From 4325974af1a08d0da17d55faf4a701b774b99eb5 Mon Sep 17 00:00:00 2001 From: liuyuxin Date: Thu, 10 Aug 2023 23:48:56 +0800 Subject: [PATCH] feat: Add Dart codes for chapter_backtracking and chapter_divide_and_conquer (#680) * feat: Add Dart codes for chapter_backtracking * feat: Add Dart codes for chapter_divide_and_conquer * Format Dart Code --- codes/dart/chapter_backtracking/n_queens.dart | 75 +++++++++++++++++++ .../chapter_backtracking/permutations_i.dart | 51 +++++++++++++ .../chapter_backtracking/permutations_ii.dart | 53 +++++++++++++ .../preorder_traversal_i_compact.dart | 35 +++++++++ .../preorder_traversal_ii_compact.dart | 47 ++++++++++++ .../preorder_traversal_iii_compact.dart | 49 ++++++++++++ .../preorder_traversal_iii_template.dart | 73 ++++++++++++++++++ .../chapter_backtracking/subset_sum_i.dart | 56 ++++++++++++++ .../subset_sum_i_naive.dart | 54 +++++++++++++ .../chapter_backtracking/subset_sum_ii.dart | 60 +++++++++++++++ .../binary_search_recur.dart | 42 +++++++++++ .../build_tree.dart | 56 ++++++++++++++ .../chapter_divide_and_conquer/hanota.dart | 54 +++++++++++++ .../chapter_searching/hashing_search.dart | 12 +-- .../dart/chapter_searching/linear_search.dart | 7 +- codes/dart/chapter_sorting/bubble_sort.dart | 4 +- codes/dart/chapter_sorting/counting_sort.dart | 4 +- codes/dart/chapter_sorting/radix_sort.dart | 16 +++- .../dart/chapter_tree/binary_search_tree.dart | 1 - 19 files changed, 731 insertions(+), 18 deletions(-) create mode 100644 codes/dart/chapter_backtracking/n_queens.dart create mode 100644 codes/dart/chapter_backtracking/permutations_i.dart create mode 100644 codes/dart/chapter_backtracking/permutations_ii.dart create mode 100644 codes/dart/chapter_backtracking/preorder_traversal_i_compact.dart create mode 100644 codes/dart/chapter_backtracking/preorder_traversal_ii_compact.dart create mode 100644 codes/dart/chapter_backtracking/preorder_traversal_iii_compact.dart create mode 100644 codes/dart/chapter_backtracking/preorder_traversal_iii_template.dart create mode 100644 codes/dart/chapter_backtracking/subset_sum_i.dart create mode 100644 codes/dart/chapter_backtracking/subset_sum_i_naive.dart create mode 100644 codes/dart/chapter_backtracking/subset_sum_ii.dart create mode 100644 codes/dart/chapter_divide_and_conquer/binary_search_recur.dart create mode 100644 codes/dart/chapter_divide_and_conquer/build_tree.dart create mode 100644 codes/dart/chapter_divide_and_conquer/hanota.dart diff --git a/codes/dart/chapter_backtracking/n_queens.dart b/codes/dart/chapter_backtracking/n_queens.dart new file mode 100644 index 000000000..bff248f6d --- /dev/null +++ b/codes/dart/chapter_backtracking/n_queens.dart @@ -0,0 +1,75 @@ +/** + * File: n_queens.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 回溯算法：N 皇后 */ +void backtrack( + int row, + int n, + List> state, + List>> res, + List cols, + List diags1, + List diags2, +) { + // 当放置完所有行时，记录解 + if (row == n) { + List> copyState = []; + for (List sRow in state) { + copyState.add(List.from(sRow)); + } + res.add(copyState); + return; + } + // 遍历所有列 + for (int col = 0; col < n; col++) { + // 计算该格子对应的主对角线和副对角线 + int diag1 = row - col + n - 1; + int diag2 = row + col; + // 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后 + if (!cols[col] && !diags1[diag1] && !diags2[diag2]) { + // 尝试：将皇后放置在该格子 + state[row][col] = "Q"; + cols[col] = true; + diags1[diag1] = true; + diags2[diag2] = true; + // 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] = "#"; + cols[col] = false; + diags1[diag1] = false; + diags2[diag2] = false; + } + } +} + +/* 求解 N 皇后 */ +List>> nQueens(int n) { + // 初始化 n*n 大小的棋盘，其中 'Q' 代表皇后，'#' 代表空位 + List> state = List.generate(n, (index) => List.filled(n, "#")); + List cols = List.filled(n, false); // 记录列是否有皇后 + List diags1 = List.filled(2 * n - 1, false); // 记录主对角线是否有皇后 + List diags2 = List.filled(2 * n - 1, false); // 记录副对角线是否有皇后 + List>> res = []; + + backtrack(0, n, state, res, cols, diags1, diags2); + + return res; +} + +/* Driver Code */ +void main() { + int n = 4; + List>> res = nQueens(n); + print("输入棋盘长宽为 $n"); + print("皇后放置方案共有 ${res.length} 种"); + for (List> state in res) { + print("--------------------"); + for (List row in state) { + print(row); + } + } +} diff --git a/codes/dart/chapter_backtracking/permutations_i.dart b/codes/dart/chapter_backtracking/permutations_i.dart new file mode 100644 index 000000000..29988721b --- /dev/null +++ b/codes/dart/chapter_backtracking/permutations_i.dart @@ -0,0 +1,51 @@ +/** + * File: permutations_i.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 回溯算法：全排列 I */ +void backtrack( + List state, + List choices, + List selected, + List> res, +) { + // 当状态长度等于元素数量时，记录解 + if (state.length == choices.length) { + res.add(List.from(state)); + return; + } + // 遍历所有选择 + for (int i = 0; i < choices.length; i++) { + int 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]) { + // 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.removeLast(); + } + } +} + +/* 全排列 I */ +List> permutationsI(List nums) { + List> res = []; + backtrack([], nums, List.filled(nums.length, false), res); + return res; +} + +/* Driver Code */ +void main() { + List nums = [1, 2, 3]; + + List> res = permutationsI(nums); + + print("输入数组 nums = $nums"); + print("所有排列 res = $res"); +} diff --git a/codes/dart/chapter_backtracking/permutations_ii.dart b/codes/dart/chapter_backtracking/permutations_ii.dart new file mode 100644 index 000000000..18016cc27 --- /dev/null +++ b/codes/dart/chapter_backtracking/permutations_ii.dart @@ -0,0 +1,53 @@ +/** + * File: permutations_ii.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 回溯算法：全排列 II */ +void backtrack( + List state, + List choices, + List selected, + List> res, +) { + // 当状态长度等于元素数量时，记录解 + if (state.length == choices.length) { + res.add(List.from(state)); + return; + } + // 遍历所有选择 + Set duplicated = {}; + for (int i = 0; i < choices.length; i++) { + int 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.removeLast(); + } + } +} + +/* 全排列 II */ +List> permutationsII(List nums) { + List> res = []; + backtrack([], nums, List.filled(nums.length, false), res); + return res; +} + +/* Driver Code */ +void main() { + List nums = [1, 2, 2]; + + List> res = permutationsII(nums); + + print("输入数组 nums = $nums"); + print("所有排列 res = $res"); +} diff --git a/codes/dart/chapter_backtracking/preorder_traversal_i_compact.dart b/codes/dart/chapter_backtracking/preorder_traversal_i_compact.dart new file mode 100644 index 000000000..b4d76519a --- /dev/null +++ b/codes/dart/chapter_backtracking/preorder_traversal_i_compact.dart @@ -0,0 +1,35 @@ +/** + * File: preorder_traversal_i_compact.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +import '../utils/print_util.dart'; +import '../utils/tree_node.dart'; + +/* 前序遍历：例题一 */ +void preOrder(TreeNode? root, List res) { + if (root == null) { + return; + } + if (root.val == 7) { + // 记录解 + res.add(root); + } + preOrder(root.left, res); + preOrder(root.right, res); +} + +/* Driver Code */ +void main() { + TreeNode? root = listToTree([1, 7, 3, 4, 5, 6, 7]); + print("\n初始化二叉树"); + printTree(root); + + // 前序遍历 + List res = []; + preOrder(root, res); + + print("\n输出所有值为 7 的节点"); + print(List.generate(res.length, (i) => res[i].val)); +} diff --git a/codes/dart/chapter_backtracking/preorder_traversal_ii_compact.dart b/codes/dart/chapter_backtracking/preorder_traversal_ii_compact.dart new file mode 100644 index 000000000..c3ef81f22 --- /dev/null +++ b/codes/dart/chapter_backtracking/preorder_traversal_ii_compact.dart @@ -0,0 +1,47 @@ +/** + * File: preorder_traversal_ii_compact.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +import '../utils/print_util.dart'; +import '../utils/tree_node.dart'; + +/* 前序遍历：例题二 */ +void preOrder( + TreeNode? root, + List path, + List> res, +) { + if (root == null) { + return; + } + + // 尝试 + path.add(root); + if (root.val == 7) { + // 记录解 + res.add(List.from(path)); + } + preOrder(root.left, path, res); + preOrder(root.right, path, res); + // 回退 + path.removeLast(); +} + +/* Driver Code */ +void main() { + TreeNode? root = listToTree([1, 7, 3, 4, 5, 6, 7]); + print("\n初始化二叉树"); + printTree(root); + + // 前序遍历 + List path = []; + List> res = []; + preOrder(root, path, res); + + print("\n输出所有根节点到节点 7 的路径"); + for (List vals in res) { + print(List.generate(vals.length, (i) => vals[i].val)); + } +} diff --git a/codes/dart/chapter_backtracking/preorder_traversal_iii_compact.dart b/codes/dart/chapter_backtracking/preorder_traversal_iii_compact.dart new file mode 100644 index 000000000..93137fc91 --- /dev/null +++ b/codes/dart/chapter_backtracking/preorder_traversal_iii_compact.dart @@ -0,0 +1,49 @@ +/** + * File: preorder_traversal_iii_compact.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +import '../utils/print_util.dart'; +import '../utils/tree_node.dart'; + +/* 前序遍历：例题三 */ +void preOrder( + TreeNode? root, + List path, + List> res, +) { + if (root == null || root.val == 3) { + return; + } + + // 尝试 + path.add(root); + if (root.val == 7) { + // 记录解 + res.add(List.from(path)); + path.removeLast(); + return; + } + preOrder(root.left, path, res); + preOrder(root.right, path, res); + // 回退 + path.removeLast(); +} + +/* Driver Code */ +void main() { + TreeNode? root = listToTree([1, 7, 3, 4, 5, 6, 7]); + print("\n初始化二叉树"); + printTree(root); + + // 前序遍历 + List path = []; + List> res = []; + preOrder(root, path, res); + + print("\n输出所有根节点到节点 7 的路径"); + for (List vals in res) { + print(List.generate(vals.length, (i) => vals[i].val)); + } +} diff --git a/codes/dart/chapter_backtracking/preorder_traversal_iii_template.dart b/codes/dart/chapter_backtracking/preorder_traversal_iii_template.dart new file mode 100644 index 000000000..a8ca0d8b0 --- /dev/null +++ b/codes/dart/chapter_backtracking/preorder_traversal_iii_template.dart @@ -0,0 +1,73 @@ +/** + * File: preorder_traversal_iii_template.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +import '../utils/print_util.dart'; +import '../utils/tree_node.dart'; + +/* 判断当前状态是否为解 */ +bool isSolution(List state) { + return state.isNotEmpty && state.last.val == 7; +} + +/* 记录解 */ +void recordSolution(List state, List> res) { + res.add(List.from(state)); +} + +/* 判断在当前状态下，该选择是否合法 */ +bool isValid(List state, TreeNode? choice) { + return choice != null && choice.val != 3; +} + +/* 更新状态 */ +void makeChoice(List state, TreeNode? choice) { + state.add(choice!); +} + +/* 恢复状态 */ +void undoChoice(List state, TreeNode? choice) { + state.removeLast(); +} + +/* 回溯算法：例题三 */ +void backtrack( + List state, + List choices, + List> res, +) { + // 检查是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res); + } + // 遍历所有选择 + for (TreeNode? 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, [choice!.left, choice.right], res); + // 回退：撤销选择，恢复到之前的状态 + undoChoice(state, choice); + } + } +} + +/* Driver Code */ +void main() { + TreeNode? root = listToTree([1, 7, 3, 4, 5, 6, 7]); + print("\n初始化二叉树"); + printTree(root); + + // 回溯算法 + List> res = []; + backtrack([], [root!], res); + print("\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 (List path in res) { + print(List.from(path.map((e) => e.val))); + } +} diff --git a/codes/dart/chapter_backtracking/subset_sum_i.dart b/codes/dart/chapter_backtracking/subset_sum_i.dart new file mode 100644 index 000000000..aa71c0f09 --- /dev/null +++ b/codes/dart/chapter_backtracking/subset_sum_i.dart @@ -0,0 +1,56 @@ +/** + * File: subset_sum_i.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 回溯算法：子集和 I */ +void backtrack( + List state, + int target, + List choices, + int start, + List> res, +) { + // 子集和等于 target 时，记录解 + if (target == 0) { + res.add(List.from(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 (int i = start; i < choices.length; i++) { + // 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.removeLast(); + } +} + +/* 求解子集和 I */ +List> subsetSumI(List nums, int target) { + List state = []; // 状态（子集） + nums.sort(); // 对 nums 进行排序 + int start = 0; // 遍历起始点 + List> res = []; // 结果列表（子集列表） + backtrack(state, target, nums, start, res); + return res; +} + +/* Driver Code */ +void main() { + List nums = [3, 4, 5]; + int target = 9; + + List> res = subsetSumI(nums, target); + + print("输入数组 nums = $nums, target = $target"); + print("所有和等于 $target 的子集 res = $res"); +} diff --git a/codes/dart/chapter_backtracking/subset_sum_i_naive.dart b/codes/dart/chapter_backtracking/subset_sum_i_naive.dart new file mode 100644 index 000000000..9f9d75f60 --- /dev/null +++ b/codes/dart/chapter_backtracking/subset_sum_i_naive.dart @@ -0,0 +1,54 @@ +/** + * File: subset_sum_i_naive.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 回溯算法：子集和 I */ +void backtrack( + List state, + int target, + int total, + List choices, + List> res, +) { + // 子集和等于 target 时，记录解 + if (total == target) { + res.add(List.from(state)); + return; + } + // 遍历所有选择 + for (int i = 0; i < choices.length; i++) { + // 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.removeLast(); + } +} + +/* 求解子集和 I（包含重复子集） */ +List> subsetSumINaive(List nums, int target) { + List state = []; // 状态（子集） + int total = 0; // 元素和 + List> res = []; // 结果列表（子集列表） + backtrack(state, target, total, nums, res); + return res; +} + +/* Driver Code */ +void main() { + List nums = [3, 4, 5]; + int target = 9; + + List> res = subsetSumINaive(nums, target); + + print("输入数组 nums = $nums, target = $target"); + print("所有和等于 $target 的子集 res = $res"); + print("请注意，该方法输出的结果包含重复集合"); +} diff --git a/codes/dart/chapter_backtracking/subset_sum_ii.dart b/codes/dart/chapter_backtracking/subset_sum_ii.dart new file mode 100644 index 000000000..a545c52ce --- /dev/null +++ b/codes/dart/chapter_backtracking/subset_sum_ii.dart @@ -0,0 +1,60 @@ +/** + * File: subset_sum_ii.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 回溯算法：子集和 II */ +void backtrack( + List state, + int target, + List choices, + int start, + List> res, +) { + // 子集和等于 target 时，记录解 + if (target == 0) { + res.add(List.from(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 (int i = start; i < choices.length; i++) { + // 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.removeLast(); + } +} + +/* 求解子集和 II */ +List> subsetSumII(List nums, int target) { + List state = []; // 状态（子集） + nums.sort(); // 对 nums 进行排序 + int start = 0; // 遍历起始点 + List> res = []; // 结果列表（子集列表） + backtrack(state, target, nums, start, res); + return res; +} + +void main() { + List nums = [4, 4, 5]; + int target = 9; + + List> res = subsetSumII(nums, target); + + print("输入数组 nums = $nums, target = $target"); + print("所有和等于 $target 的子集 res = $res"); +} diff --git a/codes/dart/chapter_divide_and_conquer/binary_search_recur.dart b/codes/dart/chapter_divide_and_conquer/binary_search_recur.dart new file mode 100644 index 000000000..d86d9de1b --- /dev/null +++ b/codes/dart/chapter_divide_and_conquer/binary_search_recur.dart @@ -0,0 +1,42 @@ +/** + * File: binary_search_recur.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 二分查找：问题 f(i, j) */ +int dfs(List nums, int target, int i, int j) { + // 若区间为空，代表无目标元素，则返回 -1 + if (i > j) { + return -1; + } + // 计算中点索引 m + int m = (i + j) ~/ 2; + if (nums[m] < target) { + // 递归子问题 f(m+1, j) + return dfs(nums, target, m + 1, j); + } else if (nums[m] > target) { + // 递归子问题 f(i, m-1) + return dfs(nums, target, i, m - 1); + } else { + // 找到目标元素，返回其索引 + return m; + } +} + +/* 二分查找 */ +int binarySearch(List nums, int target) { + int n = nums.length; + // 求解问题 f(0, n-1) + return dfs(nums, target, 0, n - 1); +} + +/* Driver Code */ +void main() { + int target = 6; + List nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35]; + + // 二分查找（双闭区间） + int index = binarySearch(nums, target); + print("目标元素 6 的索引 = $index"); +} diff --git a/codes/dart/chapter_divide_and_conquer/build_tree.dart b/codes/dart/chapter_divide_and_conquer/build_tree.dart new file mode 100644 index 000000000..5c7c0662c --- /dev/null +++ b/codes/dart/chapter_divide_and_conquer/build_tree.dart @@ -0,0 +1,56 @@ +/** + * File: build_tree.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +import '../utils/print_util.dart'; +import '../utils/tree_node.dart'; + +/* 构建二叉树：分治 */ +TreeNode? dfs( + List preorder, + List inorder, + Map hmap, + int i, + int l, + int r, +) { + // 子树区间为空时终止 + if (r - l < 0) { + return null; + } + // 初始化根节点 + TreeNode? root = TreeNode(preorder[i]); + // 查询 m ，从而划分左右子树 + int m = hmap[preorder[i]]!; + // 子问题：构建左子树 + root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1); + // 子问题：构建右子树 + root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r); + // 返回根节点 + return root; +} + +/* 构建二叉树 */ +TreeNode? buildTree(List preorder, List inorder) { + // 初始化哈希表，存储 inorder 元素到索引的映射 + Map hmap = {}; + for (int i = 0; i < inorder.length; i++) { + hmap[inorder[i]] = i; + } + TreeNode? root = dfs(preorder, inorder, hmap, 0, 0, inorder.length - 1); + return root; +} + +/* Driver Code */ +void main() { + List preorder = [3, 9, 2, 1, 7]; + List inorder = [9, 3, 1, 2, 7]; + print("前序遍历 = $preorder"); + print("中序遍历 = $inorder"); + + TreeNode? root = buildTree(preorder, inorder); + print("构建的二叉树为："); + printTree(root!); +} diff --git a/codes/dart/chapter_divide_and_conquer/hanota.dart b/codes/dart/chapter_divide_and_conquer/hanota.dart new file mode 100644 index 000000000..bbc4f1324 --- /dev/null +++ b/codes/dart/chapter_divide_and_conquer/hanota.dart @@ -0,0 +1,54 @@ +/** + * File: hanota.dart + * Created Time: 2023-08-10 + * Author: liuyuxin (gvenusleo@gmail.com) + */ + +/* 移动一个圆盘 */ +void move(List src, List tar) { + // 从 src 顶部拿出一个圆盘 + int pan = src.removeLast(); + // 将圆盘放入 tar 顶部 + tar.add(pan); +} + +/* 求解汉诺塔：问题 f(i) */ +void dfs(int i, List src, List buf, List tar) { + // 若 src 只剩下一个圆盘，则直接将其移到 tar + if (i == 1) { + move(src, tar); + return; + } + // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf + dfs(i - 1, src, tar, buf); + // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar + move(src, tar); + // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar + dfs(i - 1, buf, src, tar); +} + +/* 求解汉诺塔 */ +void hanota(List A, List B, List C) { + int n = A.length; + // 将 A 顶部 n 个圆盘借助 B 移到 C + dfs(n, A, B, C); +} + +/* Driver Code */ +void main() { + // 列表尾部是柱子顶部 + List A = [5, 4, 3, 2, 1]; + List B = []; + List C = []; + print("初始状态下："); + print("A = $A"); + print("B = $B"); + print("C = $C"); + + hanota(A, B, C); + + print("圆盘移动完成后："); + print("A = $A"); + print("B = $B"); + print("C = $C"); +} diff --git a/codes/dart/chapter_searching/hashing_search.dart b/codes/dart/chapter_searching/hashing_search.dart index 8c0b5e65e..6bd73de1a 100644 --- a/codes/dart/chapter_searching/hashing_search.dart +++ b/codes/dart/chapter_searching/hashing_search.dart @@ -18,7 +18,7 @@ int hashingSearchArray(Map map, int target) { } /* 哈希查找（链表） */ -ListNode? hashingSearchLinkedList(Map map, int target) { +ListNode? hashingSearchLinkedList(Map map, int target) { // 哈希表的 key: 目标节点值，value: 节点对象 // 若哈希表中无此 key ，返回 null if (!map.containsKey(target)) { @@ -28,15 +28,15 @@ ListNode? hashingSearchLinkedList(Map map, int target) { } /* Driver Code */ -void main(){ +void main() { int target = 3; /* 哈希查找（数组） */ List nums = [1, 5, 3, 2, 4, 7, 5, 9, 10, 8]; // 初始化哈希表 - Map map = HashMap(); + Map map = HashMap(); for (int i = 0; i < nums.length; i++) { - map.putIfAbsent(nums[i], () => i);// key: 元素，value: 索引 + map.putIfAbsent(nums[i], () => i); // key: 元素，value: 索引 } int index = hashingSearchArray(map, target); print('目标元素 3 的索引 = $index'); @@ -44,11 +44,11 @@ void main(){ /* 哈希查找（链表） */ ListNode? head = listToLinkedList(nums); // 初始化哈希表 - Map map1 = HashMap(); + Map map1 = HashMap(); while (head != null) { map1.putIfAbsent(head.val, () => head!); // key: 节点值，value: 节点 head = head.next; } ListNode? node = hashingSearchLinkedList(map1, target); print('目标节点值 3 的对应节点对象为 $node'); -} \ No newline at end of file +} diff --git a/codes/dart/chapter_searching/linear_search.dart b/codes/dart/chapter_searching/linear_search.dart index 24a90fc99..55b38cbbf 100644 --- a/codes/dart/chapter_searching/linear_search.dart +++ b/codes/dart/chapter_searching/linear_search.dart @@ -24,8 +24,7 @@ ListNode? linearSearchList(ListNode? head, int target) { // 遍历链表 while (head != null) { // 找到目标节点，返回之 - if (head.val == target) - return head; + if (head.val == target) return head; head = head.next; } // 未找到目标元素，返回 null @@ -33,7 +32,7 @@ ListNode? linearSearchList(ListNode? head, int target) { } /* Driver Code */ -void main(){ +void main() { int target = 3; /* 在数组中执行线性查找 */ @@ -45,4 +44,4 @@ void main(){ ListNode? head = listToLinkedList(nums); ListNode? node = linearSearchList(head, target); print('目标节点值 3 的对应节点对象为 $node'); -} \ No newline at end of file +} diff --git a/codes/dart/chapter_sorting/bubble_sort.dart b/codes/dart/chapter_sorting/bubble_sort.dart index b563ddf68..9cec180fd 100644 --- a/codes/dart/chapter_sorting/bubble_sort.dart +++ b/codes/dart/chapter_sorting/bubble_sort.dart @@ -8,7 +8,7 @@ void bubbleSort(List nums) { // 外循环：未排序区间为 [0, i] for (int i = nums.length - 1; i > 0; i--) { - // 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 + // 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 (int j = 0; j < i; j++) { if (nums[j] > nums[j + 1]) { // 交换 nums[j] 与 nums[j + 1] @@ -25,7 +25,7 @@ void bubbleSortWithFlag(List nums) { // 外循环：未排序区间为 [0, i] for (int i = nums.length - 1; i > 0; i--) { bool flag = false; // 初始化标志位 - // 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 + // 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 (int j = 0; j < i; j++) { if (nums[j] > nums[j + 1]) { // 交换 nums[j] 与 nums[j + 1] diff --git a/codes/dart/chapter_sorting/counting_sort.dart b/codes/dart/chapter_sorting/counting_sort.dart index e3ccd4ffc..d7634ef83 100644 --- a/codes/dart/chapter_sorting/counting_sort.dart +++ b/codes/dart/chapter_sorting/counting_sort.dart @@ -13,7 +13,7 @@ void countingSortNaive(List nums) { for (int num in nums) { m = max(m, num); } - // 2. 统计各数字的出现次数 + // 2. 统计各数字的出现次数 // counter[num] 代表 num 的出现次数 List counter = List.filled(m + 1, 0); for (int num in nums) { @@ -54,7 +54,7 @@ void countingSort(List nums) { for (int i = n - 1; i >= 0; i--) { int num = nums[i]; res[counter[num] - 1] = num; // 将 num 放置到对应索引处 - counter[num]--; // 令前缀和自减 1 ，得到下次放置 num 的索引 + counter[num]--; // 令前缀和自减 1 ，得到下次放置 num 的索引 } // 使用结果数组 res 覆盖原数组 nums nums.setAll(0, res); diff --git a/codes/dart/chapter_sorting/radix_sort.dart b/codes/dart/chapter_sorting/radix_sort.dart index c5894c27a..095dc90f9 100644 --- a/codes/dart/chapter_sorting/radix_sort.dart +++ b/codes/dart/chapter_sorting/radix_sort.dart @@ -40,7 +40,7 @@ void countingSortDigit(List nums, int exp) { void radixSort(List nums) { // 获取数组的最大元素，用于判断最大位数 // dart 中 int 的长度是 64 位的 - int m = -1 << 63; + int m = -1 << 63; for (int num in nums) if (num > m) m = num; // 按照从低位到高位的顺序遍历 for (int exp = 1; exp <= m; exp *= 10) @@ -54,8 +54,18 @@ void radixSort(List nums) { /* Driver Code */ void main() { // 基数排序 - List nums = [10546151, 35663510, 42865989, 34862445, 81883077, - 88906420, 72429244, 30524779, 82060337, 63832996]; + List nums = [ + 10546151, + 35663510, + 42865989, + 34862445, + 81883077, + 88906420, + 72429244, + 30524779, + 82060337, + 63832996 + ]; radixSort(nums); print("基数排序完成后 nums = $nums"); } diff --git a/codes/dart/chapter_tree/binary_search_tree.dart b/codes/dart/chapter_tree/binary_search_tree.dart index 6ae7f5958..fd7654058 100644 --- a/codes/dart/chapter_tree/binary_search_tree.dart +++ b/codes/dart/chapter_tree/binary_search_tree.dart @@ -113,7 +113,6 @@ void remove(int num) { // 若删除节点为根节点，则重新指定根节点 root = child; } - } else { // 子节点数量 = 2 // 获取中序遍历中 cur 的下一个节点