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47 lines
2.6 KiB
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<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>
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<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 <= i <= n-1</code> where <code>source[i] != target[i]</code> <strong>(0-indexed)</strong>.</p>
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<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>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> source = [1,2,3,4], target = [2,1,4,5], allowedSwaps = [[0,1],[2,3]]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> source can be transformed the following way:
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- Swap indices 0 and 1: source = [<u>2</u>,<u>1</u>,3,4]
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- Swap indices 2 and 3: source = [2,1,<u>4</u>,<u>3</u>]
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The Hamming distance of source and target is 1 as they differ in 1 position: index 3.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> source = [1,2,3,4], target = [1,3,2,4], allowedSwaps = []
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> There are no allowed swaps.
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The Hamming distance of source and target is 2 as they differ in 2 positions: index 1 and index 2.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]
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<strong>Output:</strong> 0
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == source.length == target.length</code></li>
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<li><code>1 <= n <= 10<sup>5</sup></code></li>
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<li><code>1 <= source[i], target[i] <= 10<sup>5</sup></code></li>
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<li><code>0 <= allowedSwaps.length <= 10<sup>5</sup></code></li>
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<li><code>allowedSwaps[i].length == 2</code></li>
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<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> <= n - 1</code></li>
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<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
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</ul>
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