<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 {
    int parent[100001];
    int rank[100001];
    int cnt;
public:
    int largestComponentSize(vector<int>& nums) {
        memset(parent, -1, sizeof(parent));
        memset(rank, 0, sizeof(rank));
        for(auto num: nums) rank[num]++;

        this->cnt = 1;
        int n = nums.size();
        int max_num = *max_element(nums.begin(), nums.end());
        vector<int> primes = get_prime(max_num);
        int size = primes.size();
        for(int i=0; i<n; i++){
            int num = nums[i];
            for(int p_id=0; p_id<size; p_id++){
                int prime = primes[p_id];
                if(prime>num) break;
                if(prime*prime>num){
                    __union(num, nums[i]);
                    break;
                }
                if(num%prime!=0) continue;

                while(num%prime==0) num/=prime;
                __union(prime, nums[i]);
            }
        }
        return cnt;
    }

    int __find(int x){
        if(parent[x]==-1) return x;
        return parent[x] = __find(parent[x]);
    }

    void __union(int x, int y){
        int px = __find(x);
        int py = __find(y);
        if(px==py) return;
        if(px<py){
            parent[py] = px;
            rank[px] += rank[py];
            cnt = max(cnt, rank[px]);
        }
        else{
            parent[px] = py;
            rank[py] += rank[px];
            cnt = max(cnt, rank[py]);
        }
    }

    vector<int> get_prime(int n){
        bool is_prime[n+1];
        memset(is_prime, true, sizeof(is_prime));

        for(int i=2; i*i<=n; i++){
            if(!is_prime[i]) continue;

            for(int k=i*2; k<=n; k+=2) is_prime[k] = false;
        }

        vector<int> primes;
        for(int i=2; i<=n; i++) if(is_prime[i]) primes.push_back(i);
        return primes;
    }
};
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