mirror of
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synced 2024-12-24 03:36:29 +08:00
Bug fixes and improvements (#1298)
* Fix is_empty() implementation in the stack and queue chapter * Update en/CONTRIBUTING.md * Remove "剩余" from the state definition of knapsack problem * Sync zh and zh-hant versions * Update the stylesheets of code tabs * Fix quick_sort.rb * Fix TS code * Update chapter_paperbook * Upload the manuscript of 0.1 section * Fix binary_tree_dfs.rb * Bug fixes * Update README * Update README * Update README * Update README.md * Update README * Sync zh and zh-hant versions * Bug fixes
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Yudong Jin
GitHub
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61 changed files with 1606 additions and 145 deletions
32
README.md
32
README.md
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@ -17,24 +17,24 @@
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</p>
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<p align="center">
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<img src="https://www.hello-algo.com/index.assets/animation.gif" width="389">
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||||
<img src="https://www.hello-algo.com/index.assets/running_code.gif" width="389">
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||||
<img src="https://www.hello-algo.com/index.assets/animation.gif" width="395">
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||||
<img src="https://www.hello-algo.com/index.assets/running_code.gif" width="395">
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</p>
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<p align="center">
|
||||
<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB">
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||||
<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C">
|
||||
<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02">
|
||||
<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4">
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||||
<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8">
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||||
<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138">
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||||
<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30">
|
||||
<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6">
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||||
<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2">
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||||
<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000">
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||||
<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC">
|
||||
<img src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF">
|
||||
<img src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D">
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||||
<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB" alt="" />
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||||
<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02" alt="" />
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||||
<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C" alt="" />
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||||
<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC" alt="" />
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||||
<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4" alt="" />
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||||
<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30" alt="" />
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||||
<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8" alt="" />
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||||
<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138" alt="" />
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||||
<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000" alt="" />
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||||
<img src="https://img.shields.io/badge/Ruby-snow?logo=ruby&logoColor=CC342D" alt="" />
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||||
<img src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF" alt="" />
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||||
<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6" alt="" />
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||||
<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2" alt="" />
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</p>
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<p align="center">
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@ -51,7 +51,7 @@
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- 全书采用动画图解，内容清晰易懂、学习曲线平滑，引导初学者探索数据结构与算法的知识地图。
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- 源代码可一键运行，帮助读者在练习中提升编程技能，了解算法工作原理和数据结构底层实现。
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- 鼓励读者互助学习，提问与评论通常可在两日内得到回复。
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- 鼓励读者互助学习，欢迎大家在评论区提出问题、见解和建议。
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若本书对您有所帮助，请在页面右上角点个 Star :star: 支持一下，谢谢！
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@ -18,7 +18,7 @@ class ArrayStack:
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def is_empty(self) -> bool:
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"""判断栈是否为空"""
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return self._stack == []
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return self.size() == 0
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def push(self, item: int):
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"""入栈"""
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@ -30,7 +30,7 @@ class LinkedListDeque:
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def is_empty(self) -> bool:
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"""判断双向队列是否为空"""
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return self.size() == 0
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return self._size == 0
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def push(self, num: int, is_front: bool):
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"""入队操作"""
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@ -26,7 +26,7 @@ class LinkedListQueue:
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def is_empty(self) -> bool:
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"""判断队列是否为空"""
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return not self._front
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return self._size == 0
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def push(self, num: int):
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"""入队"""
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@ -25,7 +25,7 @@ class LinkedListStack:
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def is_empty(self) -> bool:
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"""判断栈是否为空"""
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return not self._peek
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return self._size == 0
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def push(self, val: int):
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"""入栈"""
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@ -136,16 +136,17 @@ class QuickSortTailCall
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end
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### Driver Code ###
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if __FILE__ == $0
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# 快速排序
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nums = [2, 4, 1, 0, 3, 5]
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QuickSort.quick_sort(nums, 0, nums.length - 1)
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puts "快速排序完成后 nums = #{nums}"
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# 快速排序（中位基准数优化）
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nums1 = [2, 4, 1, 0, 3, 5]
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QuickSortMedian.quick_sort(nums1, 0, nums1.length - 1)
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puts "快速排序（中位基准数优化）完成后 nums1 = #{nums1}"
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# 快速排序（尾递归优化）
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nums2 = [2, 4, 1, 0, 3, 5]
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QuickSortTailCall.quick_sort(nums2, 0, nums2.length - 1)
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@ -8,13 +8,13 @@ require_relative '../utils/tree_node'
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require_relative '../utils/print_util'
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### 前序遍历 ###
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def pre_oder(root)
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def pre_order(root)
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return if root.nil?
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# 访问优先级：根节点 -> 左子树 -> 右子树
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$res << root.val
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pre_oder(root.left)
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pre_oder(root.right)
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pre_order(root.left)
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pre_order(root.right)
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end
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### 中序遍历 ###
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@ -47,7 +47,7 @@ if __FILE__ == $0
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# 前序遍历
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$res = []
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pre_oder(root)
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pre_order(root)
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puts "\n前序遍历的节点打印序列 = #{$res}"
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# 中序遍历
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BIN
docs/assets/course/hello-algo-0.1-课程简介.pdf
Normal file
BIN
docs/assets/course/hello-algo-0.1-课程简介.pdf
Normal file
Binary file not shown.
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@ -64,7 +64,7 @@ $$
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并行优化在多核或多处理器的环境中尤其有效，因为系统可以同时处理多个子问题，更加充分地利用计算资源，从而显著减少总体的运行时间。
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比如在下图所示的“桶排序”中，我们将海量的数据平均分配到各个桶中，则可所有桶的排序任务分散到各个计算单元，完成后再合并结果。
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比如在下图所示的“桶排序”中，我们将海量的数据平均分配到各个桶中，则可将所有桶的排序任务分散到各个计算单元，完成后再合并结果。
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@ -18,15 +18,15 @@
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**第一步：思考每轮的决策，定义状态，从而得到 $dp$ 表**
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对于每个物品来说，不放入背包，背包容量不变；放入背包，背包容量减小。由此可得状态定义：当前物品编号 $i$ 和剩余背包容量 $c$ ，记为 $[i, c]$ 。
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对于每个物品来说，不放入背包，背包容量不变；放入背包，背包容量减小。由此可得状态定义：当前物品编号 $i$ 和背包容量 $c$ ，记为 $[i, c]$ 。
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状态 $[i, c]$ 对应的子问题为：**前 $i$ 个物品在剩余容量为 $c$ 的背包中的最大价值**，记为 $dp[i, c]$ 。
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状态 $[i, c]$ 对应的子问题为：**前 $i$ 个物品在容量为 $c$ 的背包中的最大价值**，记为 $dp[i, c]$ 。
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待求解的是 $dp[n, cap]$ ，因此需要一个尺寸为 $(n+1) \times (cap+1)$ 的二维 $dp$ 表。
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**第二步：找出最优子结构，进而推导出状态转移方程**
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当我们做出物品 $i$ 的决策后，剩余的是前 $i-1$ 个物品的决策，可分为以下两种情况。
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当我们做出物品 $i$ 的决策后，剩余的是前 $i-1$ 个物品决策的子问题，可分为以下两种情况。
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- **不放入物品 $i$** ：背包容量不变，状态变化为 $[i-1, c]$ 。
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- **放入物品 $i$** ：背包容量减少 $wgt[i-1]$ ，价值增加 $val[i-1]$ ，状态变化为 $[i-1, c-wgt[i-1]]$ 。
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@ -41,7 +41,7 @@ $$
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**第三步：确定边界条件和状态转移顺序**
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当无物品或无剩余背包容量时最大价值为 $0$ ，即首列 $dp[i, 0]$ 和首行 $dp[0, c]$ 都等于 $0$ 。
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当无物品或背包容量为 $0$ 时最大价值为 $0$ ，即首列 $dp[i, 0]$ 和首行 $dp[0, c]$ 都等于 $0$ 。
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当前状态 $[i, c]$ 从上方的状态 $[i-1, c]$ 和左上方的状态 $[i-1, c-wgt[i-1]]$ 转移而来，因此通过两层循环正序遍历整个 $dp$ 表即可。
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@ -11,7 +11,7 @@
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**背包问题**
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- 背包问题是最典型的动态规划问题之一，具有 0-1 背包、完全背包、多重背包等变种。
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- 0-1 背包的状态定义为前 $i$ 个物品在剩余容量为 $c$ 的背包中的最大价值。根据不放入背包和放入背包两种决策，可得到最优子结构，并构建出状态转移方程。在空间优化中，由于每个状态依赖正上方和左上方的状态，因此需要倒序遍历列表，避免左上方状态被覆盖。
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- 0-1 背包的状态定义为前 $i$ 个物品在容量为 $c$ 的背包中的最大价值。根据不放入背包和放入背包两种决策，可得到最优子结构，并构建出状态转移方程。在空间优化中，由于每个状态依赖正上方和左上方的状态，因此需要倒序遍历列表，避免左上方状态被覆盖。
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- 完全背包问题的每种物品的选取数量无限制，因此选择放入物品的状态转移与 0-1 背包问题不同。由于状态依赖正上方和正左方的状态，因此在空间优化中应当正序遍历。
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- 零钱兑换问题是完全背包问题的一个变种。它从求“最大”价值变为求“最小”硬币数量，因此状态转移方程中的 $\max()$ 应改为 $\min()$ 。从追求“不超过”背包容量到追求“恰好”凑出目标金额，因此使用 $amt + 1$ 来表示“无法凑出目标金额”的无效解。
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- 零钱兑换问题 II 从求“最少硬币数量”改为求“硬币组合数量”，状态转移方程相应地从 $\min()$ 改为求和运算符。
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@ -420,7 +420,7 @@
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## 堆的实现
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下文实现的是大顶堆。若要将其转换为小顶堆，只需将所有大小逻辑判断取逆（例如，将 $\geq$ 替换为 $\leq$ ）。感兴趣的读者可以自行实现。
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下文实现的是大顶堆。若要将其转换为小顶堆，只需将所有大小逻辑判断进行逆转（例如，将 $\geq$ 替换为 $\leq$ ）。感兴趣的读者可以自行实现。
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### 堆的存储与表示
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@ -36,17 +36,18 @@ status: new
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||||
- 采用全彩印刷，能够原汁原味地发挥出本书“动画图解”的优势。
|
||||
- 考究纸张材质，既保证色彩高度还原，也保留纸质书特有的质感。
|
||||
- 纸质版比网页版的格式更加规范，例如图中的公式使用斜体。
|
||||
- 在不提升定价的前提下，附赠思维导图折页、书签。
|
||||
- 纸质书、网页版、PDF 版内容同步，随意切换阅读。
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||||
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||||
!!! tip
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||||
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||||
由于纸质书和网页版的同步成本较大，因此可能会有一些细节上的不同，请您见谅！
|
||||
由于纸质书和网页版的同步难度较大，因此可能会有一些细节上的不同，请您见谅！
|
||||
|
||||
当然，纸质书也有一些值得大家入手前考虑的地方：
|
||||
|
||||
- 使用 Python 语言，可能不匹配你的主语言（也许可以趁此机会练习 Python）。
|
||||
- 全彩印刷虽然大幅提升了阅读体验，但价格会比黑白印刷高一些。
|
||||
- 使用 Python 语言，可能不匹配你的主语言（可以把 Python 看作伪代码，重在理解思路）。
|
||||
- 全彩印刷虽然大幅提升了图解和代码的阅读体验，但价格会比黑白印刷高一些。
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!!! tip
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@ -71,7 +71,7 @@ $$
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## 算法特性
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- **时间复杂度为 $O(n + m)$** ：涉及遍历 `nums` 和遍历 `counter` ，都使用线性时间。一般情况下 $n \gg m$ ，时间复杂度趋于 $O(n)$ 。
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- **时间复杂度为 $O(n + m)$、非自适应排序** ：涉及遍历 `nums` 和遍历 `counter` ，都使用线性时间。一般情况下 $n \gg m$ ，时间复杂度趋于 $O(n)$ 。
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- **空间复杂度为 $O(n + m)$、非原地排序**：借助了长度分别为 $n$ 和 $m$ 的数组 `res` 和 `counter` 。
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- **稳定排序**：由于向 `res` 中填充元素的顺序是“从右向左”的，因此倒序遍历 `nums` 可以避免改变相等元素之间的相对位置，从而实现稳定排序。实际上，正序遍历 `nums` 也可以得到正确的排序结果，但结果是非稳定的。
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@ -36,6 +36,6 @@ $$
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相较于计数排序，基数排序适用于数值范围较大的情况，**但前提是数据必须可以表示为固定位数的格式，且位数不能过大**。例如，浮点数不适合使用基数排序，因为其位数 $k$ 过大，可能导致时间复杂度 $O(nk) \gg O(n^2)$ 。
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||||
- **时间复杂度为 $O(nk)$**：设数据量为 $n$、数据为 $d$ 进制、最大位数为 $k$ ，则对某一位执行计数排序使用 $O(n + d)$ 时间，排序所有 $k$ 位使用 $O((n + d)k)$ 时间。通常情况下，$d$ 和 $k$ 都相对较小，时间复杂度趋向 $O(n)$ 。
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- **时间复杂度为 $O(nk)$、非自适应排序**：设数据量为 $n$、数据为 $d$ 进制、最大位数为 $k$ ，则对某一位执行计数排序使用 $O(n + d)$ 时间，排序所有 $k$ 位使用 $O((n + d)k)$ 时间。通常情况下，$d$ 和 $k$ 都相对较小，时间复杂度趋向 $O(n)$ 。
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- **空间复杂度为 $O(n + d)$、非原地排序**：与计数排序相同，基数排序需要借助长度为 $n$ 和 $d$ 的数组 `res` 和 `counter` 。
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- **稳定排序**：当计数排序稳定时，基数排序也稳定；当计数排序不稳定时，基数排序无法保证得到正确的排序结果。
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@ -41,13 +41,15 @@ Don't hesitate to join us via WeChat `krahets-jyd` or on [Discord](https://disco
|
|||
**Accuracy**:
|
||||
|
||||
- Maintain consistency in terminology across translations by referring to the [Terminology](https://www.hello-algo.com/chapter_appendix/terminology/) section.
|
||||
- Prioritize technical accuracy and maintain the tone and style of the Chinese version. If you think changing the original meaning is necessary, please first submit a PR to modify the Chinese version.
|
||||
- Prioritize technical accuracy and maintain the tone and style of the Chinese version.
|
||||
- Always take into account the content and context of the Chinese version to ensure modifications are accurate and comprehensive.
|
||||
|
||||
**Authenticity**:
|
||||
|
||||
- Translations should flow naturally and fluently, adhering to English expression conventions.
|
||||
- Always consider the context of the content to harmonize the article.
|
||||
- Be aware of cultural differences between Chinese and English. For instance, Chinese "pinyin" does not exist in English.
|
||||
- If the optimized sentence could alter the original meaning, please add a comment for discussion.
|
||||
|
||||
**Formatting**:
|
||||
|
||||
|
|
|
|||
32
en/README.md
32
en/README.md
|
|
@ -15,24 +15,24 @@
|
|||
</p>
|
||||
|
||||
<p align="center">
|
||||
<img src="https://www.hello-algo.com/en/index.assets/animation.gif" width="389">
|
||||
<img src="https://www.hello-algo.com/en/index.assets/running_code.gif" width="389">
|
||||
<img src="https://www.hello-algo.com/index.assets/animation.gif" width="395">
|
||||
<img src="https://www.hello-algo.com/index.assets/running_code.gif" width="395">
|
||||
</p>
|
||||
|
||||
<p align="center">
|
||||
<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB">
|
||||
<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C">
|
||||
<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02">
|
||||
<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4">
|
||||
<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8">
|
||||
<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138">
|
||||
<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30">
|
||||
<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6">
|
||||
<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2">
|
||||
<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000">
|
||||
<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC">
|
||||
<img src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF">
|
||||
<img src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D">
|
||||
<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB" alt="" />
|
||||
<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02" alt="" />
|
||||
<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C" alt="" />
|
||||
<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC" alt="" />
|
||||
<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4" alt="" />
|
||||
<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30" alt="" />
|
||||
<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8" alt="" />
|
||||
<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138" alt="" />
|
||||
<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000" alt="" />
|
||||
<img src="https://img.shields.io/badge/Ruby-snow?logo=ruby&logoColor=CC342D" alt="" />
|
||||
<img src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF" alt="" />
|
||||
<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6" alt="" />
|
||||
<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2" alt="" />
|
||||
</p>
|
||||
|
||||
<p align="center">
|
||||
|
|
@ -49,7 +49,7 @@ This open-source project aims to create a free and beginner-friendly crash cours
|
|||
|
||||
- Animated illustrations, easy-to-understand content, and a smooth learning curve help beginners explore the "knowledge map" of data structures and algorithms.
|
||||
- Run code with just one click, helping readers improve their programming skills and understand the working principle of algorithms and the underlying implementation of data structures.
|
||||
- We encourage readers to help each other. Questions and comments are usually replied to within two days.
|
||||
- Encouraging learning through teaching, feel free to share your questions, insights, and suggestions.
|
||||
|
||||
If you find this book helpful, please give it a Star :star: to support us, thank you!
|
||||
|
||||
|
|
|
|||
|
|
@ -209,7 +209,11 @@ body {
|
|||
|
||||
/* code block tabs */
|
||||
.md-typeset .tabbed-labels>label {
|
||||
font-size: 0.545rem;
|
||||
font-size: 0.61rem;
|
||||
}
|
||||
|
||||
.md-typeset .tabbed-labels--linked>label>a {
|
||||
padding: .78125em 1.0em .625em;
|
||||
}
|
||||
|
||||
/* header banner */
|
||||
|
|
|
|||
|
|
@ -15,24 +15,24 @@
|
|||
</p>
|
||||
|
||||
<p align="center">
|
||||
<img src="https://www.hello-algo.com/index.assets/animation.gif" width="389">
|
||||
<img src="https://www.hello-algo.com/index.assets/running_code.gif" width="389">
|
||||
<img src="https://www.hello-algo.com/index.assets/animation.gif" width="395">
|
||||
<img src="https://www.hello-algo.com/index.assets/running_code.gif" width="395">
|
||||
</p>
|
||||
|
||||
<p align="center">
|
||||
<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB">
|
||||
<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C">
|
||||
<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02">
|
||||
<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4">
|
||||
<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8">
|
||||
<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138">
|
||||
<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30">
|
||||
<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6">
|
||||
<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2">
|
||||
<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000">
|
||||
<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC">
|
||||
<img src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF">
|
||||
<img src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D">
|
||||
<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB" alt="" />
|
||||
<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02" alt="" />
|
||||
<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C" alt="" />
|
||||
<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC" alt="" />
|
||||
<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4" alt="" />
|
||||
<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30" alt="" />
|
||||
<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8" alt="" />
|
||||
<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138" alt="" />
|
||||
<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000" alt="" />
|
||||
<img src="https://img.shields.io/badge/Ruby-snow?logo=ruby&logoColor=CC342D" alt="" />
|
||||
<img src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF" alt="" />
|
||||
<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6" alt="" />
|
||||
<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2" alt="" />
|
||||
</p>
|
||||
|
||||
<p align="center">
|
||||
|
|
@ -49,7 +49,7 @@
|
|||
|
||||
- 全書採用動畫圖解，內容清晰易懂、學習曲線平滑，引導初學者探索資料結構與演算法的知識地圖。
|
||||
- 源程式碼可一鍵執行，幫助讀者在練習中提升程式設計技能，瞭解演算法工作原理和資料結構底層實現。
|
||||
- 鼓勵讀者互助學習，提問與評論通常可在兩日內得到回覆。
|
||||
- 鼓勵讀者互助學習，歡迎大家在評論區提出問題、見解和建議。
|
||||
|
||||
若本書對您有所幫助，請在頁面右上角點個 Star :star: 支持一下，謝謝！
|
||||
|
||||
|
|
|
|||
|
|
@ -4,8 +4,8 @@
|
|||
* Author: MolDuM (moldum@163.com)、Reanon (793584285@qq.com)
|
||||
*/
|
||||
|
||||
#ifndef C_INCLUDE_H
|
||||
#define C_INCLUDE_H
|
||||
#ifndef COMMON_H
|
||||
#define COMMON_H
|
||||
|
||||
#include <assert.h>
|
||||
#include <stdbool.h>
|
||||
|
|
@ -33,4 +33,4 @@ extern "C" {
|
|||
}
|
||||
#endif
|
||||
|
||||
#endif // C_INCLUDE_H
|
||||
#endif // COMMON_H
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@ class ArrayStack:
|
|||
|
||||
def is_empty(self) -> bool:
|
||||
"""判斷堆疊是否為空"""
|
||||
return self._stack == []
|
||||
return self._size == 0
|
||||
|
||||
def push(self, item: int):
|
||||
"""入堆疊"""
|
||||
|
|
|
|||
|
|
@ -30,7 +30,7 @@ class LinkedListDeque:
|
|||
|
||||
def is_empty(self) -> bool:
|
||||
"""判斷雙向佇列是否為空"""
|
||||
return self.size() == 0
|
||||
return self._size == 0
|
||||
|
||||
def push(self, num: int, is_front: bool):
|
||||
"""入列操作"""
|
||||
|
|
|
|||
|
|
@ -26,7 +26,7 @@ class LinkedListQueue:
|
|||
|
||||
def is_empty(self) -> bool:
|
||||
"""判斷佇列是否為空"""
|
||||
return not self._front
|
||||
return self._size == 0
|
||||
|
||||
def push(self, num: int):
|
||||
"""入列"""
|
||||
|
|
|
|||
|
|
@ -25,7 +25,7 @@ class LinkedListStack:
|
|||
|
||||
def is_empty(self) -> bool:
|
||||
"""判斷堆疊是否為空"""
|
||||
return not self._peek
|
||||
return self._size == 0
|
||||
|
||||
def push(self, val: int):
|
||||
"""入堆疊"""
|
||||
|
|
|
|||
121
zh-hant/codes/ruby/chapter_hashing/array_hash_map.rb
Normal file
121
zh-hant/codes/ruby/chapter_hashing/array_hash_map.rb
Normal file
|
|
@ -0,0 +1,121 @@
|
|||
=begin
|
||||
File: array_hash_map.rb
|
||||
Created Time: 2024-04-13
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
### 鍵值對 ###
|
||||
class Pair
|
||||
attr_accessor :key, :val
|
||||
|
||||
def initialize(key, val)
|
||||
@key = key
|
||||
@val = val
|
||||
end
|
||||
end
|
||||
|
||||
### 基於陣列實現的雜湊表 ###
|
||||
class ArrayHashMap
|
||||
### 建構子 ###
|
||||
def initialize
|
||||
# 初始化陣列，包含 100 個桶
|
||||
@buckets = Array.new(100)
|
||||
end
|
||||
|
||||
### 雜湊函式 ###
|
||||
def hash_func(key)
|
||||
index = key % 100
|
||||
end
|
||||
|
||||
### 查詢操作 ###
|
||||
def get(key)
|
||||
index = hash_func(key)
|
||||
pair = @buckets[index]
|
||||
|
||||
return if pair.nil?
|
||||
pair.val
|
||||
end
|
||||
|
||||
### 新增操作 ###
|
||||
def put(key, val)
|
||||
pair = Pair.new(key, val)
|
||||
index = hash_func(key)
|
||||
@buckets[index] = pair
|
||||
end
|
||||
|
||||
### 刪除操作 ###
|
||||
def remove(key)
|
||||
index = hash_func(key)
|
||||
# 置為 nil ，代表刪除
|
||||
@buckets[index] = nil
|
||||
end
|
||||
|
||||
### 獲取所有鍵值對 ###
|
||||
def entry_set
|
||||
result = []
|
||||
@buckets.each { |pair| result << pair unless pair.nil? }
|
||||
result
|
||||
end
|
||||
|
||||
### 獲取所有鍵 ###
|
||||
def key_set
|
||||
result = []
|
||||
@buckets.each { |pair| result << pair.key unless pair.nil? }
|
||||
result
|
||||
end
|
||||
|
||||
### 獲取所有值 ###
|
||||
def value_set
|
||||
result = []
|
||||
@buckets.each { |pair| result << pair.val unless pair.nil? }
|
||||
result
|
||||
end
|
||||
|
||||
### 列印雜湊表 ###
|
||||
def print
|
||||
@buckets.each { |pair| puts "#{pair.key} -> #{pair.val}" unless pair.nil? }
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化雜湊表
|
||||
hmap = ArrayHashMap.new
|
||||
|
||||
# 新增操作
|
||||
# 在雜湊表中新增鍵值對 (key, value)
|
||||
hmap.put(12836, "小哈")
|
||||
hmap.put(15937, "小囉")
|
||||
hmap.put(16750, "小算")
|
||||
hmap.put(13276, "小法")
|
||||
hmap.put(10583, "小鴨")
|
||||
puts "\n新增完成後，雜湊表為\nKey -> Value"
|
||||
hmap.print
|
||||
|
||||
# 查詢操作
|
||||
# 向雜湊表中輸入鍵 key , 得到值 value
|
||||
name = hmap.get(15937)
|
||||
puts "\n輸入學號 15937 ，查詢到姓名 #{name}"
|
||||
|
||||
# 刪除操作
|
||||
# 在雜湊表中刪除值對 (key, value)
|
||||
hmap.remove(10583)
|
||||
puts "\n刪除 10583 後，雜湊表為\nKey -> Value"
|
||||
hmap.print
|
||||
|
||||
# 走訪雜湊表
|
||||
puts "\n走訪鍵值對 Key->Value"
|
||||
for pair in hmap.entry_set
|
||||
puts "#{pair.key} -> #{pair.val}"
|
||||
end
|
||||
|
||||
puts "\n單獨篇走訪鍵 Key"
|
||||
for key in hmap.key_set
|
||||
puts key
|
||||
end
|
||||
|
||||
puts "\n單獨走訪值 Value"
|
||||
for val in hmap.value_set
|
||||
puts val
|
||||
end
|
||||
end
|
||||
34
zh-hant/codes/ruby/chapter_hashing/built_in_hash.rb
Normal file
34
zh-hant/codes/ruby/chapter_hashing/built_in_hash.rb
Normal file
|
|
@ -0,0 +1,34 @@
|
|||
=begin
|
||||
File: built_in_hash.rb
|
||||
Created Time: 2024-04-13
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/list_node'
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
num = 3
|
||||
hash_num = num.hash
|
||||
puts "整數 #{num} 的雜湊值為 #{hash_num}"
|
||||
|
||||
bol = true
|
||||
hash_bol = bol.hash
|
||||
puts "布林量 #{bol} 的雜湊值為 #{hash_bol}"
|
||||
|
||||
dec = 3.14159
|
||||
hash_dec = dec.hash
|
||||
puts "小數 #{dec} 的雜湊值為 #{hash_dec}"
|
||||
|
||||
str = "Hello 演算法"
|
||||
hash_str = str.hash
|
||||
puts "字串 #{str} 的雜湊值為 #{hash_str}"
|
||||
|
||||
tup = [12836, '小哈']
|
||||
hash_tup = tup.hash
|
||||
puts "元組 #{tup} 的雜湊值為 #{hash_tup}"
|
||||
|
||||
obj = ListNode.new(0)
|
||||
hash_obj = obj.hash
|
||||
puts "節點物件 #{obj} 的雜湊值為 #{hash_obj}"
|
||||
end
|
||||
44
zh-hant/codes/ruby/chapter_hashing/hash_map.rb
Normal file
44
zh-hant/codes/ruby/chapter_hashing/hash_map.rb
Normal file
|
|
@ -0,0 +1,44 @@
|
|||
=begin
|
||||
File: hash_map.rb
|
||||
Created Time: 2024-04-14
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化雜湊表
|
||||
hmap = {}
|
||||
|
||||
# 新增操作
|
||||
# 在雜湊表中新增鍵值對 (key, value)
|
||||
hmap[12836] = "小哈"
|
||||
hmap[15937] = "小囉"
|
||||
hmap[16750] = "小算"
|
||||
hmap[13276] = "小法"
|
||||
hmap[10583] = "小鴨"
|
||||
puts "\n新增完成後，雜湊表為\nKey -> Value"
|
||||
print_hash_map(hmap)
|
||||
|
||||
# 查詢操作
|
||||
# 向雜湊表中輸入鍵 key ，得到值 value
|
||||
name = hmap[15937]
|
||||
puts "\n輸入學號 15937 ，查詢到姓名 #{name}"
|
||||
|
||||
# 刪除操作
|
||||
# 在雜湊表中刪除鍵值對 (key, value)
|
||||
hmap.delete(10583)
|
||||
puts "\n刪除 10583 後，雜湊表為\nKey -> Value"
|
||||
print_hash_map(hmap)
|
||||
|
||||
# 走訪雜湊表
|
||||
puts "\n走訪鍵值對 Key->Value"
|
||||
hmap.entries.each { |key, value| puts "#{key} -> #{value}" }
|
||||
|
||||
puts "\n單獨走訪鍵 Key"
|
||||
hmap.keys.each { |key| puts key }
|
||||
|
||||
puts "\n單獨走訪值 Value"
|
||||
hmap.values.each { |val| puts val }
|
||||
end
|
||||
128
zh-hant/codes/ruby/chapter_hashing/hash_map_chaining.rb
Normal file
128
zh-hant/codes/ruby/chapter_hashing/hash_map_chaining.rb
Normal file
|
|
@ -0,0 +1,128 @@
|
|||
=begin
|
||||
File: hash_map_chaining.rb
|
||||
Created Time: 2024-04-13
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative './array_hash_map'
|
||||
|
||||
### 鍵式位址雜湊表 ###
|
||||
class HashMapChaining
|
||||
### 建構子 ###
|
||||
def initialize
|
||||
@size = 0 # 鍵值對數量
|
||||
@capacity = 4 # 雜湊表容量
|
||||
@load_thres = 2.0 / 3.0 # 觸發擴容的負載因子閾值
|
||||
@extend_ratio = 2 # 擴容倍數
|
||||
@buckets = Array.new(@capacity) { [] } # 桶陣列
|
||||
end
|
||||
|
||||
### 雜湊函式 ###
|
||||
def hash_func(key)
|
||||
key % @capacity
|
||||
end
|
||||
|
||||
### 負載因子 ###
|
||||
def load_factor
|
||||
@size / @capacity
|
||||
end
|
||||
|
||||
### 查詢操作 ###
|
||||
def get(key)
|
||||
index = hash_func(key)
|
||||
bucket = @buckets[index]
|
||||
# 走訪桶，若找到 key ，則返回對應 val
|
||||
for pair in bucket
|
||||
return pair.val if pair.key == key
|
||||
end
|
||||
# 若未找到 key , 則返回 nil
|
||||
nil
|
||||
end
|
||||
|
||||
### 新增操作 ###
|
||||
def put(key, val)
|
||||
# 當負載因子超過閾值時，執行擴容
|
||||
extend if load_factor > @load_thres
|
||||
index = hash_func(key)
|
||||
bucket = @buckets[index]
|
||||
# 走訪桶，若遇到指定 key ，則更新對應 val 並返回
|
||||
for pair in bucket
|
||||
if pair.key == key
|
||||
pair.val = val
|
||||
return
|
||||
end
|
||||
end
|
||||
# 若無該 key ，則將鍵值對新增至尾部
|
||||
pair = Pair.new(key, val)
|
||||
bucket << pair
|
||||
@size += 1
|
||||
end
|
||||
|
||||
### 刪除操作 ###
|
||||
def remove(key)
|
||||
index = hash_func(key)
|
||||
bucket = @buckets[index]
|
||||
# 走訪桶，從中刪除鍵值對
|
||||
for pair in bucket
|
||||
if pair.key == key
|
||||
bucket.delete(pair)
|
||||
@size -= 1
|
||||
break
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### 擴容雜湊表 ###
|
||||
def extend
|
||||
# 暫存原雜湊表
|
||||
buckets = @buckets
|
||||
# 初始化擴容後的新雜湊表
|
||||
@capacity *= @extend_ratio
|
||||
@buckets = Array.new(@capacity) { [] }
|
||||
@size = 0
|
||||
# 將鍵值對從原雜湊表搬運至新雜湊表
|
||||
for bucket in buckets
|
||||
for pair in bucket
|
||||
put(pair.key, pair.val)
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### 列印雜湊表 ###
|
||||
def print
|
||||
for bucket in @buckets
|
||||
res = []
|
||||
for pair in bucket
|
||||
res << "#{pair.key} -> #{pair.val}"
|
||||
end
|
||||
pp res
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
### 初始化雜湊表
|
||||
hashmap = HashMapChaining.new
|
||||
|
||||
# 新增操作
|
||||
# 在雜湊表中新增鍵值對 (key, value)
|
||||
hashmap.put(12836, "小哈")
|
||||
hashmap.put(15937, "小囉")
|
||||
hashmap.put(16750, "小算")
|
||||
hashmap.put(13276, "小法")
|
||||
hashmap.put(10583, "小鴨")
|
||||
puts "\n新增完成後，雜湊表為\n[Key1 -> Value1, Key2 -> Value2, ...]"
|
||||
hashmap.print
|
||||
|
||||
# 查詢操作
|
||||
# 向雜湊表中輸入鍵 key ，得到值 value
|
||||
name = hashmap.get(13276)
|
||||
puts "\n輸入學號 13276 ，查詢到姓名 #{name}"
|
||||
|
||||
# 刪除操作
|
||||
# 在雜湊表中刪除鍵值對 (key, value)
|
||||
hashmap.remove(12836)
|
||||
puts "\n刪除 12836 後，雜湊表為\n[Key1 -> Value1, Key2 -> Value2, ...]"
|
||||
hashmap.print
|
||||
end
|
||||
147
zh-hant/codes/ruby/chapter_hashing/hash_map_open_addressing.rb
Normal file
147
zh-hant/codes/ruby/chapter_hashing/hash_map_open_addressing.rb
Normal file
|
|
@ -0,0 +1,147 @@
|
|||
=begin
|
||||
File: hash_map_open_addressing.rb
|
||||
Created Time: 2024-04-13
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative './array_hash_map'
|
||||
|
||||
### 開放定址雜湊表 ###
|
||||
class HashMapOpenAddressing
|
||||
TOMBSTONE = Pair.new(-1, '-1') # 刪除標記
|
||||
|
||||
### 建構子 ###
|
||||
def initialize
|
||||
@size = 0 # 鍵值對數量
|
||||
@capacity = 4 # 雜湊表容量
|
||||
@load_thres = 2.0 / 3.0 # 觸發擴容的負載因子閾值
|
||||
@extend_ratio = 2 # 擴容倍數
|
||||
@buckets = Array.new(@capacity) # 桶陣列
|
||||
end
|
||||
|
||||
### 雜湊函式 ###
|
||||
def hash_func(key)
|
||||
key % @capacity
|
||||
end
|
||||
|
||||
### 負載因子 ###
|
||||
def load_factor
|
||||
@size / @capacity
|
||||
end
|
||||
|
||||
### 搜尋 key 對應的桶索引 ###
|
||||
def find_bucket(key)
|
||||
index = hash_func(key)
|
||||
first_tombstone = -1
|
||||
# 線性探查，當遇到空桶時跳出
|
||||
while !@buckets[index].nil?
|
||||
# 若遇到 key ，返回對應的桶索引
|
||||
if @buckets[index].key == key
|
||||
# 若之前遇到了刪除標記，則將鍵值對移動至該索引處
|
||||
if first_tombstone != -1
|
||||
@buckets[first_tombstone] = @buckets[index]
|
||||
@buckets[index] = TOMBSTONE
|
||||
return first_tombstone # 返回移動後的桶索引
|
||||
end
|
||||
return index # 返回桶索引
|
||||
end
|
||||
# 記錄遇到的首個刪除標記
|
||||
first_tombstone = index if first_tombstone == -1 && @buckets[index] == TOMBSTONE
|
||||
# 計算桶索引，越過尾部則返回頭部
|
||||
index = (index + 1) % @capacity
|
||||
end
|
||||
# 若 key 不存在，則返回新增點的索引
|
||||
first_tombstone == -1 ? index : first_tombstone
|
||||
end
|
||||
|
||||
### 查詢操作 ###
|
||||
def get(key)
|
||||
# 搜尋 key 對應的桶索引
|
||||
index = find_bucket(key)
|
||||
# 若找到鍵值對，則返回對應 val
|
||||
return @buckets[index].val unless [nil, TOMBSTONE].include?(@buckets[index])
|
||||
# 若鍵值對不存在，則返回 nil
|
||||
nil
|
||||
end
|
||||
|
||||
### 新增操作 ###
|
||||
def put(key, val)
|
||||
# 當負載因子超過閾值時，執行擴容
|
||||
extend if load_factor > @load_thres
|
||||
# 搜尋 key 對應的桶索引
|
||||
index = find_bucket(key)
|
||||
# 若找到鍵值對，則覆蓋 val 開返回
|
||||
unless [nil, TOMBSTONE].include?(@buckets[index])
|
||||
@buckets[index].val = val
|
||||
return
|
||||
end
|
||||
# 若鍵值對不存在，則新增該鍵值對
|
||||
@buckets[index] = Pair.new(key, val)
|
||||
@size += 1
|
||||
end
|
||||
|
||||
### 刪除操作 ###
|
||||
def remove(key)
|
||||
# 搜尋 key 對應的桶索引
|
||||
index = find_bucket(key)
|
||||
# 若找到鍵值對，則用刪除標記覆蓋它
|
||||
unless [nil, TOMBSTONE].include?(@buckets[index])
|
||||
@buckets[index] = TOMBSTONE
|
||||
@size -= 1
|
||||
end
|
||||
end
|
||||
|
||||
### 擴容雜湊表 ###
|
||||
def extend
|
||||
# 暫存原雜湊表
|
||||
buckets_tmp = @buckets
|
||||
# 初始化擴容後的新雜湊表
|
||||
@capacity *= @extend_ratio
|
||||
@buckets = Array.new(@capacity)
|
||||
@size = 0
|
||||
# 將鍵值對從原雜湊表搬運至新雜湊表
|
||||
for pair in buckets_tmp
|
||||
put(pair.key, pair.val) unless [nil, TOMBSTONE].include?(pair)
|
||||
end
|
||||
end
|
||||
|
||||
### 列印雜湊表 ###
|
||||
def print
|
||||
for pair in @buckets
|
||||
if pair.nil?
|
||||
puts "Nil"
|
||||
elsif pair == TOMBSTONE
|
||||
puts "TOMBSTONE"
|
||||
else
|
||||
puts "#{pair.key} -> #{pair.val}"
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化雜湊表
|
||||
hashmap = HashMapOpenAddressing.new
|
||||
|
||||
# 新增操作
|
||||
# 在雜湊表中新增鍵值對 (key, val)
|
||||
hashmap.put(12836, "小哈")
|
||||
hashmap.put(15937, "小囉")
|
||||
hashmap.put(16750, "小算")
|
||||
hashmap.put(13276, "小法")
|
||||
hashmap.put(10583, "小鴨")
|
||||
puts "\n新增完成後，雜湊表為\nKey -> Value"
|
||||
hashmap.print
|
||||
|
||||
# 查詢操作
|
||||
# 向雜湊表中輸入鍵 key ，得到值 val
|
||||
name = hashmap.get(13276)
|
||||
puts "\n輸入學號 13276 ，查詢到姓名 #{name}"
|
||||
|
||||
# 刪除操作
|
||||
# 在雜湊表中刪除鍵值對 (key, val)
|
||||
hashmap.remove(16750)
|
||||
puts "\n刪除 16750 後，雜湊表為\nKey -> Value"
|
||||
hashmap.print
|
||||
end
|
||||
62
zh-hant/codes/ruby/chapter_hashing/simple_hash.rb
Normal file
62
zh-hant/codes/ruby/chapter_hashing/simple_hash.rb
Normal file
|
|
@ -0,0 +1,62 @@
|
|||
=begin
|
||||
File: simple_hash.rb
|
||||
Created Time: 2024-04-14
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
### 加法雜湊 ###
|
||||
def add_hash(key)
|
||||
hash = 0
|
||||
modulus = 1_000_000_007
|
||||
|
||||
key.each_char { |c| hash += c.ord }
|
||||
|
||||
hash % modulus
|
||||
end
|
||||
|
||||
### 乘法雜湊 ###
|
||||
def mul_hash(key)
|
||||
hash = 0
|
||||
modulus = 1_000_000_007
|
||||
|
||||
key.each_char { |c| hash = 31 * hash + c.ord }
|
||||
|
||||
hash % modulus
|
||||
end
|
||||
|
||||
### 互斥或雜湊 ###
|
||||
def xor_hash(key)
|
||||
hash = 0
|
||||
modulus = 1_000_000_007
|
||||
|
||||
key.each_char { |c| hash ^= c.ord }
|
||||
|
||||
hash % modulus
|
||||
end
|
||||
|
||||
### 旋轉雜湊 ###
|
||||
def rot_hash(key)
|
||||
hash = 0
|
||||
modulus = 1_000_000_007
|
||||
|
||||
key.each_char { |c| hash = (hash << 4) ^ (hash >> 28) ^ c.ord }
|
||||
|
||||
hash % modulus
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
key = "Hello 演算法"
|
||||
|
||||
hash = add_hash(key)
|
||||
puts "加法雜湊值為 #{hash}"
|
||||
|
||||
hash = mul_hash(key)
|
||||
puts "乘法雜湊值為 #{hash}"
|
||||
|
||||
hash = xor_hash(key)
|
||||
puts "互斥或雜湊值為 #{hash}"
|
||||
|
||||
hash = rot_hash(key)
|
||||
puts "旋轉雜湊值為 #{hash}"
|
||||
end
|
||||
154
zh-hant/codes/ruby/chapter_sorting/quick_sort.rb
Normal file
154
zh-hant/codes/ruby/chapter_sorting/quick_sort.rb
Normal file
|
|
@ -0,0 +1,154 @@
|
|||
=begin
|
||||
File: quick_sort.rb
|
||||
Created Time: 2024-04-01
|
||||
Author: Cy (3739004@gmail.com), Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
### 快速排序類別 ###
|
||||
class QuickSort
|
||||
class << self
|
||||
### 哨兵劃分 ###
|
||||
def partition(nums, left, right)
|
||||
|
||||
# 以 nums[left] 為基準數
|
||||
i, j = left, right
|
||||
while i < j
|
||||
while i < j && nums[j] >= nums[left]
|
||||
j -= 1 # 從右向左找首個小於基準數的元素
|
||||
end
|
||||
while i < j && nums[i] <= nums[left]
|
||||
i += 1 # 從左向右找首個大於基準數的元素
|
||||
end
|
||||
# 元素交換
|
||||
nums[i], nums[j] = nums[j], nums[i]
|
||||
end
|
||||
# 將基準數交換至兩子陣列的分界線
|
||||
nums[i], nums[left] = nums[left], nums[i]
|
||||
i # 返回基準數的索引
|
||||
end
|
||||
|
||||
### 快速排序類別 ###
|
||||
def quick_sort(nums, left, right)
|
||||
# 子陣列長度不為 1 時遞迴
|
||||
if left < right
|
||||
# 哨兵劃分
|
||||
pivot = partition(nums, left, right)
|
||||
# 遞迴左子陣列、右子陣列
|
||||
quick_sort(nums, left, pivot - 1)
|
||||
quick_sort(nums, pivot + 1, right)
|
||||
end
|
||||
nums
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### 快速排序類別（中位數最佳化）###
|
||||
class QuickSortMedian
|
||||
class << self
|
||||
### 選取三個候選元素的中位數 ###
|
||||
def median_three(nums, left, mid, right)
|
||||
# 選取三個候選元素的中位數
|
||||
_l, _m, _r = nums[left], nums[mid], nums[right]
|
||||
# m 在 l 和 r 之間
|
||||
return mid if (_l <= _m && _m <= _r) || (_r <= _m && _m <= _l)
|
||||
# l 在 m 和 r 之間
|
||||
return left if (_m <= _l && _l <= _r) || (_r <= _l && _l <= _m)
|
||||
return right
|
||||
end
|
||||
|
||||
### 哨兵劃分（三數取中值）###
|
||||
def partition(nums, left, right)
|
||||
### 以 nums[left] 為基準數
|
||||
med = median_three(nums, left, (left + right) / 2, right)
|
||||
# 將中位數交換至陣列最左斷
|
||||
nums[left], nums[med] = nums[med], nums[left]
|
||||
i, j = left, right
|
||||
while i < j
|
||||
while i < j && nums[j] >= nums[left]
|
||||
j -= 1 # 從右向左找首個小於基準數的元素
|
||||
end
|
||||
while i < j && nums[i] <= nums[left]
|
||||
i += 1 # 從左向右找首個大於基準數的元素
|
||||
end
|
||||
# 元素交換
|
||||
nums[i], nums[j] = nums[j], nums[i]
|
||||
end
|
||||
# 將基準數交換至兩子陣列的分界線
|
||||
nums[i], nums[left] = nums[left], nums[i]
|
||||
i # 返回基準數的索引
|
||||
end
|
||||
|
||||
### 快速排序 ###
|
||||
def quick_sort(nums, left, right)
|
||||
# 子陣列長度不為 1 時遞迴
|
||||
if left < right
|
||||
# 哨兵劃分
|
||||
pivot = partition(nums, left, right)
|
||||
# 遞迴左子陣列、右子陣列
|
||||
quick_sort(nums, left, pivot - 1)
|
||||
quick_sort(nums, pivot + 1, right)
|
||||
end
|
||||
nums
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### 快速排序類別（尾遞迴最佳化）###
|
||||
class QuickSortTailCall
|
||||
class << self
|
||||
### 哨兵劃分 ###
|
||||
def partition(nums, left, right)
|
||||
# 以 nums[left]為基準數
|
||||
i = left
|
||||
j = right
|
||||
while i < j
|
||||
while i < j && nums[j] >= nums[left]
|
||||
j -= 1 # 從右向左找首個小於基準數的元素
|
||||
end
|
||||
while i < j && nums[i] <= nums[left]
|
||||
i += 1 # 從左向右找首個大於基準數的元素
|
||||
end
|
||||
# 元素交換
|
||||
nums[i], nums[j] = nums[j], nums[i]
|
||||
end
|
||||
# 將基準數交換至兩子陣列的分界線
|
||||
nums[i], nums[left] = nums[left], nums[i]
|
||||
i # 返回基準數的索引
|
||||
end
|
||||
|
||||
### 快速排序（尾遞迴最佳化）
|
||||
def quick_sort(nums, left, right)
|
||||
# 子陣列長度不為 1 時遞迴
|
||||
while left < right
|
||||
# 哨兵劃分
|
||||
pivot = partition(nums, left, right)
|
||||
# 對兩個子陣列中較短的那個執行快速排序
|
||||
if pivot - left < right - pivot
|
||||
quick_sort(nums, left, pivot - 1)
|
||||
left = pivot + 1 # 剩餘未排序區間為 [pivot + 1, right]
|
||||
else
|
||||
quick_sort(nums, pivot + 1, right)
|
||||
right = pivot - 1 # 剩餘未排序區間為 [left, pivot - 1]
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 快速排序
|
||||
nums = [2, 4, 1, 0, 3, 5]
|
||||
QuickSort.quick_sort(nums, 0, nums.length - 1)
|
||||
puts "快速排序完成後 nums = #{nums}"
|
||||
|
||||
# 快速排序（中位基準數最佳化）
|
||||
nums1 = [2, 4, 1, 0, 3, 5]
|
||||
QuickSortMedian.quick_sort(nums1, 0, nums1.length - 1)
|
||||
puts "快速排序（中位基準數最佳化）完成後 nums1 = #{nums1}"
|
||||
|
||||
# 快速排序（尾遞迴最佳化）
|
||||
nums2 = [2, 4, 1, 0, 3, 5]
|
||||
QuickSortTailCall.quick_sort(nums2, 0, nums2.length - 1)
|
||||
puts "快速排序（尾遞迴最佳化）完成後 nums2 = #{nums2}"
|
||||
end
|
||||
124
zh-hant/codes/ruby/chapter_tree/array_binary_tree.rb
Normal file
124
zh-hant/codes/ruby/chapter_tree/array_binary_tree.rb
Normal file
|
|
@ -0,0 +1,124 @@
|
|||
=begin
|
||||
File: array_binary_tree.rb
|
||||
Created Time: 2024-04-17
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/tree_node'
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### 陣列表示下的二元樹類別 ###
|
||||
class ArrayBinaryTree
|
||||
### 建構子 ###
|
||||
def initialize(arr)
|
||||
@tree = arr.to_a
|
||||
end
|
||||
|
||||
### 串列容量 ###
|
||||
def size
|
||||
@tree.length
|
||||
end
|
||||
|
||||
### 獲取索引為 i 節點的值 ###
|
||||
def val(i)
|
||||
# 若索引越界，則返回 nil ，代表空位
|
||||
return if i < 0 || i >= size
|
||||
|
||||
@tree[i]
|
||||
end
|
||||
|
||||
### 獲取索引為 i 節點的左子節點的索引 ###
|
||||
def left(i)
|
||||
2 * i + 1
|
||||
end
|
||||
|
||||
### 獲取索引為 i 節點的右子節點的索引 ###
|
||||
def right(i)
|
||||
2 * i + 2
|
||||
end
|
||||
|
||||
### 獲取索引為 i 節點的父節點的索引 ###
|
||||
def parent(i)
|
||||
(i - 1) / 2
|
||||
end
|
||||
|
||||
### 層序走訪 ###
|
||||
def level_order
|
||||
@res = []
|
||||
|
||||
# 直接走訪陣列
|
||||
for i in 0...size
|
||||
@res << val(i) unless val(i).nil?
|
||||
end
|
||||
|
||||
@res
|
||||
end
|
||||
|
||||
### 深度優先走訪 ###
|
||||
def dfs(i, order)
|
||||
return if val(i).nil?
|
||||
# 前序走訪
|
||||
@res << val(i) if order == :pre
|
||||
dfs(left(i), order)
|
||||
# 中序走訪
|
||||
@res << val(i) if order == :in
|
||||
dfs(right(i), order)
|
||||
# 後序走訪
|
||||
@res << val(i) if order == :post
|
||||
end
|
||||
|
||||
### 前序走訪 ###
|
||||
def pre_order
|
||||
@res = []
|
||||
dfs(0, :pre)
|
||||
@res
|
||||
end
|
||||
|
||||
### 中序走訪 ###
|
||||
def in_order
|
||||
@res = []
|
||||
dfs(0, :in)
|
||||
@res
|
||||
end
|
||||
|
||||
### 後序走訪 ###
|
||||
def post_order
|
||||
@res = []
|
||||
dfs(0, :post)
|
||||
@res
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化二元樹
|
||||
# 這裡藉助了一個從陣列直接生成二元樹的函式
|
||||
arr = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]
|
||||
root = arr_to_tree(arr)
|
||||
puts "\n初始化二元樹\n\n"
|
||||
puts '二元樹的陣列表示：'
|
||||
pp arr
|
||||
puts '二元樹的鏈結串列表示：'
|
||||
print_tree(root)
|
||||
|
||||
# 陣列表示下的二元樹類別
|
||||
abt = ArrayBinaryTree.new(arr)
|
||||
|
||||
# 訪問節點
|
||||
i = 1
|
||||
l, r, _p = abt.left(i), abt.right(i), abt.parent(i)
|
||||
puts "\n當前節點的索引為 #{i} ，值為 #{abt.val(i).inspect}"
|
||||
puts "其左子節點的索引為 #{l} ，值為 #{abt.val(l).inspect}"
|
||||
puts "其右子節點的索引為 #{r} ，值為 #{abt.val(r).inspect}"
|
||||
puts "其父節點的索引為 #{_p} ，值為 #{abt.val(_p).inspect}"
|
||||
|
||||
# 走訪樹
|
||||
res = abt.level_order
|
||||
puts "\n層序走訪為： #{res}"
|
||||
res = abt.pre_order
|
||||
puts "前序走訪為： #{res}"
|
||||
res = abt.in_order
|
||||
puts "中序走訪為： #{res}"
|
||||
res = abt.post_order
|
||||
puts "後序走訪為： #{res}"
|
||||
end
|
||||
216
zh-hant/codes/ruby/chapter_tree/avl_tree.rb
Normal file
216
zh-hant/codes/ruby/chapter_tree/avl_tree.rb
Normal file
|
|
@ -0,0 +1,216 @@
|
|||
=begin
|
||||
File: avl_tree.rb
|
||||
Created Time: 2024-04-17
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/tree_node'
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### AVL 樹 ###
|
||||
class AVLTree
|
||||
### 建構子 ###
|
||||
def initialize
|
||||
@root = nil
|
||||
end
|
||||
|
||||
### 獲取二元樹根節點 ###
|
||||
def get_root
|
||||
@root
|
||||
end
|
||||
|
||||
### 獲取節點高度 ###
|
||||
def height(node)
|
||||
# 空節點高度為 -1 ，葉節點高度為 0
|
||||
return node.height unless node.nil?
|
||||
|
||||
-1
|
||||
end
|
||||
|
||||
### 更新節點高度 ###
|
||||
def update_height(node)
|
||||
# 節點高度等於最高子樹高度 + 1
|
||||
node.height = [height(node.left), height(node.right)].max + 1
|
||||
end
|
||||
|
||||
### 獲取平衡因子 ###
|
||||
def balance_factor(node)
|
||||
# 空節點平衡因子為 0
|
||||
return 0 if node.nil?
|
||||
|
||||
# 節點平衡因子 = 左子樹高度 - 右子樹高度
|
||||
height(node.left) - height(node.right)
|
||||
end
|
||||
|
||||
### 右旋操作 ###
|
||||
def right_rotate(node)
|
||||
child = node.left
|
||||
grand_child = child.right
|
||||
# 以 child 為原點，將 node 向右旋轉
|
||||
child.right = node
|
||||
node.left = grand_child
|
||||
# 更新節點高度
|
||||
update_height(node)
|
||||
update_height(child)
|
||||
# 返回旋轉後子樹的根節點
|
||||
child
|
||||
end
|
||||
|
||||
### 左旋操作 ###
|
||||
def left_rotate(node)
|
||||
child = node.right
|
||||
grand_child = child.left
|
||||
# 以 child 為原點，將 node 向左旋轉
|
||||
child.left = node
|
||||
node.right = grand_child
|
||||
# 更新節點高度
|
||||
update_height(node)
|
||||
update_height(child)
|
||||
# 返回旋轉後子樹的根節點
|
||||
child
|
||||
end
|
||||
|
||||
### 執行旋轉操作，使該子樹重新恢復平衡 ###
|
||||
def rotate(node)
|
||||
# 獲取節點 node 的平衡因子
|
||||
balance_factor = balance_factor(node)
|
||||
# 左遍樹
|
||||
if balance_factor > 1
|
||||
if balance_factor(node.left) >= 0
|
||||
# 右旋
|
||||
return right_rotate(node)
|
||||
else
|
||||
# 先左旋後右旋
|
||||
node.left = left_rotate(node.left)
|
||||
return right_rotate(node)
|
||||
end
|
||||
# 右遍樹
|
||||
elsif balance_factor < -1
|
||||
if balance_factor(node.right) <= 0
|
||||
# 左旋
|
||||
return left_rotate(node)
|
||||
else
|
||||
# 先右旋後左旋
|
||||
node.right = right_rotate(node.right)
|
||||
return left_rotate(node)
|
||||
end
|
||||
end
|
||||
# 平衡樹，無須旋轉，直接返回
|
||||
node
|
||||
end
|
||||
|
||||
### 插入節點 ###
|
||||
def insert(val)
|
||||
@root = insert_helper(@root, val)
|
||||
end
|
||||
|
||||
### 遞迴插入節點（輔助方法）###
|
||||
def insert_helper(node, val)
|
||||
return TreeNode.new(val) if node.nil?
|
||||
# 1. 查詢插入位置並插入節點
|
||||
if val < node.val
|
||||
node.left = insert_helper(node.left, val)
|
||||
elsif val > node.val
|
||||
node.right = insert_helper(node.right, val)
|
||||
else
|
||||
# 重複節點不插入，直接返回
|
||||
return node
|
||||
end
|
||||
# 更新節點高度
|
||||
update_height(node)
|
||||
# 2. 執行旋轉操作，使該子樹重新恢復平衡
|
||||
rotate(node)
|
||||
end
|
||||
|
||||
### 刪除節點 ###
|
||||
def remove(val)
|
||||
@root = remove_helper(@root, val)
|
||||
end
|
||||
|
||||
### 遞迴刪除節點（輔助方法）###
|
||||
def remove_helper(node, val)
|
||||
return if node.nil?
|
||||
# 1. 查詢節點並刪除
|
||||
if val < node.val
|
||||
node.left = remove_helper(node.left, val)
|
||||
elsif val > node.val
|
||||
node.right = remove_helper(node.right, val)
|
||||
else
|
||||
if node.left.nil? || node.right.nil?
|
||||
child = node.left || node.right
|
||||
# 子節點數量 = 0 ，直接刪除 node 並返回
|
||||
return if child.nil?
|
||||
# 子節點數量 = 1 ，直接刪除 node
|
||||
node = child
|
||||
else
|
||||
# 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點
|
||||
temp = node.right
|
||||
while !temp.left.nil?
|
||||
temp = temp.left
|
||||
end
|
||||
node.right = remove_helper(node.right, temp.val)
|
||||
node.val = temp.val
|
||||
end
|
||||
end
|
||||
# 更新節點高度
|
||||
update_height(node)
|
||||
# 2. 執行旋轉操作，使該子樹重新恢復平衡
|
||||
rotate(node)
|
||||
end
|
||||
|
||||
### 查詢節點 ###
|
||||
def search(val)
|
||||
cur = @root
|
||||
# 迴圈查詢，越過葉節點後跳出
|
||||
while !cur.nil?
|
||||
# 目標節點在 cur 的右子樹中
|
||||
if cur.val < val
|
||||
cur = cur.right
|
||||
# 目標節點在 cur 的左子樹中
|
||||
elsif cur.val > val
|
||||
cur = cur.left
|
||||
# 找到目標節點，跳出迴圈
|
||||
else
|
||||
break
|
||||
end
|
||||
end
|
||||
# 返回目標節點
|
||||
cur
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
def test_insert(tree, val)
|
||||
tree.insert(val)
|
||||
puts "\n插入節點 #{val} 後，AVL 樹為"
|
||||
print_tree(tree.get_root)
|
||||
end
|
||||
|
||||
def test_remove(tree, val)
|
||||
tree.remove(val)
|
||||
puts "\n刪除節點 #{val} 後，AVL 樹為"
|
||||
print_tree(tree.get_root)
|
||||
end
|
||||
|
||||
# 初始化空 AVL 樹
|
||||
avl_tree = AVLTree.new
|
||||
|
||||
# 插入節點
|
||||
# 請關注插入節點後，AVL 樹是如何保持平衡的
|
||||
for val in [1, 2, 3, 4, 5, 8, 7, 9, 10, 6]
|
||||
test_insert(avl_tree, val)
|
||||
end
|
||||
|
||||
# 插入重複節點
|
||||
test_insert(avl_tree, 7)
|
||||
|
||||
# 刪除節點
|
||||
# 請關注刪除節點後，AVL 樹是如何保持平衡的
|
||||
test_remove(avl_tree, 8) # 刪除度為 0 的節點
|
||||
test_remove(avl_tree, 5) # 刪除度為 1 的節點
|
||||
test_remove(avl_tree, 4) # 刪除度為 2 的節點
|
||||
|
||||
result_node = avl_tree.search(7)
|
||||
puts "\n查詢到的節點物件為 #{result_node}，節點值 = #{result_node.val}"
|
||||
end
|
||||
161
zh-hant/codes/ruby/chapter_tree/binary_search_tree.rb
Normal file
161
zh-hant/codes/ruby/chapter_tree/binary_search_tree.rb
Normal file
|
|
@ -0,0 +1,161 @@
|
|||
=begin
|
||||
File: binary_search_tree.rb
|
||||
Created Time: 2024-04-18
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/tree_node'
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### 二元搜尋樹 ###
|
||||
class BinarySearchTree
|
||||
### 建構子 ###
|
||||
def initialize
|
||||
# 初始化空樹
|
||||
@root = nil
|
||||
end
|
||||
|
||||
### 獲取二元樹根節點 ###
|
||||
def get_root
|
||||
@root
|
||||
end
|
||||
|
||||
### 查詢節點 ###
|
||||
def search(num)
|
||||
cur = @root
|
||||
|
||||
# 迴圈查詢，越過葉節點後跳出
|
||||
while !cur.nil?
|
||||
# 目標節點在 cur 的右子樹中
|
||||
if cur.val < num
|
||||
cur = cur.right
|
||||
# 目標節點在 cur 的左子樹中
|
||||
elsif cur.val > num
|
||||
cur = cur.left
|
||||
# 找到目標節點，跳出迴圈
|
||||
else
|
||||
break
|
||||
end
|
||||
end
|
||||
|
||||
cur
|
||||
end
|
||||
|
||||
### 插入節點 ###
|
||||
def insert(num)
|
||||
# 若樹為空，則初始化根節點
|
||||
if @root.nil?
|
||||
@root = TreeNode.new(num)
|
||||
return
|
||||
end
|
||||
|
||||
# 迴圈查詢，越過葉節點後跳出
|
||||
cur, pre = @root, nil
|
||||
while !cur.nil?
|
||||
# 找到重複節點，直接返回
|
||||
return if cur.val == num
|
||||
|
||||
pre = cur
|
||||
# 插入位置在 cur 的右子樹中
|
||||
if cur.val < num
|
||||
cur = cur.right
|
||||
# 插入位置在 cur 的左子樹中
|
||||
else
|
||||
cur = cur.left
|
||||
end
|
||||
end
|
||||
|
||||
# 插入節點
|
||||
node = TreeNode.new(num)
|
||||
if pre.val < num
|
||||
pre.right = node
|
||||
else
|
||||
pre.left = node
|
||||
end
|
||||
end
|
||||
|
||||
### 刪除節點 ###
|
||||
def remove(num)
|
||||
# 若樹為空，直接提前返回
|
||||
return if @root.nil?
|
||||
|
||||
# 迴圈查詢，越過葉節點後跳出
|
||||
cur, pre = @root, nil
|
||||
while !cur.nil?
|
||||
# 找到待刪除節點，跳出迴圈
|
||||
break if cur.val == num
|
||||
|
||||
pre = cur
|
||||
# 待刪除節點在 cur 的右子樹中
|
||||
if cur.val < num
|
||||
cur = cur.right
|
||||
# 待刪除節點在 cur 的左子樹中
|
||||
else
|
||||
cur = cur.left
|
||||
end
|
||||
end
|
||||
# 若無待刪除節點，則直接返回
|
||||
return if cur.nil?
|
||||
|
||||
# 子節點數量 = 0 or 1
|
||||
if cur.left.nil? || cur.right.nil?
|
||||
# 當子節點數量 = 0 / 1 時， child = null / 該子節點
|
||||
child = cur.left || cur.right
|
||||
# 刪除節點 cur
|
||||
if cur != @root
|
||||
if pre.left == cur
|
||||
pre.left = child
|
||||
else
|
||||
pre.right = child
|
||||
end
|
||||
else
|
||||
# 若刪除節點為根節點，則重新指定根節點
|
||||
@root = child
|
||||
end
|
||||
# 子節點數量 = 2
|
||||
else
|
||||
# 獲取中序走訪中 cur 的下一個節點
|
||||
tmp = cur.right
|
||||
while !tmp.left.nil?
|
||||
tmp = tmp.left
|
||||
end
|
||||
# 遞迴刪除節點 tmp
|
||||
remove(tmp.val)
|
||||
# 用 tmp 覆蓋 cur
|
||||
cur.val = tmp.val
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化二元搜尋樹
|
||||
bst = BinarySearchTree.new
|
||||
nums = [8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]
|
||||
# 請注意，不同的插入順序會生成不同的二元樹，該序列可以生成一個完美二元樹
|
||||
nums.each { |num| bst.insert(num) }
|
||||
puts "\n初始化的二元樹為\n"
|
||||
print_tree(bst.get_root)
|
||||
|
||||
# 查詢節點
|
||||
node = bst.search(7)
|
||||
puts "\n查詢到的節點物件為: #{node}，節點值 = #{node.val}"
|
||||
|
||||
# 插入節點
|
||||
bst.insert(16)
|
||||
puts "\n插入節點 16 後，二元樹為\n"
|
||||
print_tree(bst.get_root)
|
||||
|
||||
# 刪除節點
|
||||
bst.remove(1)
|
||||
puts "\n刪除節點 1 後，二元樹為\n"
|
||||
print_tree(bst.get_root)
|
||||
|
||||
bst.remove(2)
|
||||
puts "\n刪除節點 2 後，二元樹為\n"
|
||||
print_tree(bst.get_root)
|
||||
|
||||
bst.remove(4)
|
||||
puts "\n刪除節點 4 後，二元樹為\n"
|
||||
print_tree(bst.get_root)
|
||||
end
|
||||
38
zh-hant/codes/ruby/chapter_tree/binary_tree.rb
Normal file
38
zh-hant/codes/ruby/chapter_tree/binary_tree.rb
Normal file
|
|
@ -0,0 +1,38 @@
|
|||
=begin
|
||||
File: binary_tree.rb
|
||||
Created Time: 2024-04-18
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/tree_node'
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化二元樹
|
||||
# 初始化節點
|
||||
n1 = TreeNode.new(1)
|
||||
n2 = TreeNode.new(2)
|
||||
n3 = TreeNode.new(3)
|
||||
n4 = TreeNode.new(4)
|
||||
n5 = TreeNode.new(5)
|
||||
# 構建節點之間的引用（指標）
|
||||
n1.left = n2
|
||||
n1.right = n3
|
||||
n2.left = n4
|
||||
n2.right = n5
|
||||
puts "\n初始化二元樹\n\n"
|
||||
print_tree(n1)
|
||||
|
||||
# 插入與刪除節點
|
||||
_p = TreeNode.new(0)
|
||||
# 在 n1 -> n2 中間插入節點 _p
|
||||
n1.left = _p
|
||||
_p.left = n2
|
||||
puts "\n插入節點 _p 後\n\n"
|
||||
print_tree(n1)
|
||||
# 刪除節點
|
||||
n1.left = n2
|
||||
puts "\n刪除節點 _p 後\n\n"
|
||||
print_tree(n1)
|
||||
end
|
||||
36
zh-hant/codes/ruby/chapter_tree/binary_tree_bfs.rb
Normal file
36
zh-hant/codes/ruby/chapter_tree/binary_tree_bfs.rb
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
=begin
|
||||
File: binary_tree_bfs.rb
|
||||
Created Time: 2024-04-18
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/tree_node'
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### 層序走訪 ###
|
||||
def level_order(root)
|
||||
# 初始化佇列，加入根節點
|
||||
queue = [root]
|
||||
# 初始化一個串列，用於儲存走訪序列
|
||||
res = []
|
||||
while !queue.empty?
|
||||
node = queue.shift # 隊列出隊
|
||||
res << node.val # 儲存節點值
|
||||
queue << node.left unless node.left.nil? # 左子節點入列
|
||||
queue << node.right unless node.right.nil? # 右子節點入列
|
||||
end
|
||||
res
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化二元樹
|
||||
# 這裡藉助了一個從陣列直接生成二元樹的函式
|
||||
root = arr_to_tree([1, 2, 3, 4, 5, 6, 7])
|
||||
puts "\n初始化二元樹\n\n"
|
||||
print_tree(root)
|
||||
|
||||
# 層序走訪
|
||||
res = level_order(root)
|
||||
puts "\n層序走訪的節點列印序列 = #{res}"
|
||||
end
|
||||
62
zh-hant/codes/ruby/chapter_tree/binary_tree_dfs.rb
Normal file
62
zh-hant/codes/ruby/chapter_tree/binary_tree_dfs.rb
Normal file
|
|
@ -0,0 +1,62 @@
|
|||
=begin
|
||||
File: binary_tree_dfs.rb
|
||||
Created Time: 2024-04-18
|
||||
Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
|
||||
=end
|
||||
|
||||
require_relative '../utils/tree_node'
|
||||
require_relative '../utils/print_util'
|
||||
|
||||
### 前序走訪 ###
|
||||
def pre_order(root)
|
||||
return if root.nil?
|
||||
|
||||
# 訪問優先順序：根節點 -> 左子樹 -> 右子樹
|
||||
$res << root.val
|
||||
pre_order(root.left)
|
||||
pre_order(root.right)
|
||||
end
|
||||
|
||||
### 中序走訪 ###
|
||||
def in_order(root)
|
||||
return if root.nil?
|
||||
|
||||
# 訪問優先順序：左子樹 -> 根節點 -> 右子樹
|
||||
in_order(root.left)
|
||||
$res << root.val
|
||||
in_order(root.right)
|
||||
end
|
||||
|
||||
### 後序走訪 ###
|
||||
def post_order(root)
|
||||
return if root.nil?
|
||||
|
||||
# 訪問優先順序：左子樹 -> 右子樹 -> 根節點
|
||||
post_order(root.left)
|
||||
post_order(root.right)
|
||||
$res << root.val
|
||||
end
|
||||
|
||||
### Driver Code ###
|
||||
if __FILE__ == $0
|
||||
# 初始化二元樹
|
||||
# 這裡藉助了一個從陣列直接生成二元樹的函式
|
||||
root = arr_to_tree([1, 2, 3, 4, 5, 6, 7])
|
||||
puts "\n初始化二元樹\n\n"
|
||||
print_tree(root)
|
||||
|
||||
# 前序走訪
|
||||
$res = []
|
||||
pre_order(root)
|
||||
puts "\n前序走訪的節點列印序列 = #{$res}"
|
||||
|
||||
# 中序走訪
|
||||
$res.clear
|
||||
in_order(root)
|
||||
puts "\nn中序走訪的節點列印序列 = #{$res}"
|
||||
|
||||
# 後序走訪
|
||||
$res.clear
|
||||
post_order(root)
|
||||
puts "\nn後序走訪的節點列印序列 = #{$res}"
|
||||
end
|
||||
|
|
@ -56,3 +56,8 @@ def print_tree(root, prev=nil, is_right=false)
|
|||
trunk.str = " |"
|
||||
print_tree(root.left, trunk, false)
|
||||
end
|
||||
|
||||
### 列印雜湊表 ###
|
||||
def print_hash_map(hmap)
|
||||
hmap.entries.each { |key, value| puts "#{key} -> #{value}" }
|
||||
end
|
||||
|
|
|
|||
|
|
@ -16,3 +16,38 @@ class TreeNode
|
|||
@height = 0
|
||||
end
|
||||
end
|
||||
|
||||
### 將串列反序列化為二元數樹：遞迴 ###
|
||||
def arr_to_tree_dfs(arr, i)
|
||||
# 如果索引超出陣列長度，或者對應的元素為 nil ，則返回 nil
|
||||
return if i < 0 || i >= arr.length || arr[i].nil?
|
||||
# 構建當前節點
|
||||
root = TreeNode.new(arr[i])
|
||||
# 遞迴構建左右子樹
|
||||
root.left = arr_to_tree_dfs(arr, 2 * i + 1)
|
||||
root.right = arr_to_tree_dfs(arr, 2 * i + 2)
|
||||
root
|
||||
end
|
||||
|
||||
### 將串列反序列化為二元樹 ###
|
||||
def arr_to_tree(arr)
|
||||
arr_to_tree_dfs(arr, 0)
|
||||
end
|
||||
|
||||
### 將二元樹序列化為串列：遞迴 ###
|
||||
def tree_to_arr_dfs(root, i, res)
|
||||
return if root.nil?
|
||||
|
||||
res += Array.new(i - res.length + 1) if i >= res.length
|
||||
res[i] = root.val
|
||||
|
||||
tree_to_arr_dfs(root.left, 2 * i + 1, res)
|
||||
tree_to_arr_dfs(root.right, 2 * i + 2, res)
|
||||
end
|
||||
|
||||
### 將二元樹序列化為串列 ###
|
||||
def tree_to_arr(root)
|
||||
res = []
|
||||
tree_to_arr_dfs(root, 0, res)
|
||||
res
|
||||
end
|
||||
|
|
|
|||
|
|
@ -91,9 +91,8 @@ class GraphAdjList {
|
|||
}
|
||||
}
|
||||
|
||||
// need to add the package @types/node contains type definitions for Node.js, npm i --save-dev @types/node
|
||||
if (require.main === module) {
|
||||
/* Driver Code */
|
||||
if (import.meta.url.endsWith(process.argv[1])) {
|
||||
/* 初始化無向圖 */
|
||||
const v0 = new Vertex(1),
|
||||
v1 = new Vertex(3),
|
||||
|
|
|
|||
|
|
@ -122,7 +122,7 @@ class MaxHeap {
|
|||
}
|
||||
|
||||
/* Driver Code */
|
||||
if (require.main === module) {
|
||||
if (import.meta.url.endsWith(process.argv[1])) {
|
||||
/* 初始化大頂堆積 */
|
||||
const maxHeap = new MaxHeap([9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2]);
|
||||
console.log('\n輸入串列並建堆積後');
|
||||
|
|
|
|||
|
|
@ -4,8 +4,8 @@
|
|||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
const { arrToTree } = require('../modules/TreeNode');
|
||||
const { printTree } = require('../modules/PrintUtil');
|
||||
import { arrToTree } from '../modules/TreeNode';
|
||||
import { printTree } from '../modules/PrintUtil';
|
||||
|
||||
type Order = 'pre' | 'in' | 'post';
|
||||
|
||||
|
|
|
|||
|
|
@ -79,9 +79,6 @@ function showTrunks(p: Trunk | null) {
|
|||
|
||||
showTrunks(p.prev);
|
||||
process.stdout.write(p.str);
|
||||
// ts-node to execute, we need to install type definitions for node
|
||||
// solve: npm i --save-dev @types/node
|
||||
// restart the vscode
|
||||
}
|
||||
|
||||
/* 列印堆積 */
|
||||
|
|
|
|||
|
|
@ -1,8 +1,12 @@
|
|||
{
|
||||
"compilerOptions": {
|
||||
"target": "ES6",
|
||||
"module": "CommonJS",
|
||||
"outDir": "out",
|
||||
"sourceMap": true
|
||||
}
|
||||
"baseUrl": ".",
|
||||
"module": "esnext",
|
||||
"moduleResolution": "node",
|
||||
"types": ["@types/node"],
|
||||
"noEmit": true,
|
||||
"target": "esnext",
|
||||
},
|
||||
"include": ["chapter_*/*.ts"],
|
||||
"exclude": ["node_modules"]
|
||||
}
|
||||
|
|
|
|||
|
|
@ -64,7 +64,7 @@ $$
|
|||
|
||||
並行最佳化在多核或多處理器的環境中尤其有效，因為系統可以同時處理多個子問題，更加充分地利用計算資源，從而顯著減少總體的執行時間。
|
||||
|
||||
比如在下圖所示的“桶排序”中，我們將海量的資料平均分配到各個桶中，則可所有桶的排序任務分散到各個計算單元，完成後再合併結果。
|
||||
比如在下圖所示的“桶排序”中，我們將海量的資料平均分配到各個桶中，則可將所有桶的排序任務分散到各個計算單元，完成後再合併結果。
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -18,15 +18,15 @@
|
|||
|
||||
**第一步：思考每輪的決策，定義狀態，從而得到 $dp$ 表**
|
||||
|
||||
對於每個物品來說，不放入背包，背包容量不變；放入背包，背包容量減小。由此可得狀態定義：當前物品編號 $i$ 和剩餘背包容量 $c$ ，記為 $[i, c]$ 。
|
||||
對於每個物品來說，不放入背包，背包容量不變；放入背包，背包容量減小。由此可得狀態定義：當前物品編號 $i$ 和背包容量 $c$ ，記為 $[i, c]$ 。
|
||||
|
||||
狀態 $[i, c]$ 對應的子問題為：**前 $i$ 個物品在剩餘容量為 $c$ 的背包中的最大價值**，記為 $dp[i, c]$ 。
|
||||
狀態 $[i, c]$ 對應的子問題為：**前 $i$ 個物品在容量為 $c$ 的背包中的最大價值**，記為 $dp[i, c]$ 。
|
||||
|
||||
待求解的是 $dp[n, cap]$ ，因此需要一個尺寸為 $(n+1) \times (cap+1)$ 的二維 $dp$ 表。
|
||||
|
||||
**第二步：找出最優子結構，進而推導出狀態轉移方程**
|
||||
|
||||
當我們做出物品 $i$ 的決策後，剩餘的是前 $i-1$ 個物品的決策，可分為以下兩種情況。
|
||||
當我們做出物品 $i$ 的決策後，剩餘的是前 $i-1$ 個物品決策的子問題，可分為以下兩種情況。
|
||||
|
||||
- **不放入物品 $i$** ：背包容量不變，狀態變化為 $[i-1, c]$ 。
|
||||
- **放入物品 $i$** ：背包容量減少 $wgt[i-1]$ ，價值增加 $val[i-1]$ ，狀態變化為 $[i-1, c-wgt[i-1]]$ 。
|
||||
|
|
@ -41,7 +41,7 @@ $$
|
|||
|
||||
**第三步：確定邊界條件和狀態轉移順序**
|
||||
|
||||
當無物品或無剩餘背包容量時最大價值為 $0$ ，即首列 $dp[i, 0]$ 和首行 $dp[0, c]$ 都等於 $0$ 。
|
||||
當無物品或背包容量為 $0$ 時最大價值為 $0$ ，即首列 $dp[i, 0]$ 和首行 $dp[0, c]$ 都等於 $0$ 。
|
||||
|
||||
當前狀態 $[i, c]$ 從上方的狀態 $[i-1, c]$ 和左上方的狀態 $[i-1, c-wgt[i-1]]$ 轉移而來，因此透過兩層迴圈正序走訪整個 $dp$ 表即可。
|
||||
|
||||
|
|
|
|||
|
|
@ -11,7 +11,7 @@
|
|||
**背包問題**
|
||||
|
||||
- 背包問題是最典型的動態規劃問題之一，具有 0-1 背包、完全背包、多重背包等變種。
|
||||
- 0-1 背包的狀態定義為前 $i$ 個物品在剩餘容量為 $c$ 的背包中的最大價值。根據不放入背包和放入背包兩種決策，可得到最優子結構，並構建出狀態轉移方程。在空間最佳化中，由於每個狀態依賴正上方和左上方的狀態，因此需要倒序走訪串列，避免左上方狀態被覆蓋。
|
||||
- 0-1 背包的狀態定義為前 $i$ 個物品在容量為 $c$ 的背包中的最大價值。根據不放入背包和放入背包兩種決策，可得到最優子結構，並構建出狀態轉移方程。在空間最佳化中，由於每個狀態依賴正上方和左上方的狀態，因此需要倒序走訪串列，避免左上方狀態被覆蓋。
|
||||
- 完全背包問題的每種物品的選取數量無限制，因此選擇放入物品的狀態轉移與 0-1 背包問題不同。由於狀態依賴正上方和正左方的狀態，因此在空間最佳化中應當正序走訪。
|
||||
- 零錢兌換問題是完全背包問題的一個變種。它從求“最大”價值變為求“最小”硬幣數量，因此狀態轉移方程中的 $\max()$ 應改為 $\min()$ 。從追求“不超過”背包容量到追求“恰好”湊出目標金額，因此使用 $amt + 1$ 來表示“無法湊出目標金額”的無效解。
|
||||
- 零錢兌換問題 II 從求“最少硬幣數量”改為求“硬幣組合數量”，狀態轉移方程相應地從 $\min()$ 改為求和運算子。
|
||||
|
|
|
|||
|
|
@ -374,7 +374,29 @@ $$
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title="built_in_hash.rb"
|
||||
num = 3
|
||||
hash_num = num.hash
|
||||
# 整數 3 的雜湊值為 -4385856518450339636
|
||||
|
||||
bol = true
|
||||
hash_bol = bol.hash
|
||||
# 布林量 true 的雜湊值為 -1617938112149317027
|
||||
|
||||
dec = 3.14159
|
||||
hash_dec = dec.hash
|
||||
# 小數 3.14159 的雜湊值為 -1479186995943067893
|
||||
|
||||
str = "Hello 演算法"
|
||||
hash_str = str.hash
|
||||
# 字串“Hello 演算法”的雜湊值為 -4075943250025831763
|
||||
|
||||
tup = [12836, '小哈']
|
||||
hash_tup = tup.hash
|
||||
# 元組 (12836, '小哈') 的雜湊值為 1999544809202288822
|
||||
|
||||
obj = ListNode.new(0)
|
||||
hash_obj = obj.hash
|
||||
# 節點物件 #<ListNode:0x000078133140ab70> 的雜湊值為 4302940560806366381
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
|
|||
|
|
@ -293,7 +293,24 @@
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title="hash_map.rb"
|
||||
# 初始化雜湊表
|
||||
hmap = {}
|
||||
|
||||
# 新增操作
|
||||
# 在雜湊表中新增鍵值對 (key, value)
|
||||
hmap[12836] = "小哈"
|
||||
hmap[15937] = "小囉"
|
||||
hmap[16750] = "小算"
|
||||
hmap[13276] = "小法"
|
||||
hmap[10583] = "小鴨"
|
||||
|
||||
# 查詢操作
|
||||
# 向雜湊表中輸入鍵 key ，得到值 value
|
||||
name = hmap[15937]
|
||||
|
||||
# 刪除操作
|
||||
# 在雜湊表中刪除鍵值對 (key, value)
|
||||
hmap.delete(10583)
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
@ -512,7 +529,15 @@
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title="hash_map.rb"
|
||||
# 走訪雜湊表
|
||||
# 走訪鍵值對 key->value
|
||||
hmap.entries.each { |key, value| puts "#{key} -> #{value}" }
|
||||
|
||||
# 單獨走訪鍵 key
|
||||
hmap.keys.each { |key| puts key }
|
||||
|
||||
# 單獨走訪值 value
|
||||
hmap.values.each { |val| puts val }
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
|
|||
|
|
@ -420,7 +420,7 @@
|
|||
|
||||
## 堆積的實現
|
||||
|
||||
下文實現的是大頂堆積。若要將其轉換為小頂堆積，只需將所有大小邏輯判斷取逆（例如，將 $\geq$ 替換為 $\leq$ ）。感興趣的讀者可以自行實現。
|
||||
下文實現的是大頂堆積。若要將其轉換為小頂堆積，只需將所有大小邏輯判斷進行逆轉（例如，將 $\geq$ 替換為 $\leq$ ）。感興趣的讀者可以自行實現。
|
||||
|
||||
### 堆積的儲存與表示
|
||||
|
||||
|
|
|
|||
|
|
@ -71,7 +71,7 @@ $$
|
|||
|
||||
## 演算法特性
|
||||
|
||||
- **時間複雜度為 $O(n + m)$** ：涉及走訪 `nums` 和走訪 `counter` ，都使用線性時間。一般情況下 $n \gg m$ ，時間複雜度趨於 $O(n)$ 。
|
||||
- **時間複雜度為 $O(n + m)$、非自適應排序** ：涉及走訪 `nums` 和走訪 `counter` ，都使用線性時間。一般情況下 $n \gg m$ ，時間複雜度趨於 $O(n)$ 。
|
||||
- **空間複雜度為 $O(n + m)$、非原地排序**：藉助了長度分別為 $n$ 和 $m$ 的陣列 `res` 和 `counter` 。
|
||||
- **穩定排序**：由於向 `res` 中填充元素的順序是“從右向左”的，因此倒序走訪 `nums` 可以避免改變相等元素之間的相對位置，從而實現穩定排序。實際上，正序走訪 `nums` 也可以得到正確的排序結果，但結果是非穩定的。
|
||||
|
||||
|
|
|
|||
|
|
@ -36,6 +36,6 @@ $$
|
|||
|
||||
相較於計數排序，基數排序適用於數值範圍較大的情況，**但前提是資料必須可以表示為固定位數的格式，且位數不能過大**。例如，浮點數不適合使用基數排序，因為其位數 $k$ 過大，可能導致時間複雜度 $O(nk) \gg O(n^2)$ 。
|
||||
|
||||
- **時間複雜度為 $O(nk)$**：設資料量為 $n$、資料為 $d$ 進位制、最大位數為 $k$ ，則對某一位執行計數排序使用 $O(n + d)$ 時間，排序所有 $k$ 位使用 $O((n + d)k)$ 時間。通常情況下，$d$ 和 $k$ 都相對較小，時間複雜度趨向 $O(n)$ 。
|
||||
- **時間複雜度為 $O(nk)$、非自適應排序**：設資料量為 $n$、資料為 $d$ 進位制、最大位數為 $k$ ，則對某一位執行計數排序使用 $O(n + d)$ 時間，排序所有 $k$ 位使用 $O((n + d)k)$ 時間。通常情況下，$d$ 和 $k$ 都相對較小，時間複雜度趨向 $O(n)$ 。
|
||||
- **空間複雜度為 $O(n + d)$、非原地排序**：與計數排序相同，基數排序需要藉助長度為 $n$ 和 $d$ 的陣列 `res` 和 `counter` 。
|
||||
- **穩定排序**：當計數排序穩定時，基數排序也穩定；當計數排序不穩定時，基數排序無法保證得到正確的排序結果。
|
||||
|
|
|
|||
|
|
@ -123,7 +123,9 @@
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title=""
|
||||
|
||||
### 二元樹的陣列表示 ###
|
||||
# 使用 nil 來表示空位
|
||||
tree = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
|
|||
|
|
@ -214,7 +214,18 @@ AVL 樹既是二元搜尋樹，也是平衡二元樹，同時滿足這兩類二
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title=""
|
||||
### AVL 樹節點類別 ###
|
||||
class TreeNode
|
||||
attr_accessor :val # 節點值
|
||||
attr_accessor :height # 節點高度
|
||||
attr_accessor :left # 左子節點引用
|
||||
attr_accessor :right # 右子節點引用
|
||||
|
||||
def initialize(val)
|
||||
@val = val
|
||||
@height = 0
|
||||
end
|
||||
end
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
|
|||
|
|
@ -189,7 +189,16 @@
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title=""
|
||||
### 二元樹節點類別 ###
|
||||
class TreeNode
|
||||
attr_accessor :val # 節點值
|
||||
attr_accessor :left # 左子節點引用
|
||||
attr_accessor :right # 右子節點引用
|
||||
|
||||
def initialize(val)
|
||||
@val = val
|
||||
end
|
||||
end
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
@ -432,7 +441,18 @@
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title="binary_tree.rb"
|
||||
|
||||
# 初始化二元樹
|
||||
# 初始化節點
|
||||
n1 = TreeNode.new(1)
|
||||
n2 = TreeNode.new(2)
|
||||
n3 = TreeNode.new(3)
|
||||
n4 = TreeNode.new(4)
|
||||
n5 = TreeNode.new(5)
|
||||
# 構建節點之間的引用（指標）
|
||||
n1.left = n2
|
||||
n1.right = n3
|
||||
n2.left = n4
|
||||
n2.right = n5
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
@ -594,7 +614,13 @@
|
|||
=== "Ruby"
|
||||
|
||||
```ruby title="binary_tree.rb"
|
||||
|
||||
# 插入與刪除節點
|
||||
_p = TreeNode.new(0)
|
||||
# 在 n1 -> n2 中間插入節點 _p
|
||||
n1.left = _p
|
||||
_p.left = n2
|
||||
# 刪除節點
|
||||
n1.left = n2
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
|
|
|||
Loading…
Reference in a new issue