kotlin/chapter_backtracking/preorder_traversal_i_compact/preorder_traversal_i_compact.kt b/codes/kotlin/chapter_backtracking/preorder_traversal_i_compact.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/preorder_traversal_i_compact/preorder_traversal_i_compact.kt
rename to codes/kotlin/chapter_backtracking/preorder_traversal_i_compact.kt
diff --git a/codes/kotlin/chapter_backtracking/preorder_traversal_ii_compact/preorder_traversal_ii_compact.kt b/codes/kotlin/chapter_backtracking/preorder_traversal_ii_compact.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/preorder_traversal_ii_compact/preorder_traversal_ii_compact.kt
rename to codes/kotlin/chapter_backtracking/preorder_traversal_ii_compact.kt
diff --git a/codes/kotlin/chapter_backtracking/preorder_traversal_iii_compact/preorder_traversal_iii_compact.kt b/codes/kotlin/chapter_backtracking/preorder_traversal_iii_compact.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/preorder_traversal_iii_compact/preorder_traversal_iii_compact.kt
rename to codes/kotlin/chapter_backtracking/preorder_traversal_iii_compact.kt
diff --git a/codes/kotlin/chapter_backtracking/preorder_traversal_iii_template/preorder_traversal_iii_template.kt b/codes/kotlin/chapter_backtracking/preorder_traversal_iii_template.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/preorder_traversal_iii_template/preorder_traversal_iii_template.kt
rename to codes/kotlin/chapter_backtracking/preorder_traversal_iii_template.kt
diff --git a/codes/kotlin/chapter_backtracking/subset_sum_i/subset_sum_i.kt b/codes/kotlin/chapter_backtracking/subset_sum_i.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/subset_sum_i/subset_sum_i.kt
rename to codes/kotlin/chapter_backtracking/subset_sum_i.kt
diff --git a/codes/kotlin/chapter_backtracking/subset_sum_i_naive/subset_sum_i_naive.kt b/codes/kotlin/chapter_backtracking/subset_sum_i_naive.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/subset_sum_i_naive/subset_sum_i_naive.kt
rename to codes/kotlin/chapter_backtracking/subset_sum_i_naive.kt
diff --git a/codes/kotlin/chapter_backtracking/subset_sum_ii/subset_sum_ii.kt b/codes/kotlin/chapter_backtracking/subset_sum_ii.kt
similarity index 100%
rename from codes/kotlin/chapter_backtracking/subset_sum_ii/subset_sum_ii.kt
rename to codes/kotlin/chapter_backtracking/subset_sum_ii.kt
diff --git a/codes/kotlin/chapter_computational_complexity/iteration.kt b/codes/kotlin/chapter_computational_complexity/iteration.kt
new file mode 100644
index 000000000..b04a6182d
--- /dev/null
+++ b/codes/kotlin/chapter_computational_complexity/iteration.kt
@@ -0,0 +1,74 @@
+/**
+ * File: iteration.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_computational_complexity.iteration
+
+/* for 循环 */
+fun forLoop(n: Int): Int {
+    var res = 0
+    // 循环求和 1, 2, ..., n-1, n
+    for (i in 1..n) {
+        res += i
+    }
+    return res
+}
+
+/* while 循环 */
+fun whileLoop(n: Int): Int {
+    var res = 0
+    var i = 1 // 初始化条件变量
+    // 循环求和 1, 2, ..., n-1, n
+    while (i <= n) {
+        res += i
+        i++ // 更新条件变量
+    }
+    return res
+}
+
+/* while 循环（两次更新） */
+fun whileLoopII(n: Int): Int {
+    var res = 0
+    var i = 1 // 初始化条件变量
+    // 循环求和 1, 4, 10, ...
+    while (i <= n) {
+        res += i
+        // 更新条件变量
+        i++
+        i *= 2
+    }
+    return res
+}
+
+/* 双层 for 循环 */
+fun nestedForLoop(n: Int): String {
+    val res = StringBuilder()
+    // 循环 i = 1, 2, ..., n-1, n
+    for (i in 1..n) {
+        // 循环 j = 1, 2, ..., n-1, n
+        for (j in 1..n) {
+            res.append(" ($i, $j), ")
+        }
+    }
+    return res.toString()
+}
+
+/* Driver Code */
+fun main() {
+    val n = 5
+    var res: Int
+
+    res = forLoop(n)
+    println("\nfor 循环的求和结果 res = $res")
+
+    res = whileLoop(n)
+    println("\nwhile 循环的求和结果 res = $res")
+
+    res = whileLoopII(n)
+    println("\nwhile 循环 (两次更新) 求和结果 res = $res")
+
+    val resStr = nestedForLoop(n)
+    println("\n双层 for 循环的遍历结果 $resStr")
+}
\ No newline at end of file
diff --git a/codes/kotlin/chapter_computational_complexity/recursion.kt b/codes/kotlin/chapter_computational_complexity/recursion.kt
new file mode 100644
index 000000000..9de4253fb
--- /dev/null
+++ b/codes/kotlin/chapter_computational_complexity/recursion.kt
@@ -0,0 +1,76 @@
+/**
+ * File: recursion.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_computational_complexity.recursion
+
+import java.util.*
+
+/* 递归 */
+fun recur(n: Int): Int {
+    // 终止条件
+    if (n == 1)
+        return 1
+    // 递: 递归调用
+    val res = recur(n - 1)
+    // 归: 返回结果
+    return n + res
+}
+
+/* 使用迭代模拟递归 */
+fun forLoopRecur(n: Int): Int {
+    // 使用一个显式的栈来模拟系统调用栈
+    val stack = Stack<Int>()
+    var res = 0
+    // 递: 递归调用
+    for (i in n downTo 0) {
+        stack.push(i)
+    }
+    // 归: 返回结果
+    while (stack.isNotEmpty()) {
+        // 通过“出栈操作”模拟“归”
+        res += stack.pop()
+    }
+    // res = 1+2+3+...+n
+    return res
+}
+
+/* Kotlin tailrec 关键词使函数实现尾递归优化 */
+tailrec fun tailRecur(n: Int, res: Int): Int {
+    // 终止条件
+    if (n == 0)
+        return res
+    // 尾递归调用
+    return tailRecur(n - 1, res + n)
+}
+
+/* 斐波那契数列：递归 */
+fun fib(n: Int): Int {
+    // 终止条件 f(1) = 0, f(2) = 1
+    if (n == 1 || n == 2)
+        return n - 1
+    // 递归调用 f(n) = f(n-1) + f(n-2)
+    val res = fib(n - 1) + fib(n - 2)
+    // 返回结果 f(n)
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val n = 5
+    var res: Int
+
+    res = recur(n)
+    println("\n递归函数的求和结果 res = $res")
+
+    res = forLoopRecur(n)
+    println("\n使用迭代模拟递归求和结果 res = $res")
+
+    res = tailRecur(n, 0)
+    println("\n尾递归函数的求和结果 res = $res")
+
+    res = fib(n)
+    println("\n斐波那契数列的第 $n 项为 $res")
+}
\ No newline at end of file
diff --git a/codes/kotlin/chapter_computational_complexity/space_complexity.kt b/codes/kotlin/chapter_computational_complexity/space_complexity.kt
new file mode 100644
index 000000000..faa9f0ed7
--- /dev/null
+++ b/codes/kotlin/chapter_computational_complexity/space_complexity.kt
@@ -0,0 +1,109 @@
+/**
+ * File: space_complexity.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_computational_complexity.space_complexity
+
+import utils.ListNode
+import utils.TreeNode
+import utils.printTree
+
+/* 函数 */
+fun function(): Int {
+    // 执行某些操作
+    return 0
+}
+
+/* 常数阶 */
+fun constant(n: Int) {
+    // 常量、变量、对象占用 O(1) 空间
+    val a = 0
+    var b = 0
+    val nums = Array(10000) { 0 }
+    val node = ListNode(0)
+    // 循环中的变量占用 O(1) 空间
+    for (i in 0..<n) {
+        val c = 0
+    }
+    // 循环中的函数占用 O(1) 空间
+    for (i in 0..<n) {
+        function()
+    }
+}
+
+/* 线性阶 */
+fun linear(n: Int) {
+    // 长度为 n 的数组占用 O(n) 空间
+    val nums = Array(n) { 0 }
+    // 长度为 n 的列表占用 O(n) 空间
+    val nodes = mutableListOf<ListNode>()
+    for (i in 0..<n) {
+        nodes.add(ListNode(i))
+    }
+    // 长度为 n 的哈希表占用 O(n) 空间
+    val map = mutableMapOf<Int, String>()
+    for (i in 0..<n) {
+        map[i] = i.toString()
+    }
+}
+
+/* 线性阶（递归实现） */
+fun linearRecur(n: Int) {
+    println("递归 n = $n")
+    if (n == 1)
+        return
+    linearRecur(n - 1)
+}
+
+/* 平方阶 */
+fun quadratic(n: Int) {
+    // 矩阵占用 O(n^2) 空间
+    val numMatrix: Array<Array<Int>?> = arrayOfNulls(n)
+    // 二维列表占用 O(n^2) 空间
+    val numList: MutableList<MutableList<Int>> = arrayListOf()
+    for (i in 0..<n) {
+        val tmp = mutableListOf<Int>()
+        for (j in 0..<n) {
+            tmp.add(0)
+        }
+        numList.add(tmp)
+    }
+}
+
+/* 平方阶（递归实现） */
+tailrec fun quadraticRecur(n: Int): Int {
+    if (n <= 0)
+        return 0
+    // 数组 nums 长度为 n, n-1, ..., 2, 1
+    val nums = Array(n) { 0 }
+    println("递归 n = $n 中的 nums 长度 = ${nums.size}")
+    return quadraticRecur(n - 1)
+}
+
+/* 指数阶（建立满二叉树） */
+fun buildTree(n: Int): TreeNode? {
+    if (n == 0)
+        return null
+    val root = TreeNode(0)
+    root.left = buildTree(n - 1)
+    root.right = buildTree(n - 1)
+    return root
+}
+
+/* Driver Code */
+fun main() {
+    val n = 5
+    // 常数阶
+    constant(n)
+    // 线性阶
+    linear(n)
+    linearRecur(n)
+    // 平方阶
+    quadratic(n)
+    quadraticRecur(n)
+    // 指数阶
+    val root: TreeNode? = buildTree(n)
+    printTree(root)
+}
\ No newline at end of file
diff --git a/codes/kotlin/chapter_computational_complexity/time_complexity.kt b/codes/kotlin/chapter_computational_complexity/time_complexity.kt
new file mode 100644
index 000000000..485001408
--- /dev/null
+++ b/codes/kotlin/chapter_computational_complexity/time_complexity.kt
@@ -0,0 +1,166 @@
+/**
+ * File: time_complexity.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_computational_complexity.time_complexity
+
+/* 常数阶 */
+fun constant(n: Int): Int {
+    var count = 0
+    val size = 10_0000
+    for (i in 0..<size)
+        count++
+    return count
+}
+
+/* 线性阶 */
+fun linear(n: Int): Int {
+    var count = 0
+    // 循环次数与数组长度成正比
+    for (i in 0..<n)
+        count++
+    return count
+}
+
+/* 线性阶（遍历数组） */
+fun arrayTraversal(nums: IntArray): Int {
+    var count = 0
+    // 循环次数与数组长度成正比
+    for (num in nums) {
+        count++
+    }
+    return count
+}
+
+/* 平方阶 */
+fun quadratic(n: Int): Int {
+    var count = 0
+    // 循环次数与数组长度成平方关系
+    for (i in 0..<n) {
+        for (j in 0..<n) {
+            count++
+        }
+    }
+    return count
+}
+
+/* 平方阶（冒泡排序） */
+fun bubbleSort(nums: IntArray): Int {
+    var count = 0
+    // 外循环：未排序区间为 [0, i]
+    for (i in nums.size - 1 downTo 1) {
+        // 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端
+        for (j in 0..<i) {
+            if (nums[j] > nums[j + 1]) {
+                // 交换 nums[j] 与 nums[j + 1]
+                nums[j] = nums[j + 1].also { nums[j + 1] = nums[j] }
+                count += 3 // 元素交换包含 3 个单元操作
+            }
+        }
+    }
+    return count
+}
+
+/* 指数阶（循环实现） */
+fun exponential(n: Int): Int {
+    var count = 0
+    // 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+    var base = 1
+    for (i in 0..<n) {
+        for (j in 0..<base) {
+            count++
+        }
+        base *= 2
+    }
+    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+    return count
+}
+
+/* 指数阶（递归实现） */
+fun expRecur(n: Int): Int {
+    if (n == 1) {
+        return 1
+    }
+    return expRecur(n - 1) + expRecur(n - 1) + 1
+}
+
+/* 对数阶（循环实现） */
+fun logarithmic(n: Float): Int {
+    var n1 = n
+    var count = 0
+    while (n1 > 1) {
+        n1 /= 2
+        count++
+    }
+    return count
+}
+
+/* 对数阶（递归实现） */
+fun logRecur(n: Float): Int {
+    if (n <= 1)
+        return 0
+    return logRecur(n / 2) + 1
+}
+
+/* 线性对数阶 */
+fun linearLogRecur(n: Float): Int {
+    if (n <= 1)
+        return 1
+    var count = linearLogRecur(n / 2) + linearLogRecur(n / 2)
+    for (i in 0..<n.toInt()) {
+        count++
+    }
+    return count
+}
+
+/* 阶乘阶（递归实现） */
+fun factorialRecur(n: Int): Int {
+    if (n == 0)
+        return 1
+    var count = 0
+    // 从 1 个分裂出 n 个
+    for (i in 0..<n) {
+        count += factorialRecur(n - 1)
+    }
+    return count
+}
+
+/* Driver Code */
+fun 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
+    val n = 8
+    println("输入数据大小 n = $n")
+
+    var count: Int = constant(n)
+    println("常数阶的操作数量 = $count")
+
+    count = linear(n)
+    println("线性阶的操作数量 = $count")
+    count = arrayTraversal(IntArray(n))
+    println("线性阶（遍历数组）的操作数量 = $count")
+
+    count = quadratic(n)
+    println("平方阶的操作数量 = $count")
+    val nums = IntArray(n)
+    for (i in 0..<n) nums[i] = n - i // [n,n-1,...,2,1]
+    count = bubbleSort(nums)
+    println("平方阶（冒泡排序）的操作数量 = $count")
+
+    count = exponential(n)
+    println("指数阶（循环实现）的操作数量 = $count")
+    count = expRecur(n)
+    println("指数阶（递归实现）的操作数量 = $count")
+
+    count = logarithmic(n.toFloat())
+    println("对数阶（循环实现）的操作数量 = $count")
+    count = logRecur(n.toFloat())
+    println("对数阶（递归实现）的操作数量 = $count")
+
+    count = linearLogRecur(n.toFloat())
+    println("线性对数阶（递归实现）的操作数量 = $count")
+
+    count = factorialRecur(n)
+    println("阶乘阶（递归实现）的操作数量 = $count")
+}
\ No newline at end of file
diff --git a/codes/kotlin/chapter_computational_complexity/worst_best_time_complexity.kt b/codes/kotlin/chapter_computational_complexity/worst_best_time_complexity.kt
new file mode 100644
index 000000000..3263153a7
--- /dev/null
+++ b/codes/kotlin/chapter_computational_complexity/worst_best_time_complexity.kt
@@ -0,0 +1,47 @@
+/**
+ * File: worst_best_time_complexity.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_computational_complexity.worst_best_time_complexity
+
+/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
+fun randomNumbers(n: Int): Array<Int?> {
+    val nums = IntArray(n)
+    // 生成数组 nums = { 1, 2, 3, ..., n }
+    for (i in 0..<n) {
+        nums[i] = i + 1
+    }
+    // 随机打乱数组元素
+    val mutableList = nums.toMutableList()
+    mutableList.shuffle()
+    // Integer[] -> int[]
+    val res = arrayOfNulls<Int>(n)
+    for (i in 0..<n) {
+        res[i] = mutableList[i]
+    }
+    return res
+}
+
+/* 查找数组 nums 中数字 1 所在索引 */
+fun findOne(nums: Array<Int?>): Int {
+    for (i in nums.indices) {
+        // 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)
+        // 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)
+        if (nums[i] == 1)
+            return i
+    }
+    return -1
+}
+
+/* Driver Code */
+fun main() {
+    for (i in 0..9) {
+        val n = 100
+        val nums: Array<Int?> = randomNumbers(n)
+        val index: Int = findOne(nums)
+        println("\n数组 [ 1, 2, ..., n ] 被打乱后 = ${nums.contentToString()}")
+        println("数字 1 的索引为 $index")
+    }
+}
\ No newline at end of file