leetcode-problemset/leetcode-cn/originData/find-xor-sum-of-all-pairs-bitwise-and.json

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        "question": {
            "questionId": "1963",
            "questionFrontendId": "1835",
            "categoryTitle": "Algorithms",
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            "title": "Find XOR Sum of All Pairs Bitwise AND",
            "titleSlug": "find-xor-sum-of-all-pairs-bitwise-and",
            "content": "<p>The <strong>XOR sum</strong> of a list is the bitwise <code>XOR</code> of all its elements. If the list only contains one element, then its <strong>XOR sum</strong> will be equal to this element.</p>\n\n<ul>\n\t<li>For example, the <strong>XOR sum</strong> of <code>[1,2,3,4]</code> is equal to <code>1 XOR 2 XOR 3 XOR 4 = 4</code>, and the <strong>XOR sum</strong> of <code>[3]</code> is equal to <code>3</code>.</li>\n</ul>\n\n<p>You are given two <strong>0-indexed</strong> arrays <code>arr1</code> and <code>arr2</code> that consist only of non-negative integers.</p>\n\n<p>Consider the list containing the result of <code>arr1[i] AND arr2[j]</code> (bitwise <code>AND</code>) for every <code>(i, j)</code> pair where <code>0 &lt;= i &lt; arr1.length</code> and <code>0 &lt;= j &lt; arr2.length</code>.</p>\n\n<p>Return <em>the <strong>XOR sum</strong> of the aforementioned list</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr1 = [1,2,3], arr2 = [6,5]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> The list = [1 AND 6, 1 AND 5, 2 AND 6, 2 AND 5, 3 AND 6, 3 AND 5] = [0,1,2,0,2,1].\nThe XOR sum = 0 XOR 1 XOR 2 XOR 0 XOR 2 XOR 1 = 0.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr1 = [12], arr2 = [4]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The list = [12 AND 4] = [4]. The XOR sum = 4.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr1.length, arr2.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= arr1[i], arr2[j] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "所有数对按位与结果的异或和",
            "translatedContent": "<p>列表的 <strong>异或和</strong>（<strong>XOR sum</strong>）指对所有元素进行按位 <code>XOR</code> 运算的结果。如果列表中仅有一个元素，那么其 <strong>异或和</strong> 就等于该元素。</p>\n\n<ul>\n\t<li>例如，<code>[1,2,3,4]</code> 的 <strong>异或和</strong> 等于 <code>1 XOR 2 XOR 3 XOR 4 = 4</code> ，而 <code>[3]</code> 的 <strong>异或和</strong> 等于 <code>3</code> 。</li>\n</ul>\n\n<p>给你两个下标 <strong>从 0 开始</strong> 计数的数组 <code>arr1</code> 和 <code>arr2</code> ，两数组均由非负整数组成。</p>\n\n<p>根据每个 <code>(i, j)</code> 数对，构造一个由 <code>arr1[i] AND arr2[j]</code>（按位 <code>AND</code> 运算）结果组成的列表。其中 <code>0 &lt;= i &lt; arr1.length</code> 且 <code>0 &lt;= j &lt; arr2.length</code> 。</p>\n\n<p>返回上述列表的 <strong>异或和</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>arr1 = [1,2,3], arr2 = [6,5]\n<strong>输出：</strong>0\n<strong>解释：</strong>列表 = [1 AND 6, 1 AND 5, 2 AND 6, 2 AND 5, 3 AND 6, 3 AND 5] = [0,1,2,0,2,1] ，\n异或和 = 0 XOR 1 XOR 2 XOR 0 XOR 2 XOR 1 = 0 。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>arr1 = [12], arr2 = [4]\n<strong>输出：</strong>4\n<strong>解释：</strong>列表 = [12 AND 4] = [4] ，异或和 = 4 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr1.length, arr2.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= arr1[i], arr2[j] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    int getXORSum(vector<int>& arr1, vector<int>& arr2) {\n\n    }\n};",
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                    "code": "class Solution {\n  int getXORSum(List<int> arr1, List<int> arr2) {\n    \n  }\n}",
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                    "code": "# @param {Integer[]} arr1\n# @param {Integer[]} arr2\n# @return {Integer}\ndef get_xor_sum(arr1, arr2)\n\nend",
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                    "code": "object Solution {\n    def getXORSum(arr1: Array[Int], arr2: Array[Int]): Int = {\n\n    }\n}",
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                    "code": "impl Solution {\n    pub fn get_xor_sum(arr1: Vec<i32>, arr2: Vec<i32>) -> i32 {\n\n    }\n}",
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                    "code": "defmodule Solution do\n  @spec get_xor_sum(arr1 :: [integer], arr2 :: [integer]) :: integer\n  def get_xor_sum(arr1, arr2) do\n    \n  end\nend",
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            "hints": [
                "Think about (a&b) ^ (a&c). Can you simplify this expression?",
                "It is equal to a&(b^c). Then, (arr1[i]&arr2[0])^(arr1[i]&arr2[1]).. = arr1[i]&(arr2[0]^arr2[1]^arr[2]...).",
                "Let arr2XorSum = (arr2[0]^arr2[1]^arr2[2]...), arr1XorSum = (arr1[0]^arr1[1]^arr1[2]...) so the final answer is (arr2XorSum&arr1[0]) ^ (arr2XorSum&arr1[1]) ^ (arr2XorSum&arr1[2]) ^ ... = arr2XorSum & arr1XorSum."
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