total-hamming-distance

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Algorithms

The <a href="https://en.wikipedia.org/wiki/Hamming_distance" target="_blank">Hamming distance</a> between two integers is the number of positions at which the corresponding bits are different.

Given an integer array <code>nums</code>, return the sum of Hamming distances between all the pairs of the integers in <code>nums</code>.

&nbsp;
Example 1:

<pre>
Input: nums = [4,14,2]
Output: 6
Explanation: In binary representation, the 4 is 0100, 14 is 1110, and 2 is 0010 (just
showing the four bits relevant in this case).
The answer will be:
HammingDistance(4, 14) + HammingDistance(4, 2) + HammingDistance(14, 2) = 2 + 2 + 2 = 6.
</pre>

Example 2:

<pre>
Input: nums = [4,14,4]
Output: 4
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 104</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 109</code></li>
	<li>The answer for the given input will fit in a 32-bit integer.</li>
</ul>

totalHammingDistance

Total Hamming Distance

Hamming Distance

hamming-distance

汉明距离

Sum of Digit Differences of All Pairs

sum-of-digit-differences-of-all-pairs

所有数对中数位差之和

Bit Manipulation

Array

Math

两个整数的&nbsp;<a href="https://baike.baidu.com/item/%E6%B1%89%E6%98%8E%E8%B7%9D%E7%A6%BB/475174?fr=aladdin">汉明距离</a> 指的是这两个数字的二进制数对应位不同的数量。

给你一个整数数组 <code>nums</code>，请你计算并返回 <code>nums</code> 中任意两个数之间 汉明距离的总和 。

&nbsp;

示例 1：

<pre>
输入：nums = [4,14,2]
输出：6
解释：在二进制表示中，4 表示为 0100 ，14 表示为 1110 ，2表示为 0010 。（这样表示是为了体现后四位之间关系）
所以答案为：
HammingDistance(4, 14) + HammingDistance(4, 2) + HammingDistance(14, 2) = 2 + 2 + 2 = 6
</pre>

示例 2：

<pre>
输入：nums = [4,14,4]
输出：4
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= nums.length &lt;= 104</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 109</code></li>
	<li>给定输入的对应答案符合 32-bit 整数范围</li>
</ul>