leetcode-problemset/leetcode-cn/originData/sum-of-all-subset-xor-totals.json

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            "title": "Sum of All Subset XOR Totals",
            "titleSlug": "sum-of-all-subset-xor-totals",
            "content": "<p>The <strong>XOR total</strong> of an array is defined as the bitwise <code>XOR</code> of<strong> all its elements</strong>, or <code>0</code> if the array is<strong> empty</strong>.</p>\n\n<ul>\n\t<li>For example, the <strong>XOR total</strong> of the array <code>[2,5,6]</code> is <code>2 XOR 5 XOR 6 = 1</code>.</li>\n</ul>\n\n<p>Given an array <code>nums</code>, return <em>the <strong>sum</strong> of all <strong>XOR totals</strong> for every <strong>subset</strong> of </em><code>nums</code>.&nbsp;</p>\n\n<p><strong>Note:</strong> Subsets with the <strong>same</strong> elements should be counted <strong>multiple</strong> times.</p>\n\n<p>An array <code>a</code> is a <strong>subset</strong> of an array <code>b</code> if <code>a</code> can be obtained from <code>b</code> by deleting some (possibly zero) elements of <code>b</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,3]\n<strong>Output:</strong> 6\n<strong>Explanation: </strong>The 4 subsets of [1,3] are:\n- The empty subset has an XOR total of 0.\n- [1] has an XOR total of 1.\n- [3] has an XOR total of 3.\n- [1,3] has an XOR total of 1 XOR 3 = 2.\n0 + 1 + 3 + 2 = 6\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,1,6]\n<strong>Output:</strong> 28\n<strong>Explanation: </strong>The 8 subsets of [5,1,6] are:\n- The empty subset has an XOR total of 0.\n- [5] has an XOR total of 5.\n- [1] has an XOR total of 1.\n- [6] has an XOR total of 6.\n- [5,1] has an XOR total of 5 XOR 1 = 4.\n- [5,6] has an XOR total of 5 XOR 6 = 3.\n- [1,6] has an XOR total of 1 XOR 6 = 7.\n- [5,1,6] has an XOR total of 5 XOR 1 XOR 6 = 2.\n0 + 5 + 1 + 6 + 4 + 3 + 7 + 2 = 28\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,4,5,6,7,8]\n<strong>Output:</strong> 480\n<strong>Explanation:</strong> The sum of all XOR totals for every subset is 480.\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;= 12</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 20</code></li>\n</ul>\n",
            "translatedTitle": "找出所有子集的异或总和再求和",
            "translatedContent": "<p>一个数组的<strong> 异或总和</strong> 定义为数组中所有元素按位 <code>XOR</code> 的结果；如果数组为 <strong>空</strong> ，则异或总和为 <code>0</code> 。</p>\n\n<ul>\n\t<li>例如，数组 <code>[2,5,6]</code> 的 <strong>异或总和</strong> 为 <code>2 XOR 5 XOR 6 = 1</code> 。</li>\n</ul>\n\n<p>给你一个数组 <code>nums</code> ，请你求出 <code>nums</code> 中每个 <strong>子集</strong> 的 <strong>异或总和</strong> ，计算并返回这些值相加之 <strong>和</strong> 。</p>\n\n<p><strong>注意：</strong>在本题中，元素 <strong>相同</strong> 的不同子集应 <strong>多次</strong> 计数。</p>\n\n<p>数组 <code>a</code> 是数组 <code>b</code> 的一个 <strong>子集</strong> 的前提条件是：从 <code>b</code> 删除几个（也可能不删除）元素能够得到 <code>a</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [1,3]\n<strong>输出：</strong>6\n<strong>解释：</strong>[1,3] 共有 4 个子集：\n- 空子集的异或总和是 0 。\n- [1] 的异或总和为 1 。\n- [3] 的异或总和为 3 。\n- [1,3] 的异或总和为 1 XOR 3 = 2 。\n0 + 1 + 3 + 2 = 6\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [5,1,6]\n<strong>输出：</strong>28\n<strong>解释：</strong>[5,1,6] 共有 8 个子集：\n- 空子集的异或总和是 0 。\n- [5] 的异或总和为 5 。\n- [1] 的异或总和为 1 。\n- [6] 的异或总和为 6 。\n- [5,1] 的异或总和为 5 XOR 1 = 4 。\n- [5,6] 的异或总和为 5 XOR 6 = 3 。\n- [1,6] 的异或总和为 1 XOR 6 = 7 。\n- [5,1,6] 的异或总和为 5 XOR 1 XOR 6 = 2 。\n0 + 5 + 1 + 6 + 4 + 3 + 7 + 2 = 28\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>nums = [3,4,5,6,7,8]\n<strong>输出：</strong>480\n<strong>解释：</strong>每个子集的全部异或总和值之和为 480 。\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 &lt;= 12</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 20</code></li>\n</ul>\n",
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