# GeetCode Hub

You are given two integer arrays, `source` and `target`, both of length `n`. You are also given an array `allowedSwaps` where each `allowedSwaps[i] = [ai, bi]` indicates that you are allowed to swap the elements at index `ai` and index `bi` (0-indexed) of array `source`. 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, `source` and `target`, is the number of positions where the elements are different. Formally, it is the number of indices `i` for `0 <= i <= n-1` where `source[i] != target[i]` (0-indexed).

Return the minimum Hamming distance of `source` and `target` after performing any amount of swap operations on array `source`.

Example 1:

```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.
```

Example 2:

```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.
```

Example 3:

```Input: source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]
Output: 0
```

Constraints:

• `n == source.length == target.length`
• `1 <= n <= 105`
• `1 <= source[i], target[i] <= 105`
• `0 <= allowedSwaps.length <= 105`
• `allowedSwaps[i].length == 2`
• `0 <= ai, bi <= n - 1`
• `ai != bi`

class Solution { public int minimumHammingDistance(int[] source, int[] target, int[][] allowedSwaps) { } }