leetcode-problemset/leetcode-cn/originData/count-the-number-of-beautiful-subarrays.json

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            "title": "Count the Number of Beautiful Subarrays",
            "titleSlug": "count-the-number-of-beautiful-subarrays",
            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. In one operation, you can:</p>\n\n<ul>\n\t<li>Choose two different indices <code>i</code> and <code>j</code> such that <code>0 &lt;= i, j &lt; nums.length</code>.</li>\n\t<li>Choose a non-negative integer <code>k</code> such that the <code>k<sup>th</sup></code> bit (<strong>0-indexed</strong>) in the binary representation of <code>nums[i]</code> and <code>nums[j]</code> is <code>1</code>.</li>\n\t<li>Subtract <code>2<sup>k</sup></code> from <code>nums[i]</code> and <code>nums[j]</code>.</li>\n</ul>\n\n<p>A subarray is <strong>beautiful</strong> if it is possible to make all of its elements equal to <code>0</code> after applying the above operation any number of times.</p>\n\n<p>Return <em>the number of <strong>beautiful subarrays</strong> in the array</em> <code>nums</code>.</p>\n\n<p>A subarray is a contiguous <strong>non-empty</strong> sequence of elements within an array.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,3,1,2,4]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are 2 beautiful subarrays in nums: [4,<u>3,1,2</u>,4] and [<u>4,3,1,2,4</u>].\n- We can make all elements in the subarray [3,1,2] equal to 0 in the following way:\n  - Choose [<u>3</u>, 1, <u>2</u>] and k = 1. Subtract 2<sup>1</sup> from both numbers. The subarray becomes [1, 1, 0].\n  - Choose [<u>1</u>, <u>1</u>, 0] and k = 0. Subtract 2<sup>0</sup> from both numbers. The subarray becomes [0, 0, 0].\n- We can make all elements in the subarray [4,3,1,2,4] equal to 0 in the following way:\n  - Choose [<u>4</u>, 3, 1, 2, <u>4</u>] and k = 2. Subtract 2<sup>2</sup> from both numbers. The subarray becomes [0, 3, 1, 2, 0].\n  - Choose [0, <u>3</u>, <u>1</u>, 2, 0] and k = 0. Subtract 2<sup>0</sup> from both numbers. The subarray becomes [0, 2, 0, 2, 0].\n  - Choose [0, <u>2</u>, 0, <u>2</u>, 0] and k = 1. Subtract 2<sup>1</sup> from both numbers. The subarray becomes [0, 0, 0, 0, 0].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,10,4]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no beautiful subarrays in nums.\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;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
            "translatedTitle": "统计美丽子数组数目",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组<code>nums</code>&nbsp;。每次操作中，你可以：</p>\n\n<ul>\n\t<li>选择两个满足&nbsp;<code>0 &lt;= i, j &lt; nums.length</code>&nbsp;的不同下标&nbsp;<code>i</code>&nbsp;和&nbsp;<code>j</code>&nbsp;。</li>\n\t<li>选择一个非负整数&nbsp;<code>k</code>&nbsp;，满足 <code>nums[i]</code>&nbsp;和 <code>nums[j]</code>&nbsp;在二进制下的第 <code>k</code>&nbsp;位（下标编号从 <strong>0</strong>&nbsp;开始）是 <code>1</code>&nbsp;。</li>\n\t<li>将 <code>nums[i]</code>&nbsp;和 <code>nums[j]</code>&nbsp;都减去&nbsp;<code>2<sup>k</sup></code>&nbsp;。</li>\n</ul>\n\n<p>如果一个子数组内执行上述操作若干次后，该子数组可以变成一个全为 <code>0</code>&nbsp;的数组，那么我们称它是一个 <strong>美丽</strong>&nbsp;的子数组。</p>\n\n<p>请你返回数组 <code>nums</code>&nbsp;中 <strong>美丽子数组</strong>&nbsp;的数目。</p>\n\n<p>子数组是一个数组中一段连续 <strong>非空</strong>&nbsp;的元素序列。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [4,3,1,2,4]\n<b>输出：</b>2\n<b>解释：</b>nums 中有 2 个美丽子数组：[4,<em><strong>3,1,2</strong></em>,4] 和 [<em><strong>4,3,1,2,4</strong></em>] 。\n- 按照下述步骤，我们可以将子数组 [3,1,2] 中所有元素变成 0 ：\n  - 选择 [<em><strong>3</strong></em>, 1, <em><strong>2</strong></em>] 和 k = 1 。将 2 个数字都减去 2<sup>1</sup> ，子数组变成 [1, 1, 0] 。\n  - 选择 [<em><strong>1</strong></em>, <em><strong>1</strong></em>, 0] 和 k = 0 。将 2 个数字都减去 2<sup>0</sup> ，子数组变成 [0, 0, 0] 。\n- 按照下述步骤，我们可以将子数组 [4,3,1,2,4] 中所有元素变成 0 ：\n  - 选择 [<em><strong>4</strong></em>, 3, 1, 2, <em><strong>4</strong></em>] 和 k = 2 。将 2 个数字都减去 2<sup>2</sup> ，子数组变成 [0, 3, 1, 2, 0] 。\n  - 选择 [0, <em><strong>3</strong></em>, <em><strong>1</strong></em>, 2, 0] 和 k = 0 。将 2 个数字都减去 2<sup>0</sup> ，子数组变成 [0, 2, 0, 2, 0] 。\n  - 选择 [0, <em><strong>2</strong></em>, 0, <em><strong>2</strong></em>, 0] 和 k = 1 。将 2 个数字都减去 2<sup>1</sup> ，子数组变成 [0, 0, 0, 0, 0] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,10,4]\n<b>输出：</b>0\n<b>解释：</b>nums 中没有任何美丽子数组。\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;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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