765. Couples Holding Hands 

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class Solution {
    private static class UnionFind {

        private final int[] parent;
        private final int[] size;

        public UnionFind(int n) {
            this.parent = new int[n];
            for (int i = 0; i < this.parent.length; i++) {
                parent[i] = i;
            }
            this.size = new int[n];
            Arrays.fill(size, 1);
        }

        public void union(int x, int y) {
            int xRoot = getRoot(x), yRoot = getRoot(y);
            if (xRoot == yRoot) {
                return;
            }

            if (size[xRoot] < size[yRoot]) {
                // 将 xRoot 子树嫁接至 yRoot 子树
                parent[xRoot] = yRoot;
                size[yRoot] += size[xRoot];
            } else {
                parent[yRoot] = xRoot;
                size[xRoot] += size[yRoot];
            }
        }

        public int getRoot(int x) {
            if (parent[x] != x) {
                parent[x] = getRoot(parent[x]);
            }

            return parent[x];
        }

    }

    public int minSwapsCouples(int[] row) {
        int n = row.length;
        int pairs = n / 2;

        UnionFind unionFind = new UnionFind(pairs);
        for (int i = 0; i < row.length; i += 2) {
            unionFind.union(row[i] / 2, row[i + 1] / 2); // 如果是情侣则会连接至同一个连通分量，如果不是则会成环连在一起
        }

        int circle = 0;
        for (int i = 0; i < pairs; i++) {
            if (i == unionFind.getRoot(i)) {
                circle++;
            }
        }

        return pairs - circle;
    }
}

References

765. Couples Holding Hands