leetcode-problemset/leetcode-cn/originData/count-pairs-with-xor-in-a-range.json

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        "question": {
            "questionId": "1907",
            "questionFrontendId": "1803",
            "categoryTitle": "Algorithms",
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            "title": "Count Pairs With XOR in a Range",
            "titleSlug": "count-pairs-with-xor-in-a-range",
            "content": "<p>Given a <strong>(0-indexed)</strong> integer array <code>nums</code> and two integers <code>low</code> and <code>high</code>, return <em>the number of <strong>nice pairs</strong></em>.</p>\r\n\r\n<p>A <strong>nice pair</strong> is a pair <code>(i, j)</code> where <code>0 &lt;= i &lt; j &lt; nums.length</code> and <code>low &lt;= (nums[i] XOR nums[j]) &lt;= high</code>.</p>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Example 1:</strong></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> nums = [1,4,2,7], low = 2, high = 6\r\n<strong>Output:</strong> 6\r\n<strong>Explanation:</strong> All nice pairs (i, j) are as follows:\r\n    - (0, 1): nums[0] XOR nums[1] = 5 \r\n    - (0, 2): nums[0] XOR nums[2] = 3\r\n    - (0, 3): nums[0] XOR nums[3] = 6\r\n    - (1, 2): nums[1] XOR nums[2] = 6\r\n    - (1, 3): nums[1] XOR nums[3] = 3\r\n    - (2, 3): nums[2] XOR nums[3] = 5\r\n</pre>\r\n\r\n<p><strong>Example 2:</strong></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> nums = [9,8,4,2,1], low = 5, high = 14\r\n<strong>Output:</strong> 8\r\n<strong>Explanation:</strong> All nice pairs (i, j) are as follows:\r\n​​​​​    - (0, 2): nums[0] XOR nums[2] = 13\r\n&nbsp;   - (0, 3): nums[0] XOR nums[3] = 11\r\n&nbsp;   - (0, 4): nums[0] XOR nums[4] = 8\r\n&nbsp;   - (1, 2): nums[1] XOR nums[2] = 12\r\n&nbsp;   - (1, 3): nums[1] XOR nums[3] = 10\r\n&nbsp;   - (1, 4): nums[1] XOR nums[4] = 9\r\n&nbsp;   - (2, 3): nums[2] XOR nums[3] = 6\r\n&nbsp;   - (2, 4): nums[2] XOR nums[4] = 5</pre>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Constraints:</strong></p>\r\n\r\n<ul>\r\n\t<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>\r\n\t<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>\r\n\t<li><code>1 &lt;= low &lt;= high &lt;= 2 * 10<sup>4</sup></code></li>\r\n</ul>",
            "translatedTitle": "统计异或值在范围内的数对有多少",
            "translatedContent": "<p>给你一个整数数组 <code>nums</code> （下标 <strong>从 0 开始</strong> 计数）以及两个整数：<code>low</code> 和 <code>high</code> ，请返回 <strong>漂亮数对</strong> 的数目。</p>\n\n<p><strong>漂亮数对</strong> 是一个形如 <code>(i, j)</code> 的数对，其中 <code>0 &lt;= i &lt; j &lt; nums.length</code> 且 <code>low &lt;= (nums[i] XOR nums[j]) &lt;= high</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [1,4,2,7], low = 2, high = 6\n<strong>输出：</strong>6\n<strong>解释：</strong>所有漂亮数对 (i, j) 列出如下：\n    - (0, 1): nums[0] XOR nums[1] = 5 \n    - (0, 2): nums[0] XOR nums[2] = 3\n    - (0, 3): nums[0] XOR nums[3] = 6\n    - (1, 2): nums[1] XOR nums[2] = 6\n    - (1, 3): nums[1] XOR nums[3] = 3\n    - (2, 3): nums[2] XOR nums[3] = 5\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [9,8,4,2,1], low = 5, high = 14\n<strong>输出：</strong>8\n<strong>解释：</strong>所有漂亮数对 (i, j) 列出如下：\n​​​​​    - (0, 2): nums[0] XOR nums[2] = 13\n    - (0, 3): nums[0] XOR nums[3] = 11\n    - (0, 4): nums[0] XOR nums[4] = 8\n    - (1, 2): nums[1] XOR nums[2] = 12\n    - (1, 3): nums[1] XOR nums[3] = 10\n    - (1, 4): nums[1] XOR nums[4] = 9\n    - (2, 3): nums[2] XOR nums[3] = 6\n    - (2, 4): nums[2] XOR nums[4] = 5</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= low &lt;= high &lt;= 2 * 10<sup>4</sup></code></li>\n</ul>\n",
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            "hints": [
                "Let's note that we can count all pairs with XOR ≤ K, so the answer would be to subtract the number of pairs withs XOR < low from the number of pairs with XOR ≤ high.",
                "For each value, find out the number of values when you XOR it with the result is  ≤ K using a trie."
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