feat(kotlin): Add kotlin code for backtracking chapter (#1088)

* 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.

codes/kotlin/chapter_backtracking/n_queens/n_queens.kt

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+/**
+ * File: n_queens.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.n_queens
+
+/* 回溯算法：n 皇后 */
+fun backtrack(
+    row: Int,
+    n: Int,
+    state: List<MutableList<String>>,
+    res: MutableList<List<List<String>>?>,
+    cols: BooleanArray,
+    diags1: BooleanArray,
+    diags2: BooleanArray
+) {
+    // 当放置完所有行时，记录解
+    if (row == n) {
+        val copyState: MutableList<List<String>> = ArrayList()
+        for (sRow in state) {
+            copyState.add(ArrayList(sRow))
+        }
+        res.add(copyState)
+        return
+    }
+    // 遍历所有列
+    for (col in 0..<n) {
+        // 计算该格子对应的主对角线和次对角线
+        val diag1 = row - col + n - 1
+        val diag2 = row + col
+        // 剪枝：不允许该格子所在列、主对角线、次对角线上存在皇后
+        if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
+            // 尝试：将皇后放置在该格子
+            state[row][col] = "Q"
+            diags2[diag2] = true
+            diags1[diag1] = diags2[diag2]
+            cols[col] = diags1[diag1]
+            // 放置下一行
+            backtrack(row + 1, n, state, res, cols, diags1, diags2)
+            // 回退：将该格子恢复为空位
+            state[row][col] = "#"
+            diags2[diag2] = false
+            diags1[diag1] = diags2[diag2]
+            cols[col] = diags1[diag1]
+        }
+    }
+}
+
+/* 求解 n 皇后 */
+fun nQueens(n: Int): List<List<List<String>>?> {
+    // 初始化 n*n 大小的棋盘，其中 'Q' 代表皇后，'#' 代表空位
+    val state: MutableList<MutableList<String>> = ArrayList()
+    for (i in 0..<n) {
+        val row: MutableList<String> = ArrayList()
+        for (j in 0..<n) {
+            row.add("#")
+        }
+        state.add(row)
+    }
+    val cols = BooleanArray(n) // 记录列是否有皇后
+    val diags1 = BooleanArray(2 * n - 1) // 记录主对角线上是否有皇后
+    val diags2 = BooleanArray(2 * n - 1) // 记录次对角线上是否有皇后
+    val res: MutableList<List<List<String>>?> = ArrayList()
+
+    backtrack(0, n, state, res, cols, diags1, diags2)
+
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val n = 4
+    val res: List<List<List<String?>?>?> = nQueens(n)
+
+    println("输入棋盘长宽为 $n")
+    println("皇后放置方案共有 ${res.size} 种")
+    for (state in res) {
+        println("--------------------")
+        for (row in state!!) {
+            println(row)
+        }
+    }
+}

codes/kotlin/chapter_backtracking/permutations_i/permutations_i.kt

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+/**
+ * File: permutations_i.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.permutations_i
+
+/* 回溯算法：全排列 I */
+fun backtrack(
+    state: MutableList<Int>,
+    choices: IntArray,
+    selected: BooleanArray,
+    res: MutableList<List<Int>?>
+) {
+    // 当状态长度等于元素数量时，记录解
+    if (state.size == choices.size) {
+        res.add(ArrayList(state))
+        return
+    }
+    // 遍历所有选择
+    for (i in choices.indices) {
+        val choice = choices[i]
+        // 剪枝：不允许重复选择元素
+        if (!selected[i]) {
+            // 尝试：做出选择，更新状态
+            selected[i] = true
+            state.add(choice)
+            // 进行下一轮选择
+            backtrack(state, choices, selected, res)
+            // 回退：撤销选择，恢复到之前的状态
+            selected[i] = false
+            state.removeAt(state.size - 1)
+        }
+    }
+}
+
+/* 全排列 I */
+fun permutationsI(nums: IntArray): List<List<Int>?> {
+    val res: MutableList<List<Int>?> = ArrayList()
+    backtrack(ArrayList(), nums, BooleanArray(nums.size), res)
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val nums = intArrayOf(1, 2, 3)
+
+    val res = permutationsI(nums)
+
+    println("输入数组 nums = ${nums.contentToString()}")
+    println("所有排列 res = $res")
+}

codes/kotlin/chapter_backtracking/permutations_ii/permutations_ii.kt

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+/**
+ * File: permutations_ii.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.permutations_ii
+
+/* 回溯算法：全排列 II */
+fun backtrack(
+    state: MutableList<Int>,
+    choices: IntArray,
+    selected: BooleanArray,
+    res: MutableList<MutableList<Int>?>
+) {
+    // 当状态长度等于元素数量时，记录解
+    if (state.size == choices.size) {
+        res.add(ArrayList(state))
+        return
+    }
+    // 遍历所有选择
+    val duplicated: MutableSet<Int> = HashSet()
+    for (i in choices.indices) {
+        val choice = choices[i]
+        // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
+        if (!selected[i] && !duplicated.contains(choice)) {
+            // 尝试：做出选择，更新状态
+            duplicated.add(choice) // 记录选择过的元素值
+            selected[i] = true
+            state.add(choice)
+            // 进行下一轮选择
+            backtrack(state, choices, selected, res)
+            // 回退：撤销选择，恢复到之前的状态
+            selected[i] = false
+            state.removeAt(state.size - 1)
+        }
+    }
+}
+
+/* 全排列 II */
+fun permutationsII(nums: IntArray): MutableList<MutableList<Int>?> {
+    val res: MutableList<MutableList<Int>?> = ArrayList()
+    backtrack(ArrayList(), nums, BooleanArray(nums.size), res)
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val nums = intArrayOf(1, 2, 2)
+
+    val res = permutationsII(nums)
+
+    println("输入数组 nums = ${nums.contentToString()}")
+    println("所有排列 res = $res")
+}

codes/kotlin/chapter_backtracking/preorder_traversal_i_compact/preorder_traversal_i_compact.kt

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+/**
+ * File: preorder_traversal_i_compact.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.preorder_traversal_i_compact
+
+import utils.TreeNode
+import utils.printTree
+
+var res: MutableList<TreeNode>? = null
+
+/* 前序遍历：例题一 */
+fun preOrder(root: TreeNode?) {
+    if (root == null) {
+        return
+    }
+    if (root.value == 7) {
+        // 记录解
+        res!!.add(root)
+    }
+    preOrder(root.left)
+    preOrder(root.right)
+}
+
+/* Driver Code */
+fun main() {
+    val root = TreeNode.listToTree(mutableListOf(1, 7, 3, 4, 5, 6, 7))
+    println("\n初始化二叉树")
+    printTree(root)
+
+    // 前序遍历
+    res = ArrayList()
+    preOrder(root)
+
+    println("\n输出所有值为 7 的节点")
+    val vals: MutableList<Int> = ArrayList()
+    for (node in res as ArrayList<TreeNode>) {
+        vals.add(node.value)
+    }
+    println(vals)
+}

codes/kotlin/chapter_backtracking/preorder_traversal_ii_compact/preorder_traversal_ii_compact.kt

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+/**
+ * File: preorder_traversal_ii_compact.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.preorder_traversal_ii_compact
+
+import utils.TreeNode
+import utils.printTree
+
+var path: MutableList<TreeNode>? = null
+var res: MutableList<List<TreeNode>>? = null
+
+/* 前序遍历：例题二 */
+fun preOrder(root: TreeNode?) {
+    if (root == null) {
+        return
+    }
+    // 尝试
+    path!!.add(root)
+    if (root.value == 7) {
+        // 记录解
+        res!!.add(ArrayList(path!!))
+    }
+    preOrder(root.left)
+    preOrder(root.right)
+    // 回退
+    path!!.removeAt(path!!.size - 1)
+}
+
+/* Driver Code */
+fun main() {
+    val root = TreeNode.listToTree(mutableListOf(1, 7, 3, 4, 5, 6, 7))
+    println("\n初始化二叉树")
+    printTree(root)
+
+    // 前序遍历
+    path = java.util.ArrayList<TreeNode>()
+    res = java.util.ArrayList<List<TreeNode>>()
+    preOrder(root)
+
+    println("\n输出所有根节点到节点 7 的路径")
+    for (path in res as ArrayList<List<TreeNode>>) {
+        val values: MutableList<Int> = ArrayList()
+        for (node in path) {
+            values.add(node.value)
+        }
+        println(values)
+    }
+}

codes/kotlin/chapter_backtracking/preorder_traversal_iii_compact/preorder_traversal_iii_compact.kt

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+/**
+ * File: preorder_traversal_iii_compact.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.preorder_traversal_iii_compact
+
+import utils.TreeNode
+import utils.printTree
+
+var path: MutableList<TreeNode>? = null
+var res: MutableList<List<TreeNode>>? = null
+
+/* 前序遍历：例题三 */
+fun preOrder(root: TreeNode?) {
+    // 剪枝
+    if (root == null || root.value == 3) {
+        return
+    }
+    // 尝试
+    path!!.add(root)
+    if (root.value == 7) {
+        // 记录解
+        res!!.add(ArrayList(path!!))
+    }
+    preOrder(root.left)
+    preOrder(root.right)
+    // 回退
+    path!!.removeAt(path!!.size - 1)
+}
+
+/* Driver Code */
+fun main() {
+    val root = TreeNode.listToTree(mutableListOf(1, 7, 3, 4, 5, 6, 7))
+    println("\n初始化二叉树")
+    printTree(root)
+
+    // 前序遍历
+    path = ArrayList()
+    res = ArrayList()
+    preOrder(root)
+
+    println("\n输出所有根节点到节点 7 的路径，路径中不包含值为 3 的节点")
+    for (path in res as ArrayList<List<TreeNode>>) {
+        val values: MutableList<Int> = ArrayList()
+        for (node in path) {
+            values.add(node.value)
+        }
+        println(values)
+    }
+}

codes/kotlin/chapter_backtracking/preorder_traversal_iii_template/preorder_traversal_iii_template.kt

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+/**
+ * File: preorder_traversal_iii_template.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.preorder_traversal_iii_template
+
+import utils.TreeNode
+import utils.printTree
+import java.util.*
+
+/* 判断当前状态是否为解 */
+fun isSolution(state: List<TreeNode?>): Boolean {
+    return state.isNotEmpty() && state[state.size - 1]?.value == 7
+}
+
+/* 记录解 */
+fun recordSolution(state: MutableList<TreeNode?>?, res: MutableList<List<TreeNode?>?>) {
+    res.add(state?.let { ArrayList(it) })
+}
+
+/* 判断在当前状态下，该选择是否合法 */
+fun isValid(state: List<TreeNode?>?, choice: TreeNode?): Boolean {
+    return choice != null && choice.value != 3
+}
+
+/* 更新状态 */
+fun makeChoice(state: MutableList<TreeNode?>, choice: TreeNode?) {
+    state.add(choice)
+}
+
+/* 恢复状态 */
+fun undoChoice(state: MutableList<TreeNode?>, choice: TreeNode?) {
+    state.removeLast()
+}
+
+/* 回溯算法：例题三 */
+fun backtrack(
+    state: MutableList<TreeNode?>,
+    choices: List<TreeNode?>,
+    res: MutableList<List<TreeNode?>?>
+) {
+    // 检查是否为解
+    if (isSolution(state)) {
+        // 记录解
+        recordSolution(state, res)
+    }
+    // 遍历所有选择
+    for (choice in choices) {
+        // 剪枝：检查选择是否合法
+        if (isValid(state, choice)) {
+            // 尝试：做出选择，更新状态
+            makeChoice(state, choice)
+            // 进行下一轮选择
+            backtrack(state, listOf(choice!!.left, choice.right), res)
+            // 回退：撤销选择，恢复到之前的状态
+            undoChoice(state, choice)
+        }
+    }
+}
+
+/* Driver Code */
+fun main() {
+    val root = TreeNode.listToTree(mutableListOf(1, 7, 3, 4, 5, 6, 7))
+    println("\n初始化二叉树")
+    printTree(root)
+
+    // 回溯算法
+    val res: MutableList<List<TreeNode?>?> = ArrayList()
+    backtrack(ArrayList(), mutableListOf(root), res)
+
+    println("\n输出所有根节点到节点 7 的路径，要求路径中不包含值为 3 的节点")
+    for (path in res) {
+        val vals = ArrayList<Int>()
+        for (node in path!!) {
+            if (node != null) {
+                vals.add(node.value)
+            }
+        }
+        println(vals)
+    }
+}

codes/kotlin/chapter_backtracking/subset_sum_i/subset_sum_i.kt

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+/**
+ * File: subset_sum_i.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.subset_sum_i
+
+import java.util.*
+
+/* 回溯算法：子集和 I */
+fun backtrack(
+    state: MutableList<Int>,
+    target: Int,
+    choices: IntArray,
+    start: Int,
+    res: MutableList<List<Int>?>
+) {
+    // 子集和等于 target 时，记录解
+    if (target == 0) {
+        res.add(ArrayList(state))
+        return
+    }
+    // 遍历所有选择
+    // 剪枝二：从 start 开始遍历，避免生成重复子集
+    for (i in start..<choices.size) {
+        // 剪枝一：若子集和超过 target ，则直接结束循环
+        // 这是因为数组已排序，后边元素更大，子集和一定超过 target
+        if (target - choices[i] < 0) {
+            break
+        }
+        // 尝试：做出选择，更新 target, start
+        state.add(choices[i])
+        // 进行下一轮选择
+        backtrack(state, target - choices[i], choices, i, res)
+        // 回退：撤销选择，恢复到之前的状态
+        state.removeAt(state.size - 1)
+    }
+}
+
+/* 求解子集和 I */
+fun subsetSumI(nums: IntArray, target: Int): List<List<Int>?> {
+    val state: MutableList<Int> = ArrayList() // 状态（子集）
+    Arrays.sort(nums) // 对 nums 进行排序
+    val start = 0 // 遍历起始点
+    val res: MutableList<List<Int>?> = ArrayList() // 结果列表（子集列表）
+    backtrack(state, target, nums, start, res)
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val nums = intArrayOf(3, 4, 5)
+    val target = 9
+
+    val res = subsetSumI(nums, target)
+
+    println("输入数组 nums = ${nums.contentToString()}, target = $target")
+    println("所有和等于 $target 的子集 res = $res")
+}

codes/kotlin/chapter_backtracking/subset_sum_i_naive/subset_sum_i_naive.kt

@@ -0,0 +1,56 @@
+/**
+ * File: subset_sum_i_native.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.subset_sum_i_naive
+
+/* 回溯算法：子集和 I */
+fun backtrack(
+    state: MutableList<Int>,
+    target: Int,
+    total: Int,
+    choices: IntArray,
+    res: MutableList<List<Int>?>
+) {
+    // 子集和等于 target 时，记录解
+    if (total == target) {
+        res.add(ArrayList(state))
+        return
+    }
+    // 遍历所有选择
+    for (i in choices.indices) {
+        // 剪枝：若子集和超过 target ，则跳过该选择
+        if (total + choices[i] > target) {
+            continue
+        }
+        // 尝试：做出选择，更新元素和 total
+        state.add(choices[i])
+        // 进行下一轮选择
+        backtrack(state, target, total + choices[i], choices, res)
+        // 回退：撤销选择，恢复到之前的状态
+        state.removeAt(state.size - 1)
+    }
+}
+
+/* 求解子集和 I（包含重复子集） */
+fun subsetSumINaive(nums: IntArray, target: Int): List<List<Int>?> {
+    val state: MutableList<Int> = ArrayList() // 状态（子集）
+    val total = 0 // 子集和
+    val res: MutableList<List<Int>?> = ArrayList() // 结果列表（子集列表）
+    backtrack(state, target, total, nums, res)
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val nums = intArrayOf(3, 4, 5)
+    val target = 9
+
+    val res: List<List<Int>?> = subsetSumINaive(nums, target)
+
+    println("输入数组 nums = ${nums.contentToString()}, target = $target")
+    println("所有和等于 $target 的子集 res = $res")
+    println("请注意，该方法输出的结果包含重复集合")
+}

codes/kotlin/chapter_backtracking/subset_sum_ii/subset_sum_ii.kt

@@ -0,0 +1,65 @@
+/**
+ * File: subset_sum_ii.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_backtracking.subset_sum_ii
+
+import java.util.*
+
+/* 回溯算法：子集和 II */
+fun backtrack(
+    state: MutableList<Int>,
+    target: Int,
+    choices: IntArray,
+    start: Int,
+    res: MutableList<List<Int>?>
+) {
+    // 子集和等于 target 时，记录解
+    if (target == 0) {
+        res.add(ArrayList(state))
+        return
+    }
+    // 遍历所有选择
+    // 剪枝二：从 start 开始遍历，避免生成重复子集
+    // 剪枝三：从 start 开始遍历，避免重复选择同一元素
+    for (i in start..<choices.size) {
+        // 剪枝一：若子集和超过 target ，则直接结束循环
+        // 这是因为数组已排序，后边元素更大，子集和一定超过 target
+        if (target - choices[i] < 0) {
+            break
+        }
+        // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过
+        if (i > start && choices[i] == choices[i - 1]) {
+            continue
+        }
+        // 尝试：做出选择，更新 target, start
+        state.add(choices[i])
+        // 进行下一轮选择
+        backtrack(state, target - choices[i], choices, i + 1, res)
+        // 回退：撤销选择，恢复到之前的状态
+        state.removeAt(state.size - 1)
+    }
+}
+
+/* 求解子集和 II */
+fun subsetSumII(nums: IntArray, target: Int): List<List<Int>?> {
+    val state: MutableList<Int> = ArrayList() // 状态（子集）
+    Arrays.sort(nums) // 对 nums 进行排序
+    val start = 0 // 遍历起始点
+    val res: MutableList<List<Int>?> = ArrayList() // 结果列表（子集列表）
+    backtrack(state, target, nums, start, res)
+    return res
+}
+
+/* Driver Code */
+fun main() {
+    val nums = intArrayOf(4, 4, 5)
+    val target = 9
+
+    val res = subsetSumII(nums, target)
+
+    println("输入数组 nums = ${nums.contentToString()}, target = $target")
+    println("所有和等于 $target 的子集 res = $res")
+}