<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>

// DSU
class UnionFind {
public:
    vector<int> rank, parent;
    UnionFind(int n): parent(n), rank(n,0) {
        for(int i=0; i<n; i++)
            parent[i]=i;
    }
    int find(int x) {
        if(parent[x]!=x)
            parent[x]=find(parent[x]);
        return parent[x];
   }
   void doUnion(int x, int y)
   {
        int xParent=find(x);
        int yParent=find(y);

        if(xParent!=yParent)
        {
            if(rank[xParent]>rank[yParent])
                parent[yParent]=xParent;
            else if(rank[xParent]<rank[yParent])
                parent[xParent]=yParent;
            else {
                parent[yParent]=xParent;
                rank[xParent]++;
            }
            
        }
   }
};

class Solution {
public:
    vector<int> findFactors(int num){
        vector<int> factors;
        // Check for factors from 2 to sqrt(num)
        for (int i = 2; i <= sqrt(num); ++i) {
            // If i is a factor of num
            if (num % i == 0) {
                // Divide num by i as long as it is divisible
                while (num % i == 0) {
                    num /= i;
                }
                // Add i to the list of factors
                factors.push_back(i);
            }
        }

        // If num is still greater than 1, it is a prime factor
        if (num > 1) {
            factors.push_back(num);
        }
        return factors;
    }
    int largestComponentSize(vector<int>& nums) {
        int n=*max_element(nums.begin(),nums.end());
        UnionFind uf(n+1);

        int components=0;

        // calculate factors of each element in nums and
        // do the union of each number with its factor
        for(int ele:nums) {
            vector<int> factors=findFactors(ele);
            for(int f:factors) {
                if(uf.find(ele)!=uf.find(f))
                    uf.doUnion(ele,f);
            }
        }
        // after the DSU union operation, multiple components will be formed where each number and its factors will be connected

        // create a map, key:root of the component, values:count of elemnts of the component under node
        unordered_map<int,int> componentsMap;
        int componentSize=0;
        for(auto ele:nums)
        {
            int node=uf.find(ele);
            componentsMap[node]++;
            componentSize=max(componentSize,componentsMap[node]);
        }

        return componentSize;
    }
};
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