leetcode-problemset/leetcode-cn/originData/number-of-subarrays-with-and-value-of-k.json

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            "categoryTitle": "Algorithms",
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            "title": "Number of Subarrays With AND Value of K",
            "titleSlug": "number-of-subarrays-with-and-value-of-k",
            "content": "<p>Given an array of integers <code>nums</code> and an integer <code>k</code>, return the number of <span data-keyword=\"subarray-nonempty\">subarrays</span> of <code>nums</code> where the bitwise <code>AND</code> of the elements of the subarray equals <code>k</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,1,1], k = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">6</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>All subarrays contain only 1&#39;s.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,1,2], k = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Subarrays having an <code>AND</code> value of 1 are: <code>[<u><strong>1</strong></u>,1,2]</code>, <code>[1,<u><strong>1</strong></u>,2]</code>, <code>[<u><strong>1,1</strong></u>,2]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,2,3], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Subarrays having an <code>AND</code> value of 2 are: <code>[1,<b><u>2</u></b>,3]</code>, <code>[1,<u><strong>2,3</strong></u>]</code>.</p>\n</div>\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], k &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "子数组按位与值为 K 的数目",
            "translatedContent": "<p>给你一个整数数组&nbsp;<code>nums</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;，请你返回&nbsp;<code>nums</code>&nbsp;中有多少个<span data-keyword=\"subarray-nonempty\">子数组</span>满足：子数组中所有元素按位&nbsp;<code>AND</code>&nbsp;的结果为 <code>k</code>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [1,1,1], k = 1</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>6</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>所有子数组都只含有元素 1 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [1,1,2], k = 1</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>3</span></p>\n\n<p><b>解释：</b></p>\n\n<p>按位&nbsp;<code>AND</code>&nbsp;值为 1 的子数组包括：<code>[<u><strong>1</strong></u>,1,2]</code>, <code>[1,<u><strong>1</strong></u>,2]</code>, <code>[<u><strong>1,1</strong></u>,2]</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [1,2,3], k = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>按位&nbsp;<code>AND</code>&nbsp;值为 2 的子数组包括：<code>[1,<b><u>2</u></b>,3]</code>, <code>[1,<u><strong>2,3</strong></u>]</code>&nbsp;。</p>\n</div>\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], k &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                    "name": "Bit Manipulation",
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            "hints": [
                "Let’s say we want to count the number of pairs <code>(l, r)</code> such that <code>nums[l] & nums[l + 1] & … & nums[r] == k</code>.",
                "Fix the left index <code>l</code>.",
                "Note that if you increase <code>r</code> for a fixed <code>l</code>, then the AND value of the subarray either decreases or remains unchanged.",
                "Therefore, consider using binary search.",
                "To calculate the AND value of a subarray, use sparse tables."
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