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feat: add new leetcode problems
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# [1822. 数组元素积的符号](https://leetcode-cn.com/problems/sign-of-the-product-of-an-array)
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[English Version](/solution/1800-1899/1822.Sign%20of%20the%20Product%20of%20an%20Array/README_EN.md)
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## 题目描述
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<!-- 这里写题目描述 -->
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<p>已知函数 <code>signFunc(x)</code> 将会根据 <code>x</code> 的正负返回特定值:</p>
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<ul>
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<li>如果 <code>x</code> 是正数,返回 <code>1</code> 。</li>
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<li>如果 <code>x</code> 是负数,返回 <code>-1</code> 。</li>
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<li>如果 <code>x</code> 是等于 <code>0</code> ,返回 <code>0</code> 。</li>
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</ul>
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<p>给你一个整数数组 <code>nums</code> 。令 <code>product</code> 为数组 <code>nums</code> 中所有元素值的乘积。</p>
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<p>返回 <code>signFunc(product)</code> 。</p>
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<p> </p>
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<p><strong>示例 1:</strong></p>
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<pre>
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<strong>输入:</strong>nums = [-1,-2,-3,-4,3,2,1]
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<strong>输出:</strong>1
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<strong>解释:</strong>数组中所有值的乘积是 144 ,且 signFunc(144) = 1
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</pre>
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<p><strong>示例 2:</strong></p>
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<pre>
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<strong>输入:</strong>nums = [1,5,0,2,-3]
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<strong>输出:</strong>0
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<strong>解释:</strong>数组中所有值的乘积是 0 ,且 signFunc(0) = 0
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</pre>
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<p><strong>示例 3:</strong></p>
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<pre>
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<strong>输入:</strong>nums = [-1,1,-1,1,-1]
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<strong>输出:</strong>-1
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<strong>解释:</strong>数组中所有值的乘积是 -1 ,且 signFunc(-1) = -1
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</pre>
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<p> </p>
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<p><strong>提示:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 1000</code></li>
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<li><code>-100 <= nums[i] <= 100</code></li>
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</ul>
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## 解法
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<!-- 这里可写通用的实现逻辑 -->
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->
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# [1822. Sign of the Product of an Array](https://leetcode.com/problems/sign-of-the-product-of-an-array)
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[中文文档](/solution/1800-1899/1822.Sign%20of%20the%20Product%20of%20an%20Array/README.md)
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## Description
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<p>There is a function <code>signFunc(x)</code> that returns:</p>
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<ul>
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<li><code>1</code> if <code>x</code> is positive.</li>
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<li><code>-1</code> if <code>x</code> is negative.</li>
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<li><code>0</code> if <code>x</code> is equal to <code>0</code>.</li>
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</ul>
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<p>You are given an integer array <code>nums</code>. Let <code>product</code> be the product of all values in the array <code>nums</code>.</p>
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<p>Return <code>signFunc(product)</code>.</p>
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<p>&nbsp;</p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [-1,-2,-3,-4,3,2,1]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> The product of all values in the array is 144, and signFunc(144) = 1
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,5,0,2,-3]
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> The product of all values in the array is 0, and signFunc(0) = 0
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [-1,1,-1,1,-1]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong> The product of all values in the array is -1, and signFunc(-1) = -1
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</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
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<li><code>-100 &lt;= nums[i] &lt;= 100</code></li>
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</ul>
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## Solutions
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<!-- tabs:start -->
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### **Python3**
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```python
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```
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### **Java**
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->
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# [1823. 找出游戏的获胜者](https://leetcode-cn.com/problems/find-the-winner-of-the-circular-game)
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[English Version](/solution/1800-1899/1823.Find%20the%20Winner%20of%20the%20Circular%20Game/README_EN.md)
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## 题目描述
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<!-- 这里写题目描述 -->
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<p>共有 <code>n</code> 名小伙伴一起做游戏。小伙伴们围成一圈,按 <strong>顺时针顺序</strong> 从 <code>1</code> 到 <code>n</code> 编号。确切地说,从第 <code>i</code> 名小伙伴顺时针移动一位会到达第 <code>(i+1)</code> 名小伙伴的位置,其中 <code>1 <= i < n</code> ,从第 <code>n</code> 名小伙伴顺时针移动一位会回到第 <code>1</code> 名小伙伴的位置。</p>
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<p>游戏遵循如下规则:</p>
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<ol>
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<li>从第 <code>1</code> 名小伙伴所在位置 <strong>开始</strong> 。</li>
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<li>沿着顺时针方向数 <code>k</code> 名小伙伴,计数时需要 <strong>包含</strong> 起始时的那位小伙伴。逐个绕圈进行计数,一些小伙伴可能会被数过不止一次。</li>
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<li>你数到的最后一名小伙伴需要离开圈子,并视作输掉游戏。</li>
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<li>如果圈子中仍然有不止一名小伙伴,从刚刚输掉的小伙伴的 <strong>顺时针下一位</strong> 小伙伴 <strong>开始</strong>,回到步骤 <code>2</code> 继续执行。</li>
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<li>否则,圈子中最后一名小伙伴赢得游戏。</li>
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</ol>
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<p>给你参与游戏的小伙伴总数 <code>n</code> ,和一个整数 <code>k</code> ,返回游戏的获胜者。</p>
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<p> </p>
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<p><strong>示例 1:</strong></p>
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![](./images/ic234-q2-ex11.png)
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<pre>
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<strong>输入:</strong>n = 5, k = 2
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<strong>输出:</strong>3
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<strong>解释:</strong>游戏运行步骤如下:
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1) 从小伙伴 1 开始。
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2) 顺时针数 2 名小伙伴,也就是小伙伴 1 和 2 。
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3) 小伙伴 2 离开圈子。下一次从小伙伴 3 开始。
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4) 顺时针数 2 名小伙伴,也就是小伙伴 3 和 4 。
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5) 小伙伴 4 离开圈子。下一次从小伙伴 5 开始。
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6) 顺时针数 2 名小伙伴,也就是小伙伴 5 和 1 。
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7) 小伙伴 1 离开圈子。下一次从小伙伴 3 开始。
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8) 顺时针数 2 名小伙伴,也就是小伙伴 3 和 5 。
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9) 小伙伴 5 离开圈子。只剩下小伙伴 3 。所以小伙伴 3 是游戏的获胜者。</pre>
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<p><strong>示例 2:</strong></p>
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<pre>
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<strong>输入:</strong>n = 6, k = 5
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<strong>输出:</strong>1
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<strong>解释:</strong>小伙伴离开圈子的顺序:5、4、6、2、3 。小伙伴 1 是游戏的获胜者。
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</pre>
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<p> </p>
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<p><strong>提示:</strong></p>
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<ul>
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<li><code>1 <= k <= n <= 500</code></li>
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</ul>
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## 解法
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<!-- 这里可写通用的实现逻辑 -->
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->
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# [1823. Find the Winner of the Circular Game](https://leetcode.com/problems/find-the-winner-of-the-circular-game)
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[中文文档](/solution/1800-1899/1823.Find%20the%20Winner%20of%20the%20Circular%20Game/README.md)
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## Description
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<p>There are <code>n</code> friends that are playing a game. The friends are sitting in a circle and are numbered from <code>1</code> to <code>n</code> in <strong>clockwise order</strong>. More formally, moving clockwise from the <code>i<sup>th</sup></code> friend brings you to the <code>(i+1)<sup>th</sup></code> friend for <code>1 &lt;= i &lt; n</code>, and moving clockwise from the <code>n<sup>th</sup></code> friend brings you to the <code>1<sup>st</sup></code> friend.</p>
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<p>The rules of the game are as follows:</p>
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<ol>
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<li><strong>Start</strong> at the <code>1<sup>st</sup></code> friend.</li>
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<li>Count the next <code>k</code> friends in the clockwise direction <strong>including</strong> the friend you started at. The counting wraps around the circle and may count some friends more than once.</li>
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<li>The last friend you counted leaves the circle and loses the game.</li>
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<li>If there is still more than one friend in the circle, go back to step <code>2</code> <strong>starting</strong> from the friend <strong>immediately clockwise</strong> of the friend who just lost and repeat.</li>
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<li>Else, the last friend in the circle wins the game.</li>
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</ol>
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<p>Given the number of friends, <code>n</code>, and an integer <code>k</code>, return <em>the winner of the game</em>.</p>
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<p>&nbsp;</p>
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<p><strong>Example 1:</strong></p>
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![](./images/ic234-q2-ex11.png)
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<pre>
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<strong>Input:</strong> n = 5, k = 2
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<strong>Output:</strong> 3
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<strong>Explanation:</strong> Here are the steps of the game:
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1) Start at friend 1.
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2) Count 2 friends clockwise, which are friends 1 and 2.
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3) Friend 2 leaves the circle. Next start is friend 3.
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4) Count 2 friends clockwise, which are friends 3 and 4.
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5) Friend 4 leaves the circle. Next start is friend 5.
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6) Count 2 friends clockwise, which are friends 5 and 1.
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7) Friend 1 leaves the circle. Next start is friend 3.
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8) Count 2 friends clockwise, which are friends 3 and 5.
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9) Friend 5 leaves the circle. Only friend 3 is left, so they are the winner.</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 6, k = 5
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> The friends leave in this order: 5, 4, 6, 2, 3. The winner is friend 1.
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</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= k &lt;= n &lt;= 500</code></li>
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</ul>
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## Solutions
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<!-- tabs:start -->
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### **Python3**
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```python
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```
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### **Java**
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```java
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```
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### **...**
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```
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```
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<!-- tabs:end -->
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