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

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Algorithms

You are given an array <code>nums</code> consisting of positive integers where all integers have the same number of digits.

The digit difference between two integers is the count of different digits that are in the same position in the two integers.

Return the sum of the digit differences between all pairs of integers in <code>nums</code>.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [13,23,12]

Output: 4

Explanation: 
We have the following: 
- The digit difference between 13 and 23 is 1. 
- The digit difference between 13 and 12 is 1. 
- The digit difference between 23 and 12 is 2. 
So the total sum of digit differences between all pairs of integers is <code>1 + 1 + 2 = 4</code>.
</div>

Example 2:

<div class="example-block">
Input: nums = [10,10,10,10]

Output: 0

Explanation: 
All the integers in the array are the same. So the total sum of digit differences between all pairs of integers will be 0.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt; 109</code></li>
	<li>All integers in <code>nums</code> have the same number of digits.</li>
</ul>

sumDigitDifferences

Sum of Digit Differences of All Pairs

Total Hamming Distance

total-hamming-distance

汉明距离总和

Array

Hash Table

Math

Counting

你有一个数组&nbsp;<code>nums</code>&nbsp;，它只包含 正&nbsp;整数，所有正整数的数位长度都 相同&nbsp;。

两个整数的 数位差&nbsp;指的是两个整数 相同&nbsp;位置上不同数字的数目。

请你返回 <code>nums</code>&nbsp;中 所有&nbsp;整数对里，数位差之和。

&nbsp;

示例 1：

<div class="example-block">
输入：nums = [13,23,12]

输出：4

解释： 
计算过程如下： 
-&nbsp;13 和&nbsp;23 的数位差为&nbsp;1 。 
- 13 和 12&nbsp;的数位差为&nbsp;1 。 
-&nbsp;23 和&nbsp;12&nbsp;的数位差为&nbsp;2 。 
所以所有整数数对的数位差之和为&nbsp;<code>1 + 1 + 2 = 4</code>&nbsp;。
</div>

示例 2：

<div class="example-block">
输入：nums = [10,10,10,10]

输出：0

解释： 
数组中所有整数都相同，所以所有整数数对的数位不同之和为 0 。
</div>

&nbsp;

提示：

<ul>
	<li><code>2 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt; 109</code></li>
	<li><code>nums</code>&nbsp;中的整数都有相同的数位长度。</li>
</ul>