leetcode-problemset/leetcode-cn/originData/find-the-losers-of-the-circular-game.json

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            "questionId": "2791",
            "questionFrontendId": "2682",
            "categoryTitle": "Algorithms",
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            "title": "Find the Losers of the Circular Game",
            "titleSlug": "find-the-losers-of-the-circular-game",
            "content": "<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>\n\n<p>The rules of the game are as follows:</p>\n\n<p><code>1<sup>st</sup></code> friend receives the ball.</p>\n\n<ul>\n\t<li>After that, <code>1<sup>st</sup></code> friend passes it to the friend who is <code>k</code> steps away from them in the <strong>clockwise</strong> direction.</li>\n\t<li>After that, the friend who receives the ball should pass it to the friend who is <code>2 * k</code> steps away from them in the <strong>clockwise</strong> direction.</li>\n\t<li>After that, the friend who receives the ball should pass it to the friend who is <code>3 * k</code> steps away from them in the <strong>clockwise</strong> direction, and so on and so forth.</li>\n</ul>\n\n<p>In other words, on the <code>i<sup>th</sup></code> turn, the friend holding the ball should pass it to the friend who is <code>i * k</code> steps away from them in the <strong>clockwise</strong> direction.</p>\n\n<p>The game is finished when some friend receives the ball for the second time.</p>\n\n<p>The <strong>losers</strong> of the game are friends who did not receive the ball in the entire game.</p>\n\n<p>Given the number of friends, <code>n</code>, and an integer <code>k</code>, return <em>the array answer, which contains the losers of the game in the <strong>ascending</strong> order</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, k = 2\n<strong>Output:</strong> [4,5]\n<strong>Explanation:</strong> The game goes as follows:\n1) Start at 1<sup>st</sup>&nbsp;friend and pass the ball to the friend who is 2 steps away from them - 3<sup>rd</sup>&nbsp;friend.\n2) 3<sup>rd</sup>&nbsp;friend passes the ball to the friend who is 4 steps away from them - 2<sup>nd</sup>&nbsp;friend.\n3) 2<sup>nd</sup>&nbsp;friend passes the ball to the friend who is 6 steps away from them  - 3<sup>rd</sup>&nbsp;friend.\n4) The game ends as 3<sup>rd</sup>&nbsp;friend receives the ball for the second time.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, k = 4\n<strong>Output:</strong> [2,3,4]\n<strong>Explanation:</strong> The game goes as follows:\n1) Start at the 1<sup>st</sup>&nbsp;friend and pass the ball to the friend who is 4 steps away from them - 1<sup>st</sup>&nbsp;friend.\n2) The game ends as 1<sup>st</sup>&nbsp;friend receives the ball for the second time.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= n &lt;= 50</code></li>\n</ul>\n",
            "translatedTitle": "找出转圈游戏输家",
            "translatedContent": "<p><code>n</code> 个朋友在玩游戏。这些朋友坐成一个圈，按 <strong>顺时针方向</strong> 从 <code>1</code> 到 <code>n</code> 编号。准确的说，从第 <code>i</code> 个朋友的位置开始顺时针移动 <code>1</code> 步会到达第 <code>(i + 1)</code> 个朋友的位置（<code>1 &lt;= i &lt; n</code>），而从第 <code>n</code> 个朋友的位置开始顺时针移动 <code>1</code> 步会回到第 <code>1</code> 个朋友的位置。</p>\n\n<p>游戏规则如下：</p>\n\n<p>第 <code>1</code> 个朋友接球。</p>\n\n<ul>\n\t<li>接着，第 <code>1</code> 个朋友将球传给距离他顺时针方向 <code>k</code> 步的朋友。</li>\n\t<li>然后，接球的朋友应该把球传给距离他顺时针方向 <code>2 * k</code> 步的朋友。</li>\n\t<li>接着，接球的朋友应该把球传给距离他顺时针方向 <code>3 * k</code> 步的朋友，以此类推。</li>\n</ul>\n\n<p>换句话说，在第 <code>i</code> 轮中持有球的那位朋友需要将球传递给距离他顺时针方向 <code>i * k</code> 步的朋友。</p>\n\n<p>当某个朋友第 2 次接到球时，游戏结束。</p>\n\n<p>在整场游戏中没有接到过球的朋友是 <strong>输家</strong> 。</p>\n\n<p>给你参与游戏的朋友数量 <code>n</code> 和一个整数 <code>k</code> ，请按升序排列返回包含所有输家编号的数组 <code>answer</code> 作为答案。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 5, k = 2\n<strong>输出：</strong>[4,5]\n<strong>解释：</strong>以下为游戏进行情况：\n1）第 1 个朋友接球，第 1 个朋友将球传给距离他顺时针方向 2 步的玩家 —— 第 3 个朋友。\n2）第 3 个朋友将球传给距离他顺时针方向 4 步的玩家 —— 第 2 个朋友。\n3）第 2 个朋友将球传给距离他顺时针方向 6 步的玩家 —— 第 3 个朋友。\n4）第 3 个朋友接到两次球，游戏结束。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 4, k = 4\n<strong>输出：</strong>[2,3,4]\n<strong>解释：</strong>以下为游戏进行情况：\n1）第 1 个朋友接球，第 1 个朋友将球传给距离他顺时针方向 4 步的玩家 —— 第 1 个朋友。\n2）第 1 个朋友接到两次球，游戏结束。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= n &lt;= 50</code></li>\n</ul>\n",
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