<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 DisjointSet{
    public:
    vector<int> parent, size;
    DisjointSet(int n) {
        parent.resize(n+1);
        size.resize(n+1, 1);
        for(int i = 0; i <= n; i++) {
            parent[i] = i;
        }
    }

    int findParent(int u) {
        if(parent[u] == u) return u;
        return parent[u] = findParent(parent[u]);
    }
    void union_(int u, int v) {
        int pu = findParent(u);
        int pv = findParent(v);
        if(pu == pv) return;

        if(size[pu] < size[pv]) {
            parent[pu] = pv;
            size[pv]+=size[pu];
        }else{
            parent[pv] = pu;
            size[pu]+=size[pv];
        }
    }
};
class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        DisjointSet ds(n);
        unordered_map<int, int> m;
        for(int i = 0; i < n; i++) {
            cout << nums[i] <<"\n";
            for(int factor = 2; factor*factor <= nums[i]; factor++) {
                if(nums[i] % factor == 0) {
                    if(m.count(factor)) {
                        // cout << "factor in map " << factor << "\n";
                        ds.union_(m[factor], i);
                    }else{
                        // cout << "no factor in map " << factor << "\n";
                        m[factor] = i;
                    }
                    while(nums[i] % factor == 0) {
                        nums[i] = nums[i]/factor;
                    }
                }   
            }
            if(nums[i] > 1) {
                if(m.count(nums[i])) {
                    // cout << "nums[i] in map " << nums[i] << "\n";
                    ds.union_(m[nums[i]], i);
                }else{
                    // cout << "no nums[i] in map " << nums[i] << "\n";
                    m[nums[i]] = i;
                }
            }
        }
        int ans = 0;
        for(int i = 0; i < n; i++) {
            if(ds.parent[i] == i) {
                ans = max(ans, ds.size[i]);    
            }
            
        }
        return ans;
    }
};
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