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{
"data": {
"question": {
"questionId": "1826",
"questionFrontendId": "1707",
"categoryTitle": "Algorithms",
"boundTopicId": 533210,
"title": "Maximum XOR With an Element From Array",
"titleSlug": "maximum-xor-with-an-element-from-array",
"content": "<p>You are given an array <code>nums</code> consisting of non-negative integers. You are also given a <code>queries</code> array, where <code>queries[i] = [x<sub>i</sub>, m<sub>i</sub>]</code>.</p>\n\n<p>The answer to the <code>i<sup>th</sup></code> query is the maximum bitwise <code>XOR</code> value of <code>x<sub>i</sub></code> and any element of <code>nums</code> that does not exceed <code>m<sub>i</sub></code>. In other words, the answer is <code>max(nums[j] XOR x<sub>i</sub>)</code> for all <code>j</code> such that <code>nums[j] &lt;= m<sub>i</sub></code>. If all elements in <code>nums</code> are larger than <code>m<sub>i</sub></code>, then the answer is <code>-1</code>.</p>\n\n<p>Return <em>an integer array </em><code>answer</code><em> where </em><code>answer.length == queries.length</code><em> and </em><code>answer[i]</code><em> is the answer to the </em><code>i<sup>th</sup></code><em> query.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [0,1,2,3,4], queries = [[3,1],[1,3],[5,6]]\n<strong>Output:</strong> [3,3,7]\n<strong>Explanation:</strong>\n1) 0 and 1 are the only two integers not greater than 1. 0 XOR 3 = 3 and 1 XOR 3 = 2. The larger of the two is 3.\n2) 1 XOR 2 = 3.\n3) 5 XOR 2 = 7.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,2,4,6,6,3], queries = [[12,4],[8,1],[6,3]]\n<strong>Output:</strong> [15,-1,5]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length, queries.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>queries[i].length == 2</code></li>\n\t<li><code>0 &lt;= nums[j], x<sub>i</sub>, m<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
"translatedTitle": "与数组中元素的最大异或值",
"translatedContent": "<p>给你一个由非负整数组成的数组 <code>nums</code> 。另有一个查询数组 <code>queries</code> ,其中 <code>queries[i] = [x<sub>i</sub>, m<sub>i</sub>]</code> 。</p>\n\n<p>第 <code>i</code> 个查询的答案是 <code>x<sub>i</sub></code> 和任何 <code>nums</code> 数组中不超过 <code>m<sub>i</sub></code> 的元素按位异或(<code>XOR</code>)得到的最大值。换句话说,答案是 <code>max(nums[j] XOR x<sub>i</sub>)</code> ,其中所有 <code>j</code> 均满足 <code>nums[j] &lt;= m<sub>i</sub></code> 。如果 <code>nums</code> 中的所有元素都大于 <code>m<sub>i</sub></code>,最终答案就是 <code>-1</code> 。</p>\n\n<p>返回一个整数数组<em> </em><code>answer</code><em> </em>作为查询的答案,其中<em> </em><code>answer.length == queries.length</code><em> </em>且<em> </em><code>answer[i]</code><em> </em>是第<em> </em><code>i</code><em> </em>个查询的答案。</p>\n\n<p> </p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><strong>输入:</strong>nums = [0,1,2,3,4], queries = [[3,1],[1,3],[5,6]]\n<strong>输出:</strong>[3,3,7]\n<strong>解释:</strong>\n1) 0 和 1 是仅有的两个不超过 1 的整数。0 XOR 3 = 3 而 1 XOR 3 = 2 。二者中的更大值是 3 。\n2) 1 XOR 2 = 3.\n3) 5 XOR 2 = 7.\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><strong>输入:</strong>nums = [5,2,4,6,6,3], queries = [[12,4],[8,1],[6,3]]\n<strong>输出:</strong>[15,-1,5]\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length, queries.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>queries[i].length == 2</code></li>\n\t<li><code>0 &lt;= nums[j], x<sub>i</sub>, m<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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"hints": [
"In problems involving bitwise operations, we often think on the bits level. In this problem, we can think that to maximize the result of an xor operation, we need to maximize the most significant bit, then the next one, and so on.",
"If there's some number in the array that is less than m and whose the most significant bit is different than that of x, then xoring with this number maximizes the most significant bit, so I know this bit in the answer is 1.",
"To check the existence of such numbers and narrow your scope for further bits based on your choice, you can use trie.",
"You can sort the array and the queries, and maintain the trie such that in each query the trie consists exactly of the valid elements."
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