83 lines
2.6 KiB
Markdown
83 lines
2.6 KiB
Markdown
# [3227] Vowels Game In A String
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## 題目資訊
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- **難度**: Medium
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- **標籤**: Math, String, Brainteaser, Game Theory
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- **題目連結**: https://leetcode.com/problems/vowels-game-in-a-string/
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- **練習日期**: 2025-09-12
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- **目標複雜度**: 時間 O(n)、空間 O(1)
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## 題目描述
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Alice and Bob are playing a game on a string.
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You are given a string `s`, Alice and Bob will take turns playing the following game where Alice starts **first**:
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On Alice's turn, she has to remove any **non-empty** substring from `s` that contains an odd number of vowels.
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On Bob's turn, he has to remove any non-empty substring from `s` that contains an even number of vowels.
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The first player who cannot make a move on their turn loses the game. We assume that both Alice and Bob play optimally.
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Return `true` if Alice wins the game, and `false` otherwise.
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The English vowels are: `a`, `e`, `i`, `o`, and `u`.
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## 先備條件與限制
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- 輸入限制：n ∈ [1, 10^5]、字符為小寫英文字母
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- 回傳/輸出格式：boolean 值，true 表示 Alice 獲勝
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## 解題思路
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### 初步分析
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- 類型：博弈論 / 數學 / 腦筋急轉彎
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- 關鍵觀察：
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- Alice 先手，需移除含奇數個母音的子字串
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- Bob 後手，需移除含偶數個母音的子字串
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- 複雜度目標理由：只需檢查是否存在母音
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### 解法比較
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1. 解法A（基準/暴力）：
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- 思路：
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發現 Alice 獲勝條件極其簡單
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- 正確性：
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只需檢查是否存在母音
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- 複雜度：O(n) / O(1)
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### 常見陷阱
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- 邊界：空字串（題目保證 n≥1）、全母音、無母音
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- 過度複雜化：誤以為需要複雜的博弈分析
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- 計數錯誤：誤以為需要精確計算母音數量
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- 大小寫：題目保證小寫字母
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## 測試案例
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### 範例輸入輸出
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```
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Input: s = "leetcode"
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Output: true
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Explanation: Alice 可以移除 "leetcod"（含3個母音），剩下 "e"，Bob 無法移除含偶數母音的子字串
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```
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### 邊界清單
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- 全母音字串：Alice 立即移除整個字串獲勝
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- 無母音字串：Alice 無法行動敗北
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- 單一字符（母音/子音）
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- 混合字串（含有母音和子音）
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- 長字串壓力測試
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## 複雜度分析
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- 最壞：時間 O(n)、空間 O(1)
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- 最佳：時間 O(1)（首字符即為母音）、空間 O(1)
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## 相關題目 / Follow-up
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- LeetCode 345: Reverse Vowels of a String
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- LeetCode 1456: Maximum Number of Vowels in a Substring of Given Length
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- LeetCode 2062: Count Vowel Substrings of a String
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## 學習筆記
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- 今天學到：
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- 卡住與修正：
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- 待優化：
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---
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**總結**：這題的核心在於 ______，適合練習 ______。
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