mirror of
https://github.com/krahets/hello-algo.git
synced 2026-07-16 00:46:06 +00:00
feat: Traditional Chinese version (#1163)
* First commit * Update mkdocs.yml * Translate all the docs to traditional Chinese * Translate the code files. * Translate the docker file * Fix mkdocs.yml * Translate all the figures from SC to TC * 二叉搜尋樹 -> 二元搜尋樹 * Update terminology. * Update terminology * 构造函数/构造方法 -> 建構子 异或 -> 互斥或 * 擴充套件 -> 擴展 * constant - 常量 - 常數 * 類 -> 類別 * AVL -> AVL 樹 * 數組 -> 陣列 * 係統 -> 系統 斐波那契數列 -> 費波那契數列 運算元量 -> 運算量 引數 -> 參數 * 聯絡 -> 關聯 * 麵試 -> 面試 * 面向物件 -> 物件導向 歸併排序 -> 合併排序 范式 -> 範式 * Fix 算法 -> 演算法 * 錶示 -> 表示 反碼 -> 一補數 補碼 -> 二補數 列列尾部 -> 佇列尾部 區域性性 -> 區域性 一摞 -> 一疊 * Synchronize with main branch * 賬號 -> 帳號 推匯 -> 推導 * Sync with main branch * First commit * Update mkdocs.yml * Translate all the docs to traditional Chinese * Translate the code files. * Translate the docker file * Fix mkdocs.yml * Translate all the figures from SC to TC * 二叉搜尋樹 -> 二元搜尋樹 * Update terminology * 构造函数/构造方法 -> 建構子 异或 -> 互斥或 * 擴充套件 -> 擴展 * constant - 常量 - 常數 * 類 -> 類別 * AVL -> AVL 樹 * 數組 -> 陣列 * 係統 -> 系統 斐波那契數列 -> 費波那契數列 運算元量 -> 運算量 引數 -> 參數 * 聯絡 -> 關聯 * 麵試 -> 面試 * 面向物件 -> 物件導向 歸併排序 -> 合併排序 范式 -> 範式 * Fix 算法 -> 演算法 * 錶示 -> 表示 反碼 -> 一補數 補碼 -> 二補數 列列尾部 -> 佇列尾部 區域性性 -> 區域性 一摞 -> 一疊 * Synchronize with main branch * 賬號 -> 帳號 推匯 -> 推導 * Sync with main branch * Update terminology.md * 操作数量（num. of operations）-> 操作數量 * 字首和->前綴和 * Update figures * 歸 -> 迴 記憶體洩漏 -> 記憶體流失 * Fix the bug of the file filter * 支援 -> 支持 Add zh-Hant/README.md * Add the zh-Hant chapter covers. Bug fixes. * 外掛 -> 擴充功能 * Add the landing page for zh-Hant version * Unify the font of the chapter covers for the zh, en, and zh-Hant version * Move zh-Hant/ to zh-hant/ * Translate terminology.md to traditional Chinese
This commit is contained in:
Yudong Jin
@@ -0,0 +1,10 @@
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add_executable(preorder_traversal_i_compact preorder_traversal_i_compact.cpp)
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add_executable(preorder_traversal_ii_compact preorder_traversal_ii_compact.cpp)
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add_executable(preorder_traversal_iii_compact preorder_traversal_iii_compact.cpp)
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add_executable(preorder_traversal_iii_template preorder_traversal_iii_template.cpp)
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add_executable(permutations_i permutations_i.cpp)
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add_executable(permutations_ii permutations_ii.cpp)
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add_executable(n_queens n_queens.cpp)
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add_executable(subset_sum_i_naive subset_sum_i_naive.cpp)
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add_executable(subset_sum_i subset_sum_i.cpp)
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add_executable(subset_sum_ii subset_sum_ii.cpp)
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@@ -0,0 +1,65 @@
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/**
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* File: n_queens.cpp
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* Created Time: 2023-05-04
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 回溯演算法：n 皇后 */
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void backtrack(int row, int n, vector<vector<string>> &state, vector<vector<vector<string>>> &res, vector<bool> &cols,
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vector<bool> &diags1, vector<bool> &diags2) {
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// 當放置完所有行時，記錄解
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if (row == n) {
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res.push_back(state);
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return;
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}
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// 走訪所有列
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for (int col = 0; col < n; col++) {
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// 計算該格子對應的主對角線和次對角線
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int diag1 = row - col + n - 1;
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int diag2 = row + col;
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// 剪枝：不允許該格子所在列、主對角線、次對角線上存在皇后
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if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
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// 嘗試：將皇后放置在該格子
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state[row][col] = "Q";
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cols[col] = diags1[diag1] = diags2[diag2] = true;
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// 放置下一行
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backtrack(row + 1, n, state, res, cols, diags1, diags2);
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// 回退：將該格子恢復為空位
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state[row][col] = "#";
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cols[col] = diags1[diag1] = diags2[diag2] = false;
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}
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}
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}
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/* 求解 n 皇后 */
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vector<vector<vector<string>>> nQueens(int n) {
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// 初始化 n*n 大小的棋盤，其中 'Q' 代表皇后，'#' 代表空位
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vector<vector<string>> state(n, vector<string>(n, "#"));
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vector<bool> cols(n, false); // 記錄列是否有皇后
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vector<bool> diags1(2 * n - 1, false); // 記錄主對角線上是否有皇后
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vector<bool> diags2(2 * n - 1, false); // 記錄次對角線上是否有皇后
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vector<vector<vector<string>>> res;
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backtrack(0, n, state, res, cols, diags1, diags2);
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return res;
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}
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/* Driver Code */
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int main() {
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int n = 4;
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vector<vector<vector<string>>> res = nQueens(n);
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cout << "輸入棋盤長寬為 " << n << endl;
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cout << "皇后放置方案共有 " << res.size() << " 種" << endl;
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for (const vector<vector<string>> &state : res) {
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cout << "--------------------" << endl;
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for (const vector<string> &row : state) {
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printVector(row);
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}
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}
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return 0;
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}
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@@ -0,0 +1,54 @@
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/**
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* File: permutations_i.cpp
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* Created Time: 2023-04-24
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 回溯演算法：全排列 I */
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void backtrack(vector<int> &state, const vector<int> &choices, vector<bool> &selected, vector<vector<int>> &res) {
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// 當狀態長度等於元素數量時，記錄解
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if (state.size() == choices.size()) {
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res.push_back(state);
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return;
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}
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// 走訪所有選擇
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for (int i = 0; i < choices.size(); i++) {
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int choice = choices[i];
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// 剪枝：不允許重複選擇元素
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if (!selected[i]) {
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// 嘗試：做出選擇，更新狀態
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selected[i] = true;
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state.push_back(choice);
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// 進行下一輪選擇
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backtrack(state, choices, selected, res);
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// 回退：撤銷選擇，恢復到之前的狀態
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selected[i] = false;
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state.pop_back();
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}
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}
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}
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/* 全排列 I */
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vector<vector<int>> permutationsI(vector<int> nums) {
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vector<int> state;
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vector<bool> selected(nums.size(), false);
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vector<vector<int>> res;
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backtrack(state, nums, selected, res);
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return res;
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}
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/* Driver Code */
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int main() {
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vector<int> nums = {1, 2, 3};
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vector<vector<int>> res = permutationsI(nums);
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cout << "輸入陣列 nums = ";
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printVector(nums);
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cout << "所有排列 res = ";
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printVectorMatrix(res);
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return 0;
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}
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@@ -0,0 +1,56 @@
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/**
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* File: permutations_ii.cpp
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* Created Time: 2023-04-24
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 回溯演算法：全排列 II */
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void backtrack(vector<int> &state, const vector<int> &choices, vector<bool> &selected, vector<vector<int>> &res) {
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// 當狀態長度等於元素數量時，記錄解
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if (state.size() == choices.size()) {
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res.push_back(state);
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return;
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}
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// 走訪所有選擇
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unordered_set<int> duplicated;
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for (int i = 0; i < choices.size(); i++) {
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int choice = choices[i];
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// 剪枝：不允許重複選擇元素 且 不允許重複選擇相等元素
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if (!selected[i] && duplicated.find(choice) == duplicated.end()) {
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// 嘗試：做出選擇，更新狀態
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duplicated.emplace(choice); // 記錄選擇過的元素值
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selected[i] = true;
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state.push_back(choice);
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// 進行下一輪選擇
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backtrack(state, choices, selected, res);
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// 回退：撤銷選擇，恢復到之前的狀態
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selected[i] = false;
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state.pop_back();
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}
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}
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}
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/* 全排列 II */
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vector<vector<int>> permutationsII(vector<int> nums) {
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vector<int> state;
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vector<bool> selected(nums.size(), false);
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vector<vector<int>> res;
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backtrack(state, nums, selected, res);
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return res;
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}
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/* Driver Code */
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int main() {
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vector<int> nums = {1, 1, 2};
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vector<vector<int>> res = permutationsII(nums);
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cout << "輸入陣列 nums = ";
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printVector(nums);
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cout << "所有排列 res = ";
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printVectorMatrix(res);
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return 0;
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}
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@@ -0,0 +1,39 @@
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/**
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* File: preorder_traversal_i_compact.cpp
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* Created Time: 2023-04-16
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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vector<TreeNode *> res;
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/* 前序走訪：例題一 */
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void preOrder(TreeNode *root) {
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if (root == nullptr) {
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return;
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}
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if (root->val == 7) {
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// 記錄解
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res.push_back(root);
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}
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preOrder(root->left);
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preOrder(root->right);
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}
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/* Driver Code */
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int main() {
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TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
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cout << "\n初始化二元樹" << endl;
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printTree(root);
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// 前序走訪
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preOrder(root);
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cout << "\n輸出所有值為 7 的節點" << endl;
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vector<int> vals;
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for (TreeNode *node : res) {
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vals.push_back(node->val);
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}
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printVector(vals);
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}
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@@ -0,0 +1,46 @@
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/**
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* File: preorder_traversal_ii_compact.cpp
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* Created Time: 2023-04-16
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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vector<TreeNode *> path;
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vector<vector<TreeNode *>> res;
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/* 前序走訪：例題二 */
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void preOrder(TreeNode *root) {
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if (root == nullptr) {
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return;
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}
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// 嘗試
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path.push_back(root);
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if (root->val == 7) {
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// 記錄解
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res.push_back(path);
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}
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preOrder(root->left);
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preOrder(root->right);
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// 回退
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path.pop_back();
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}
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/* Driver Code */
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int main() {
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TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
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cout << "\n初始化二元樹" << endl;
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printTree(root);
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// 前序走訪
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preOrder(root);
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cout << "\n輸出所有根節點到節點 7 的路徑" << endl;
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for (vector<TreeNode *> &path : res) {
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vector<int> vals;
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for (TreeNode *node : path) {
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vals.push_back(node->val);
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}
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printVector(vals);
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}
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}
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@@ -0,0 +1,47 @@
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/**
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* File: preorder_traversal_iii_compact.cpp
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* Created Time: 2023-04-16
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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vector<TreeNode *> path;
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vector<vector<TreeNode *>> res;
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/* 前序走訪：例題三 */
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void preOrder(TreeNode *root) {
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// 剪枝
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if (root == nullptr || root->val == 3) {
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return;
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}
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// 嘗試
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path.push_back(root);
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if (root->val == 7) {
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// 記錄解
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res.push_back(path);
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}
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preOrder(root->left);
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preOrder(root->right);
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// 回退
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path.pop_back();
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}
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/* Driver Code */
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int main() {
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TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
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cout << "\n初始化二元樹" << endl;
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printTree(root);
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// 前序走訪
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preOrder(root);
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cout << "\n輸出所有根節點到節點 7 的路徑，要求路徑中不包含值為 3 的節點" << endl;
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for (vector<TreeNode *> &path : res) {
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vector<int> vals;
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for (TreeNode *node : path) {
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vals.push_back(node->val);
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}
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printVector(vals);
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}
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}
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@@ -0,0 +1,76 @@
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/**
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* File: preorder_traversal_iii_template.cpp
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* Created Time: 2023-04-16
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 判斷當前狀態是否為解 */
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bool isSolution(vector<TreeNode *> &state) {
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return !state.empty() && state.back()->val == 7;
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}
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/* 記錄解 */
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void recordSolution(vector<TreeNode *> &state, vector<vector<TreeNode *>> &res) {
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res.push_back(state);
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}
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/* 判斷在當前狀態下，該選擇是否合法 */
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bool isValid(vector<TreeNode *> &state, TreeNode *choice) {
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return choice != nullptr && choice->val != 3;
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}
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/* 更新狀態 */
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void makeChoice(vector<TreeNode *> &state, TreeNode *choice) {
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state.push_back(choice);
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}
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/* 恢復狀態 */
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void undoChoice(vector<TreeNode *> &state, TreeNode *choice) {
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state.pop_back();
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}
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/* 回溯演算法：例題三 */
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void backtrack(vector<TreeNode *> &state, vector<TreeNode *> &choices, vector<vector<TreeNode *>> &res) {
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// 檢查是否為解
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if (isSolution(state)) {
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// 記錄解
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recordSolution(state, res);
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}
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// 走訪所有選擇
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for (TreeNode *choice : choices) {
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// 剪枝：檢查選擇是否合法
|
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if (isValid(state, choice)) {
|
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// 嘗試：做出選擇，更新狀態
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makeChoice(state, choice);
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// 進行下一輪選擇
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vector<TreeNode *> nextChoices{choice->left, choice->right};
|
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backtrack(state, nextChoices, res);
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// 回退：撤銷選擇，恢復到之前的狀態
|
||||
undoChoice(state, choice);
|
||||
}
|
||||
}
|
||||
}
|
||||
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/* Driver Code */
|
||||
int main() {
|
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TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
|
||||
cout << "\n初始化二元樹" << endl;
|
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printTree(root);
|
||||
|
||||
// 回溯演算法
|
||||
vector<TreeNode *> state;
|
||||
vector<TreeNode *> choices = {root};
|
||||
vector<vector<TreeNode *>> res;
|
||||
backtrack(state, choices, res);
|
||||
|
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cout << "\n輸出所有根節點到節點 7 的路徑，要求路徑中不包含值為 3 的節點" << endl;
|
||||
for (vector<TreeNode *> &path : res) {
|
||||
vector<int> vals;
|
||||
for (TreeNode *node : path) {
|
||||
vals.push_back(node->val);
|
||||
}
|
||||
printVector(vals);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,57 @@
|
||||
/**
|
||||
* File: subset_sum_i.cpp
|
||||
* Created Time: 2023-06-21
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
#include "../utils/common.hpp"
|
||||
|
||||
/* 回溯演算法：子集和 I */
|
||||
void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
|
||||
// 子集和等於 target 時，記錄解
|
||||
if (target == 0) {
|
||||
res.push_back(state);
|
||||
return;
|
||||
}
|
||||
// 走訪所有選擇
|
||||
// 剪枝二：從 start 開始走訪，避免生成重複子集
|
||||
for (int i = start; i < choices.size(); i++) {
|
||||
// 剪枝一：若子集和超過 target ，則直接結束迴圈
|
||||
// 這是因為陣列已排序，後邊元素更大，子集和一定超過 target
|
||||
if (target - choices[i] < 0) {
|
||||
break;
|
||||
}
|
||||
// 嘗試：做出選擇，更新 target, start
|
||||
state.push_back(choices[i]);
|
||||
// 進行下一輪選擇
|
||||
backtrack(state, target - choices[i], choices, i, res);
|
||||
// 回退：撤銷選擇，恢復到之前的狀態
|
||||
state.pop_back();
|
||||
}
|
||||
}
|
||||
|
||||
/* 求解子集和 I */
|
||||
vector<vector<int>> subsetSumI(vector<int> &nums, int target) {
|
||||
vector<int> state; // 狀態（子集）
|
||||
sort(nums.begin(), nums.end()); // 對 nums 進行排序
|
||||
int start = 0; // 走訪起始點
|
||||
vector<vector<int>> res; // 結果串列（子集串列）
|
||||
backtrack(state, target, nums, start, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
int main() {
|
||||
vector<int> nums = {3, 4, 5};
|
||||
int target = 9;
|
||||
|
||||
vector<vector<int>> res = subsetSumI(nums, target);
|
||||
|
||||
cout << "輸入陣列 nums = ";
|
||||
printVector(nums);
|
||||
cout << "target = " << target << endl;
|
||||
cout << "所有和等於 " << target << " 的子集 res = " << endl;
|
||||
printVectorMatrix(res);
|
||||
|
||||
return 0;
|
||||
}
|
||||
@@ -0,0 +1,54 @@
|
||||
/**
|
||||
* File: subset_sum_i_naive.cpp
|
||||
* Created Time: 2023-06-21
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
#include "../utils/common.hpp"
|
||||
|
||||
/* 回溯演算法：子集和 I */
|
||||
void backtrack(vector<int> &state, int target, int total, vector<int> &choices, vector<vector<int>> &res) {
|
||||
// 子集和等於 target 時，記錄解
|
||||
if (total == target) {
|
||||
res.push_back(state);
|
||||
return;
|
||||
}
|
||||
// 走訪所有選擇
|
||||
for (size_t i = 0; i < choices.size(); i++) {
|
||||
// 剪枝：若子集和超過 target ，則跳過該選擇
|
||||
if (total + choices[i] > target) {
|
||||
continue;
|
||||
}
|
||||
// 嘗試：做出選擇，更新元素和 total
|
||||
state.push_back(choices[i]);
|
||||
// 進行下一輪選擇
|
||||
backtrack(state, target, total + choices[i], choices, res);
|
||||
// 回退：撤銷選擇，恢復到之前的狀態
|
||||
state.pop_back();
|
||||
}
|
||||
}
|
||||
|
||||
/* 求解子集和 I（包含重複子集） */
|
||||
vector<vector<int>> subsetSumINaive(vector<int> &nums, int target) {
|
||||
vector<int> state; // 狀態（子集）
|
||||
int total = 0; // 子集和
|
||||
vector<vector<int>> res; // 結果串列（子集串列）
|
||||
backtrack(state, target, total, nums, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
int main() {
|
||||
vector<int> nums = {3, 4, 5};
|
||||
int target = 9;
|
||||
|
||||
vector<vector<int>> res = subsetSumINaive(nums, target);
|
||||
|
||||
cout << "輸入陣列 nums = ";
|
||||
printVector(nums);
|
||||
cout << "target = " << target << endl;
|
||||
cout << "所有和等於 " << target << " 的子集 res = " << endl;
|
||||
printVectorMatrix(res);
|
||||
|
||||
return 0;
|
||||
}
|
||||
@@ -0,0 +1,62 @@
|
||||
/**
|
||||
* File: subset_sum_ii.cpp
|
||||
* Created Time: 2023-06-21
|
||||
* Author: krahets (krahets@163.com)
|
||||
*/
|
||||
|
||||
#include "../utils/common.hpp"
|
||||
|
||||
/* 回溯演算法：子集和 II */
|
||||
void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
|
||||
// 子集和等於 target 時，記錄解
|
||||
if (target == 0) {
|
||||
res.push_back(state);
|
||||
return;
|
||||
}
|
||||
// 走訪所有選擇
|
||||
// 剪枝二：從 start 開始走訪，避免生成重複子集
|
||||
// 剪枝三：從 start 開始走訪，避免重複選擇同一元素
|
||||
for (int i = start; i < choices.size(); i++) {
|
||||
// 剪枝一：若子集和超過 target ，則直接結束迴圈
|
||||
// 這是因為陣列已排序，後邊元素更大，子集和一定超過 target
|
||||
if (target - choices[i] < 0) {
|
||||
break;
|
||||
}
|
||||
// 剪枝四：如果該元素與左邊元素相等，說明該搜尋分支重複，直接跳過
|
||||
if (i > start && choices[i] == choices[i - 1]) {
|
||||
continue;
|
||||
}
|
||||
// 嘗試：做出選擇，更新 target, start
|
||||
state.push_back(choices[i]);
|
||||
// 進行下一輪選擇
|
||||
backtrack(state, target - choices[i], choices, i + 1, res);
|
||||
// 回退：撤銷選擇，恢復到之前的狀態
|
||||
state.pop_back();
|
||||
}
|
||||
}
|
||||
|
||||
/* 求解子集和 II */
|
||||
vector<vector<int>> subsetSumII(vector<int> &nums, int target) {
|
||||
vector<int> state; // 狀態（子集）
|
||||
sort(nums.begin(), nums.end()); // 對 nums 進行排序
|
||||
int start = 0; // 走訪起始點
|
||||
vector<vector<int>> res; // 結果串列（子集串列）
|
||||
backtrack(state, target, nums, start, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
int main() {
|
||||
vector<int> nums = {4, 4, 5};
|
||||
int target = 9;
|
||||
|
||||
vector<vector<int>> res = subsetSumII(nums, target);
|
||||
|
||||
cout << "輸入陣列 nums = ";
|
||||
printVector(nums);
|
||||
cout << "target = " << target << endl;
|
||||
cout << "所有和等於 " << target << " 的子集 res = " << endl;
|
||||
printVectorMatrix(res);
|
||||
|
||||
return 0;
|
||||
}
|
||||
Reference in New Issue
Block a user