<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 DSU{

    public: 
    vector<int> parent, rank;
    bool debug = false;

    DSU(int n){
        parent.resize(n);
        rank.resize(n);

        for(int i = 0; i < n; i++) parent[i] = i;
    }

    void getUnion(int a, int b){        // get union with rank

        // if(debug) cout << "Get union for " << a << "  " << b << endl;

        int pa = find(a);
        int pb = find(b);

        if(pa == pb){ // already connected
            return;
        }

        if(rank[pa] < rank[pb]){
            parent[pa] = pb;
            rank[pb]++;
        }else{
            parent[pb] = pa;
            rank[pa]++;
        }
    }

    int find(int a){
        // if(debug) cout << "Find for " << a << " " << parent[a] << endl;
        if(parent[a] == a) return a;
        return parent[a] = find(parent[a]);
    }
};

class Solution {
    public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        DSU *dsu = new DSU(1e5 + 1);

        for(int i = 0; i < n; i++){
            for(int j = 2; j <= sqrt(nums[i]); j++){
                if(nums[i] % j == 0){ 
                    dsu->getUnion(nums[i], j);
                    dsu->getUnion(nums[i], nums[i] / j);
                }
            }
        }

        unordered_map<int, int> m;
        int res = 0;
        for(int i = 0; i < n; i++){ 
            int parent = dsu->find(nums[i]);
            m[parent]++;
            res = max(res, m[parent]);
        }

        return res;
    }
};

class SolutionV2 {
public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        DSU *dsu = new DSU(n);

        for(int i = 0; i < n; i++){
            for(int j = i + 1; j < n; j++){
                if(__gcd(nums[i], nums[j]) != 1) dsu->getUnion(i, j);
            }
        }



        unordered_map<int, int> m;
        int res = 0;
        for(int i = 0; i < n; i++){ 
            m[dsu->parent[i]]++;
            res = max(res, m[dsu->parent[i]]);
        }

        return res;
    }
};
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