Largest Component Size by Common Factor
<p>You are given an integer array of unique positive integers <code>nums</code>. Consider the following graph:</p>

<ul>
	<li>There are <code>nums.length</code> nodes, labeled <code>nums[0]</code> to <code>nums[nums.length - 1]</code>,</li>
	<li>There is an undirected edge between <code>nums[i]</code> and <code>nums[j]</code> if <code>nums[i]</code> and <code>nums[j]</code> share a common factor greater than <code>1</code>.</li>
</ul>

<p>Return <em>the size of the largest connected component in the graph</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0952.Largest%20Component%20Size%20by%20Common%20Factor/images/ex1.png" style="width: 500px; height: 97px;" />
<pre>
<strong>Input:</strong> nums = [4,6,15,35]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0952.Largest%20Component%20Size%20by%20Common%20Factor/images/ex2.png" style="width: 500px; height: 85px;" />
<pre>
<strong>Input:</strong> nums = [20,50,9,63]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0900-0999/0952.Largest%20Component%20Size%20by%20Common%20Factor/images/ex3.png" style="width: 500px; height: 260px;" />
<pre>
<strong>Input:</strong> nums = [2,3,6,7,4,12,21,39]
<strong>Output:</strong> 8
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
	<li>All the values of <code>nums</code> are <strong>unique</strong>.</li>
</ul>
Union Find; Array; Hash Table; Math; Number Theory
class UnionFind {
    int[] p;

    UnionFind(int n) {
        p = new int[n];
        for (int i = 0; i < n; ++i) {
            p[i] = i;
        }
    }

    void union(int a, int b) {
        int pa = find(a), pb = find(b);
        if (pa != pb) {
            p[pa] = pb;
        }
    }

    int find(int x) {
        if (p[x] != x) {
            p[x] = find(p[x]);
        }
        return p[x];
    }
}

class Solution {
    public int largestComponentSize(int[] nums) {
        int m = 0;
        for (int v : nums) {
            m = Math.max(m, v);
        }
        UnionFind uf = new UnionFind(m + 1);
        for (int v : nums) {
            int i = 2;
            while (i <= v / i) {
                if (v % i == 0) {
                    uf.union(v, i);
                    uf.union(v, v / i);
                }
                ++i;
            }
        }
        int[] cnt = new int[m + 1];
        int ans = 0;
        for (int v : nums) {
            int t = uf.find(v);
            ++cnt[t];
            ans = Math.max(ans, cnt[t]);
        }
        return ans;
    }
}