<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 {
public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        int maxEle = *max_element(nums.begin(), nums.end())+1;
        unordered_map<int, int> parent;
        for(int i=0; i<maxEle; i++){
            parent[i] = i;
        }


        for(int c: nums){
            for(int f=2; f<=sqrt(c); f++){
                if(c%f == 0){
                    unionAll(c, f, parent);
                    unionAll(c, c/f, parent);
                }
            }
        }
        unordered_map<int, int> mp;   
        int ans = 0;          
        for(int i=0; i<n; i++){
            ans = max(ans, ++mp[find(nums[i], parent)]);
        }
        return ans;
    }

    int find(int x, unordered_map<int, int> &parent){
        if(x == parent[x]){
            return x;
        }
        return parent[x] = find(parent[x], parent);
    }
    void unionAll(int x, int y, unordered_map<int, int> &parent){
        int px = find(x, parent);
        int py = find(y, parent);
        parent[py]=px;
    }

    bool hasCommon(int x, int y){
        for(int i=2; i<=min(x,y); i++){
            if(x%i==0 && y%i==0){
                return true;
            }
        }
        return false;
    }
};
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