<p>There are <code>n</code> couples sitting in <code>2n</code> seats arranged in a row and want to hold hands.</p>

<p>The people and seats are represented by an integer array <code>row</code> where <code>row[i]</code> is the ID of the person sitting in the <code>i<sup>th</sup></code> seat. The couples are numbered in order, the first couple being <code>(0, 1)</code>, the second couple being <code>(2, 3)</code>, and so on with the last couple being <code>(2n - 2, 2n - 1)</code>.</p>

<p>Return <em>the minimum number of swaps so that every couple is sitting side by side</em>. A swap consists of choosing any two people, then they stand up and switch seats.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> row = [0,2,1,3]
<strong>Output:</strong> 1
<strong>Explanation:</strong> We only need to swap the second (row[1]) and third (row[2]) person.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> row = [3,2,0,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All couples are already seated side by side.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2n == row.length</code></li>
	<li><code>2 &lt;= n &lt;= 30</code></li>
	<li><code>n</code> is even.</li>
	<li><code>0 &lt;= row[i] &lt; 2n</code></li>
	<li>All the elements of <code>row</code> are <strong>unique</strong>.</li>
</ul>

class DSU {
public:
    vector<int> rank, parent;
    int count;
    DSU(int n) {
        rank.resize(n);
        parent.resize(n);
        for (int i = 0; i < n; i++) parent[i] = i;
        count = n;
    }

    int find(int x) {
        return parent[x] = parent[x] == x ? x : find(parent[x]);
    }

    bool unite(int x, int y) {
        int xset = find(x), yset = find(y);
        if (xset != yset) {
            rank[xset] < rank[yset] ? parent[xset] = yset : parent[yset] = xset;
            rank[xset] += rank[xset] == rank[yset];
            count--;
            return true;
        }
        return false;
    }
};
class Solution {
public:
    int minSwapsCouples(vector<int>& row) {
        int N = row.size()/2;
        DSU myUnion = DSU(N);
        for (int i = 0; i < N; i++) {
            int a = row[2 * i];
            int b = row[2 * i + 1];
            myUnion.unite(a / 2, b / 2);
        }
        return N - myUnion.count;
    }
};
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