<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://assets.leetcode.com/uploads/2018/12/01/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://assets.leetcode.com/uploads/2018/12/01/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://assets.leetcode.com/uploads/2018/12/01/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>

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using ll = long long;
using ll = long long;
using ll = long long;
using ll = long long;

class Dsu
{
private:
    vector<int> p;
    vector<int> size;

public:
    Dsu(int n)
    {
        p = vector<int>(n);
        size = vector<int>(n);

        for (int i = 0; i < n; i++)
        {
            make_set(i);
        }
    }
    void make_set(int a)
    {
        p[a] = a;
        size[a] = 1;
    }

    int find_set(int a)
    {
        if (p[a] == a)
        {
            return p[a];
        }
        return p[a] = find_set(p[a]);
    }

    void union_set(int a, int b)
    {
        a = find_set(a);
        b = find_set(b);

        if (a != b)
        {
            if (size[a] < size[b])
            {
                swap(a, b);
            }

            p[b] = a;
            size[a] += size[b];
        }
    }
};

class Solution
{
public:
    int largestComponentSize(vector<int> &nums)
    {
        int n = (int)1e5 + 2;
        Dsu dsu(n);

        for (auto &j : nums)
        {
            int sqroot = sqrt(j);
            for (int i = 2; i <= sqroot; i++)
            {
                if (j % i == 0)
                {
                    int x = j / i;
                    dsu.union_set(i, x);
                    dsu.union_set(j, x);
                }
            }
        }

        vector<int> mp(n);

        for (int &j : nums)
        {
            int s = dsu.find_set(j);

            mp[s] += 1;

        }

        return *max_element(mp.begin(), mp.end());


    }

};
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