leetcode-problemset/leetcode/problem/sum-of-all-subset-xor-totals.html

<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>

<ul>
	<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>
</ul>

<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>

<p><strong>Note:</strong> Subsets with the <strong>same</strong> elements should be counted <strong>multiple</strong> times.</p>

<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>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,3]
<strong>Output:</strong> 6
<strong>Explanation: </strong>The 4 subsets of [1,3] are:
- The empty subset has an XOR total of 0.
- [1] has an XOR total of 1.
- [3] has an XOR total of 3.
- [1,3] has an XOR total of 1 XOR 3 = 2.
0 + 1 + 3 + 2 = 6
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,1,6]
<strong>Output:</strong> 28
<strong>Explanation: </strong>The 8 subsets of [5,1,6] are:
- The empty subset has an XOR total of 0.
- [5] has an XOR total of 5.
- [1] has an XOR total of 1.
- [6] has an XOR total of 6.
- [5,1] has an XOR total of 5 XOR 1 = 4.
- [5,6] has an XOR total of 5 XOR 6 = 3.
- [1,6] has an XOR total of 1 XOR 6 = 7.
- [5,1,6] has an XOR total of 5 XOR 1 XOR 6 = 2.
0 + 5 + 1 + 6 + 4 + 3 + 7 + 2 = 28
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,4,5,6,7,8]
<strong>Output:</strong> 480
<strong>Explanation:</strong> The sum of all XOR totals for every subset is 480.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 12</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 20</code></li>
</ul>