leetcode-problemset/leetcode-cn/originData/circular-array-loop.json

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            "title": "Circular Array Loop",
            "titleSlug": "circular-array-loop",
            "content": "<p>You are playing a game involving a <strong>circular</strong> array of non-zero integers <code>nums</code>. Each <code>nums[i]</code> denotes the number of indices forward/backward you must move if you are located at index <code>i</code>:</p>\n\n<ul>\n\t<li>If <code>nums[i]</code> is positive, move <code>nums[i]</code> steps <strong>forward</strong>, and</li>\n\t<li>If <code>nums[i]</code> is negative, move <code>nums[i]</code> steps <strong>backward</strong>.</li>\n</ul>\n\n<p>Since the array is <strong>circular</strong>, you may assume that moving forward from the last element puts you on the first element, and moving backwards from the first element puts you on the last element.</p>\n\n<p>A <strong>cycle</strong> in the array consists of a sequence of indices <code>seq</code> of length <code>k</code> where:</p>\n\n<ul>\n\t<li>Following the movement rules above results in the repeating index sequence <code>seq[0] -&gt; seq[1] -&gt; ... -&gt; seq[k - 1] -&gt; seq[0] -&gt; ...</code></li>\n\t<li>Every <code>nums[seq[j]]</code> is either <strong>all positive</strong> or <strong>all negative</strong>.</li>\n\t<li><code>k &gt; 1</code></li>\n</ul>\n\n<p>Return <code>true</code><em> if there is a <strong>cycle</strong> in </em><code>nums</code><em>, or </em><code>false</code><em> otherwise</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/09/01/img1.jpg\" style=\"width: 402px; height: 289px;\" />\n<pre>\n<strong>Input:</strong> nums = [2,-1,1,2,2]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> The graph shows how the indices are connected. White nodes are jumping forward, while red is jumping backward.\nWe can see the cycle 0 --&gt; 2 --&gt; 3 --&gt; 0 --&gt; ..., and all of its nodes are white (jumping in the same direction).\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/09/01/img2.jpg\" style=\"width: 402px; height: 390px;\" />\n<pre>\n<strong>Input:</strong> nums = [-1,-2,-3,-4,-5,6]\n<strong>Output:</strong> false\n<strong>Explanation:</strong> The graph shows how the indices are connected. White nodes are jumping forward, while red is jumping backward.\nThe only cycle is of size 1, so we return false.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/09/01/img3.jpg\" style=\"width: 497px; height: 242px;\" />\n<pre>\n<strong>Input:</strong> nums = [1,-1,5,1,4]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> The graph shows how the indices are connected. White nodes are jumping forward, while red is jumping backward.\nWe can see the cycle 0 --&gt; 1 --&gt; 0 --&gt; ..., and while it is of size &gt; 1, it has a node jumping forward and a node jumping backward, so <strong>it is not a cycle</strong>.\nWe can see the cycle 3 --&gt; 4 --&gt; 3 --&gt; ..., and all of its nodes are white (jumping in the same direction).\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 5000</code></li>\n\t<li><code>-1000 &lt;= nums[i] &lt;= 1000</code></li>\n\t<li><code>nums[i] != 0</code></li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong>Follow up:</strong> Could you solve it in <code>O(n)</code> time complexity and <code>O(1)</code> extra space complexity?</p>\n",
            "translatedTitle": "环形数组是否存在循环",
            "translatedContent": "<p>存在一个不含 <code>0</code> 的<strong> 环形 </strong>数组&nbsp;<code>nums</code> ，每个 <code>nums[i]</code> 都表示位于下标 <code>i</code> 的角色应该向前或向后移动的下标个数：</p>\n\n<ul>\n\t<li>如果 <code>nums[i]</code> 是正数，<strong>向前</strong>（下标递增方向）移动 <code>|nums[i]|</code> 步</li>\n\t<li>如果&nbsp;<code>nums[i]</code> 是负数，<strong>向后</strong>（下标递减方向）移动 <code>|nums[i]|</code> 步</li>\n</ul>\n\n<p>因为数组是 <strong>环形</strong> 的，所以可以假设从最后一个元素向前移动一步会到达第一个元素，而第一个元素向后移动一步会到达最后一个元素。</p>\n\n<p>数组中的 <strong>循环</strong> 由长度为 <code>k</code> 的下标序列 <code>seq</code> 标识：</p>\n\n<ul>\n\t<li>遵循上述移动规则将导致一组重复下标序列 <code>seq[0] -&gt; seq[1] -&gt; ... -&gt; seq[k - 1] -&gt; seq[0] -&gt; ...</code></li>\n\t<li>所有 <code>nums[seq[j]]</code> 应当不是 <strong>全正</strong> 就是 <strong>全负</strong></li>\n\t<li><code>k &gt; 1</code></li>\n</ul>\n\n<p>如果 <code>nums</code> 中存在循环，返回 <code>true</code> ；否则，返回<em> </em><code>false</code><em> </em>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n<img alt=\"\" src=\"https://pic.leetcode.cn/1723688159-qYjpWT-image.png\" style=\"width: 402px; height: 289px;\" />\n<pre>\n<strong>输入：</strong>nums = [2,-1,1,2,2]\n<strong>输出：</strong>true\n<strong>解释：</strong>图片展示了节点间如何连接。白色节点向前跳跃，而红色节点向后跳跃。\n我们可以看到存在循环，按下标 0 -&gt; 2 -&gt; 3 -&gt; 0 --&gt; ...，并且其中的所有节点都是白色（以相同方向跳跃）。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n<img alt=\"\" src=\"https://pic.leetcode.cn/1723688183-lRSkjp-image.png\" style=\"width: 402px; height: 390px;\" />\n<pre>\n<strong>输入：</strong>nums = [-1,-2,-3,-4,-5,6]\n<strong>输出：</strong>false\n<strong>解释：</strong>图片展示了节点间如何连接。白色节点向前跳跃，而红色节点向后跳跃。\n唯一的循环长度为 1，所以返回 false。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n<img alt=\"\" src=\"https://pic.leetcode.cn/1723688199-nhaMuF-image.png\" style=\"width: 497px; height: 242px;\" />\n<pre>\n<strong>输入：</strong>nums = [1,-1,5,1,4]\n<strong>输出：</strong>true\n<strong>解释：</strong>图片展示了节点间如何连接。白色节点向前跳跃，而红色节点向后跳跃。\n我们可以看到存在循环，按下标 0 --&gt; 1 --&gt; 0 --&gt; ...，当它的大小大于 1 时，它有一个向前跳的节点和一个向后跳的节点，所以 <strong>它不是一个循环</strong>。\n我们可以看到存在循环，按下标 3 --&gt; 4 --&gt; 3 --&gt; ...，并且其中的所有节点都是白色（以相同方向跳跃）。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 5000</code></li>\n\t<li><code>-1000 &lt;= nums[i] &lt;= 1000</code></li>\n\t<li><code>nums[i] != 0</code></li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong>进阶：</strong>你能设计一个时间复杂度为 <code>O(n)</code> 且额外空间复杂度为 <code>O(1)</code> 的算法吗？</p>\n",
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\\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.11<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 <a href=\\\"http:\\/\\/www.grantjenks.com\\/docs\\/sortedcontainers\\/\\\" target=\\\"_blank\\\">sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"<p>\\u7248\\u672c\\uff1a<code>Scala 3.3.1<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"<p>\\u7248\\u672c\\uff1a<code>Kotlin 1.9.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u6211\\u4eec\\u4f7f\\u7528\\u7684\\u662f JetBrains \\u63d0\\u4f9b\\u7684 experimental compiler\\u3002\\u5982\\u679c\\u60a8\\u8ba4\\u4e3a\\u60a8\\u9047\\u5230\\u4e86\\u7f16\\u8bd1\\u5668\\u76f8\\u5173\\u7684\\u95ee\\u9898\\uff0c\\u8bf7\\u5411\\u6211\\u4eec\\u53cd\\u9988<\\/p>\"],\"rust\":[\"Rust\",\"<p>\\u7248\\u672c\\uff1a<code>rust 1.79.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 crates.io \\u7684 <a href=\\\"https:\\/\\/crates.io\\/crates\\/rand\\\" target=\\\"_blank\\\">rand<\\/a> \\u548c <a href=\\\"https:\\/\\/crates.io\\/crates\\/regex\\\" target=\\\"_blank\\\">regex<\\/a><\\/p>\"],\"php\":[\"PHP\",\"<p><code>PHP 8.2<\\/code>.<\\/p>\\r\\n\\r\\n<p>With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"<p>TypeScript 5.1.6<\\/p>\\r\\n\\r\\n<p>Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022<\\/p>\\r\\n\\r\\n<p><a href=\\\"https:\\/\\/lodash.com\\\" target=\\\"_blank\\\">lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n<p> \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 <a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/priority-queue\\/blob\\/v5\\/README.md\\\" target=\\\"_blank\\\"> datastructures-js\\/priority-queue@5.4.0<\\/a>\\uff0c<a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/queue\\/tree\\/v4.2.3\\\" target=\\\"_blank\\\"> datastructures-js\\/queue@4.2.3<\\/a> \\u4ee5\\u53ca <a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/deque\\/tree\\/v1.0.4\\\" target=\\\"_blank\\\"> datastructures-js\\/deque@1.0.4<\\/a>\\u3002<\\/p>\"],\"racket\":[\"Racket\",\"<p><a href=\\\"https:\\/\\/docs.racket-lang.org\\/guide\\/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS<\\/a> v8.15<\\/p>\\r\\n\\r\\n<p>\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n<p>\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 26\"],\"elixir\":[\"Elixir\",\"Elixir 1.17 with Erlang\\/OTP 26\"],\"dart\":[\"Dart\",\"<p>Dart 3.2\\u3002\\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 <a href=\\\"https:\\/\\/pub.dev\\/packages\\/collection\\/versions\\/1.18.0\\\" target=\\\"_blank\\\">collection<\\/a> \\u5305<\\/p>\\r\\n\\r\\n<p>\\u60a8\\u7684\\u4ee3\\u7801\\u5c06\\u4f1a\\u88ab\\u4e0d\\u7f16\\u8bd1\\u76f4\\u63a5\\u8fd0\\u884c<\\/p>\"],\"cangjie\":[\"Cangjie\",\"<p>\\u7248\\u672c\\uff1a0.53.11 (cjnative)<\\/p>\\r\\n\\r\\n<p>\\u7f16\\u8bd1\\u53c2\\u6570\\uff1a<code>-O2 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