vowels-game-in-a-string

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Algorithms

Alice and Bob are playing a game on a string.

You are given a string <code>s</code>, Alice and Bob will take turns playing the following game where Alice starts first:

<ul>
	<li>On Alice&#39;s turn, she has to remove any non-empty substring from <code>s</code> that contains an odd number of vowels.</li>
	<li>On Bob&#39;s turn, he has to remove any non-empty substring from <code>s</code> that contains an even number of vowels.</li>
</ul>

The first player who cannot make a move on their turn loses the game. We assume that both Alice and Bob play optimally.

Return <code>true</code> if Alice wins the game, and <code>false</code> otherwise.

The English vowels are: <code>a</code>, <code>e</code>, <code>i</code>, <code>o</code>, and <code>u</code>.

&nbsp;
Example 1:

<div class="example-block">
Input: s = &quot;leetcoder&quot;

Output: true

Explanation: 
Alice can win the game as follows:

<ul>
	<li>Alice plays first, she can delete the underlined substring in <code>s = &quot;leetcoder&quot;</code> which contains 3 vowels. The resulting string is <code>s = &quot;der&quot;</code>.</li>
	<li>Bob plays second, he can delete the underlined substring in <code>s = &quot;der&quot;</code> which contains 0 vowels. The resulting string is <code>s = &quot;er&quot;</code>.</li>
	<li>Alice plays third, she can delete the whole string <code>s = &quot;er&quot;</code> which contains 1 vowel.</li>
	<li>Bob plays fourth, since the string is empty, there is no valid play for Bob. So Alice wins the game.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: s = &quot;bbcd&quot;

Output: false

Explanation: 
There is no valid play for Alice in her first turn, so Alice loses the game.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s.length &lt;= 105</code></li>
	<li><code>s</code> consists only of lowercase English letters.</li>
</ul>

doesAliceWin

Vowels Game in a String

Brainteaser

Math

String

Game Theory

小红和小明在玩一个字符串元音游戏。

给你一个字符串 <code>s</code>，小红和小明将轮流参与游戏，小红 先 开始：

<ul>
	<li>在小红的回合，她必须移除 <code>s</code> 中包含 奇数 个元音的任意 非空 子字符串。</li>
	<li>在小明的回合，他必须移除 <code>s</code> 中包含 偶数 个元音的任意 非空 子字符串。</li>
</ul>

第一个无法在其回合内进行移除操作的玩家输掉游戏。假设小红和小明都采取 最优策略 。

如果小红赢得游戏，返回 <code>true</code>，否则返回 <code>false</code>。

英文元音字母包括：<code>a</code>, <code>e</code>, <code>i</code>, <code>o</code>, 和 <code>u</code>。

&nbsp;

示例 1：

<div class="example-block">
输入： s = "leetcoder"

输出： true

解释： 
小红可以执行如下移除操作来赢得游戏：

<ul>
	<li>小红先手，她可以移除加下划线的子字符串 <code>s = "leetcoder"</code>，其中包含 3 个元音。结果字符串为 <code>s = "der"</code>。</li>
	<li>小明接着，他可以移除加下划线的子字符串 <code>s = "der"</code>，其中包含 0 个元音。结果字符串为 <code>s = "er"</code>。</li>
	<li>小红再次操作，她可以移除整个字符串 <code>s = "er"</code>，其中包含 1 个元音。</li>
	<li>又轮到小明，由于字符串为空，无法执行移除操作，因此小红赢得游戏。</li>
</ul>
</div>

示例 2：

<div class="example-block">
输入： s = "bbcd"

输出： false

解释： 
小红在她的第一回合无法执行移除操作，因此小红输掉了游戏。
</div>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= s.length &lt;= 105</code></li>
	<li><code>s</code> 仅由小写英文字母组成。</li>
</ul>