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            "title": "Minimize Hamming Distance After Swap Operations",
            "titleSlug": "minimize-hamming-distance-after-swap-operations",
            "content": "<p>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] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that you are allowed to swap the elements at index <code>a<sub>i</sub></code> and index <code>b<sub>i</sub></code> <strong>(0-indexed)</strong> of array <code>source</code>. Note that you can swap elements at a specific pair of indices <strong>multiple</strong> times and in <strong>any</strong> order.</p>\n\n<p>The <strong>Hamming distance</strong> 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> <strong>(0-indexed)</strong>.</p>\n\n<p>Return <em>the <strong>minimum Hamming distance</strong> of </em><code>source</code><em> and </em><code>target</code><em> after performing <strong>any</strong> amount of swap operations on array </em><code>source</code><em>.</em></p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = [1,2,3,4], target = [2,1,4,5], allowedSwaps = [[0,1],[2,3]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> source can be transformed the following way:\n- Swap indices 0 and 1: source = [<u>2</u>,<u>1</u>,3,4]\n- Swap indices 2 and 3: source = [2,1,<u>4</u>,<u>3</u>]\nThe Hamming distance of source and target is 1 as they differ in 1 position: index 3.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = [1,2,3,4], target = [1,3,2,4], allowedSwaps = []\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are no allowed swaps.\nThe Hamming distance of source and target is 2 as they differ in 2 positions: index 1 and index 2.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]\n<strong>Output:</strong> 0\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == source.length == target.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= source[i], target[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= allowedSwaps.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>allowedSwaps[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n</ul>\n",
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                    "lang": "C++",
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                    "code": "class Solution {\npublic:\n    int minimumHammingDistance(vector<int>& source, vector<int>& target, vector<vector<int>>& allowedSwaps) {\n        \n    }\n};",
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                    "code": "class Solution {\n    public int minimumHammingDistance(int[] source, int[] target, int[][] allowedSwaps) {\n        \n    }\n}",
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                    "code": "class Solution(object):\n    def minimumHammingDistance(self, source, target, allowedSwaps):\n        \"\"\"\n        :type source: List[int]\n        :type target: List[int]\n        :type allowedSwaps: List[List[int]]\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "class Solution:\n    def minimumHammingDistance(self, source: List[int], target: List[int], allowedSwaps: List[List[int]]) -> int:\n        ",
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                    "lang": "C",
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                    "code": "\n\nint minimumHammingDistance(int* source, int sourceSize, int* target, int targetSize, int** allowedSwaps, int allowedSwapsSize, int* allowedSwapsColSize){\n\n}",
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                    "code": "public class Solution {\n    public int MinimumHammingDistance(int[] source, int[] target, int[][] allowedSwaps) {\n        \n    }\n}",
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                    "code": "/**\n * @param {number[]} source\n * @param {number[]} target\n * @param {number[][]} allowedSwaps\n * @return {number}\n */\nvar minimumHammingDistance = function(source, target, allowedSwaps) {\n    \n};",
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                    "code": "# @param {Integer[]} source\n# @param {Integer[]} target\n# @param {Integer[][]} allowed_swaps\n# @return {Integer}\ndef minimum_hamming_distance(source, target, allowed_swaps)\n    \nend",
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                    "code": "class Solution {\n    func minimumHammingDistance(_ source: [Int], _ target: [Int], _ allowedSwaps: [[Int]]) -> Int {\n        \n    }\n}",
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                    "lang": "Go",
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                    "code": "func minimumHammingDistance(source []int, target []int, allowedSwaps [][]int) int {\n    \n}",
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                    "code": "object Solution {\n    def minimumHammingDistance(source: Array[Int], target: Array[Int], allowedSwaps: Array[Array[Int]]): Int = {\n        \n    }\n}",
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                    "code": "class Solution {\n    fun minimumHammingDistance(source: IntArray, target: IntArray, allowedSwaps: Array<IntArray>): Int {\n        \n    }\n}",
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                    "lang": "Rust",
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                    "code": "impl Solution {\n    pub fn minimum_hamming_distance(source: Vec<i32>, target: Vec<i32>, allowed_swaps: Vec<Vec<i32>>) -> i32 {\n        \n    }\n}",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $source\n     * @param Integer[] $target\n     * @param Integer[][] $allowedSwaps\n     * @return Integer\n     */\n    function minimumHammingDistance($source, $target, $allowedSwaps) {\n        \n    }\n}",
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                    "code": "function minimumHammingDistance(source: number[], target: number[], allowedSwaps: number[][]): number {\n\n};",
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                "The source array can be imagined as a graph where each index is a node and each allowedSwaps[i] is an edge.",
                "Nodes within the same component can be freely swapped with each other.",
                "For each component, find the number of common elements. The elements that are not in common will contribute to the total Hamming distance."
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