minimize-hamming-distance-after-swap-operations

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Algorithms

You are given two integer arrays, <code>source</code> and <code>target</code>, both of length <code>n</code>. You are also given an array <code>allowedSwaps</code> where each <code>allowedSwaps[i] = [ai, bi]</code> indicates that you are allowed to swap the elements at index <code>ai</code> and index <code>bi</code> (0-indexed) of array <code>source</code>. Note that you can swap elements at a specific pair of indices multiple times and in any order.

The Hamming distance of two arrays of the same length, <code>source</code> and <code>target</code>, is the number of positions where the elements are different. Formally, it is the number of indices <code>i</code> for <code>0 &lt;= i &lt;= n-1</code> where <code>source[i] != target[i]</code> (0-indexed).

Return the minimum Hamming distance of <code>source</code> and <code>target</code> after performing any amount of swap operations on array <code>source</code>.

&nbsp;
Example 1:

<pre>
Input: source = [1,2,3,4], target = [2,1,4,5], allowedSwaps = [[0,1],[2,3]]
Output: 1
Explanation: source can be transformed the following way:
- Swap indices 0 and 1: source = [2,1,3,4]
- Swap indices 2 and 3: source = [2,1,4,3]
The Hamming distance of source and target is 1 as they differ in 1 position: index 3.
</pre>

Example 2:

<pre>
Input: source = [1,2,3,4], target = [1,3,2,4], allowedSwaps = []
Output: 2
Explanation: There are no allowed swaps.
The Hamming distance of source and target is 2 as they differ in 2 positions: index 1 and index 2.
</pre>

Example 3:

<pre>
Input: source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]
Output: 0
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == source.length == target.length</code></li>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>1 &lt;= source[i], target[i] &lt;= 105</code></li>
	<li><code>0 &lt;= allowedSwaps.length &lt;= 105</code></li>
	<li><code>allowedSwaps[i].length == 2</code></li>
	<li><code>0 &lt;= ai, bi &lt;= n - 1</code></li>
	<li><code>ai != bi</code></li>
</ul>