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| 1 | +<h2><a href="https://leetcode.com/problems/sum-of-all-subset-xor-totals">Sum of All Subset XOR Totals</a></h2> <img src='https://img.shields.io/badge/Difficulty-Easy-brightgreen' alt='Difficulty: Easy' /><hr><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> |
| 2 | + |
| 3 | +<ul> |
| 4 | + <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> |
| 5 | +</ul> |
| 6 | + |
| 7 | +<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>. </p> |
| 8 | + |
| 9 | +<p><strong>Note:</strong> Subsets with the <strong>same</strong> elements should be counted <strong>multiple</strong> times.</p> |
| 10 | + |
| 11 | +<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> |
| 12 | + |
| 13 | +<p> </p> |
| 14 | +<p><strong class="example">Example 1:</strong></p> |
| 15 | + |
| 16 | +<pre> |
| 17 | +<strong>Input:</strong> nums = [1,3] |
| 18 | +<strong>Output:</strong> 6 |
| 19 | +<strong>Explanation: </strong>The 4 subsets of [1,3] are: |
| 20 | +- The empty subset has an XOR total of 0. |
| 21 | +- [1] has an XOR total of 1. |
| 22 | +- [3] has an XOR total of 3. |
| 23 | +- [1,3] has an XOR total of 1 XOR 3 = 2. |
| 24 | +0 + 1 + 3 + 2 = 6 |
| 25 | +</pre> |
| 26 | + |
| 27 | +<p><strong class="example">Example 2:</strong></p> |
| 28 | + |
| 29 | +<pre> |
| 30 | +<strong>Input:</strong> nums = [5,1,6] |
| 31 | +<strong>Output:</strong> 28 |
| 32 | +<strong>Explanation: </strong>The 8 subsets of [5,1,6] are: |
| 33 | +- The empty subset has an XOR total of 0. |
| 34 | +- [5] has an XOR total of 5. |
| 35 | +- [1] has an XOR total of 1. |
| 36 | +- [6] has an XOR total of 6. |
| 37 | +- [5,1] has an XOR total of 5 XOR 1 = 4. |
| 38 | +- [5,6] has an XOR total of 5 XOR 6 = 3. |
| 39 | +- [1,6] has an XOR total of 1 XOR 6 = 7. |
| 40 | +- [5,1,6] has an XOR total of 5 XOR 1 XOR 6 = 2. |
| 41 | +0 + 5 + 1 + 6 + 4 + 3 + 7 + 2 = 28 |
| 42 | +</pre> |
| 43 | + |
| 44 | +<p><strong class="example">Example 3:</strong></p> |
| 45 | + |
| 46 | +<pre> |
| 47 | +<strong>Input:</strong> nums = [3,4,5,6,7,8] |
| 48 | +<strong>Output:</strong> 480 |
| 49 | +<strong>Explanation:</strong> The sum of all XOR totals for every subset is 480. |
| 50 | +</pre> |
| 51 | + |
| 52 | +<p> </p> |
| 53 | +<p><strong>Constraints:</strong></p> |
| 54 | + |
| 55 | +<ul> |
| 56 | + <li><code>1 <= nums.length <= 12</code></li> |
| 57 | + <li><code>1 <= nums[i] <= 20</code></li> |
| 58 | +</ul> |
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