Project Notes

Nim Game

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Description

tab: English
 
<p>You are playing the following Nim Game with your friend:</p>
 
<ul>
	<li>Initially, there is a heap of stones on the table.</li>
	<li>You and your friend will alternate taking turns, and <strong>you go first</strong>.</li>
	<li>On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.</li>
	<li>The one who removes the last stone is the winner.</li>
</ul>
 
<p>Given <code>n</code>, the number of stones in the heap, return <code>true</code><em> if you can win the game assuming both you and your friend play optimally, otherwise return </em><code>false</code>.</p>
 
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
 
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> false
<strong>Explanation:</strong> These are the possible outcomes:
1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.
2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.
3. You remove 3 stones. Your friend removes the last stone. Your friend wins.
In all outcomes, your friend wins.
</pre>
 
<p><strong class="example">Example 2:</strong></p>
 
<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> true
</pre>
 
<p><strong class="example">Example 3:</strong></p>
 
<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> true
</pre>
 
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
 
<ul>
	<li><code>1 &lt;= n &lt;= 2<sup>31</sup> - 1</code></li>
</ul>
 
 
 
> [!tip]- Hint 1
> 
> If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?
 
 
---
 
[submissions](https://leetcode.com/problems/nim-game/submissions/) | [solutions](https://leetcode.com/problems/nim-game/solutions/)
 
 
tab: 中文
 
<p>你和你的朋友，两个人一起玩&nbsp;<a href="https://baike.baidu.com/item/Nim游戏/6737105" target="_blank">Nim 游戏</a>：</p>
 
<ul>
	<li>桌子上有一堆石头。</li>
	<li>你们轮流进行自己的回合，&nbsp;<strong>你作为先手&nbsp;</strong>。</li>
	<li>每一回合，轮到的人拿掉&nbsp;1 - 3 块石头。</li>
	<li>拿掉最后一块石头的人就是获胜者。</li>
</ul>
 
<p>假设你们每一步都是最优解。请编写一个函数，来判断你是否可以在给定石头数量为 <code>n</code> 的情况下赢得游戏。如果可以赢，返回 <code>true</code>；否则，返回 <code>false</code> 。</p>
 
<p>&nbsp;</p>
 
<p><strong>示例 1：</strong></p>
 
<pre>
<strong>输入：</strong><code>n = 4</code>
<strong>输出：</strong>false 
<strong>解释：</strong>以下是可能的结果:
1. 移除1颗石头。你的朋友移走了3块石头，包括最后一块。你的朋友赢了。
2. 移除2个石子。你的朋友移走2块石头，包括最后一块。你的朋友赢了。
3.你移走3颗石子。你的朋友移走了最后一块石头。你的朋友赢了。
在所有结果中，你的朋友是赢家。
</pre>
 
<p><strong>示例 2：</strong></p>
 
<pre>
<strong>输入：</strong>n = 1
<strong>输出：</strong>true
</pre>
 
<p><strong>示例 3：</strong></p>
 
<pre>
<strong>输入：</strong>n = 2
<strong>输出：</strong>true
</pre>
 
<p>&nbsp;</p>
 
<p><strong>提示：</strong></p>
 
<ul>
	<li><code>1 &lt;= n &lt;= 2<sup>31</sup> - 1</code></li>
</ul>
 
 
 
> [!tip]- 提示 1
> 
> If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?
 
 
---
 
[提交记录](https://leetcode.cn/problems/nim-game/submissions/) | [题解](https://leetcode.cn/problems/nim-game/solution/)

Solutions & Notes

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