<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>

class Solution {
private:   
    vector<int> parents, groupsSize;
    unordered_map<int, int> mp;
public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        int maxNum = *max_element(nums.begin(), nums.end());
        parents.resize(maxNum+1);
        groupsSize.resize(maxNum+1, 0);
        iota(parents.begin(), parents.end(), 0);
        for(int& num: nums) {
            for(int f=2; f<=sqrt(num); f++) {
                if(num % f == 0) {
                    uni(num, f);
                    uni(num, num/f);
                }
            }
        }
        int ans = 1;
        for(int num: nums) {
            ans = max(ans, ++groupsSize[find(num)]);
        }
        // printf("%d\n", *max_element(begin(nums), end(nums)));
        return ans;
    }
    int find(int x) {
        if(parents[x] == x) return x;
        return parents[x] = find(parents[x]);
    }
    void uni(int x, int y) {
        x = find(x), y = find(y);
        if(x != y) {
            parents[x] = y;
            // groupsSize[y] += groupsSize[x];
        }
    }
    int gcd(int x, int y) {
        int tmp;
        while(y) {
            tmp = y;
            y = x % y;
            x = tmp;
        }
        return x;
    }
};
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