<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>

const int N = 2e5 + 100;

class Solution {
private:
    vector<int> parent;
    vector<int> size;

public:
    Solution() : parent(N, -1), size(N, 0) {
        for (int i = 0; i < N; i++) {
            parent[i] = i;
        }
    }

    int findParent(int v) {
        if (v == parent[v])
            return v;
        return parent[v] = findParent(parent[v]);
    }

    void combineEdge(int u, int v) {
        int a = findParent(u);
        int b = findParent(v);
        if (a != b) {
            if (size[a] < size[b]) {
                swap(a, b);
            }
            parent[b] = a;
            size[a] += size[b];
        }
    }
    
    int largestComponentSize(vector<int>& arr) {
        unordered_map<int,int> memo;
        int ret = 0;
        for(int x : arr) {
            for(int i = 2; i * i <= x; ++i) {
                if(x % i == 0) {
                    combineEdge(i, x);
                    if (i != x / i) {
                        combineEdge(x, x / i);
                    }
                }
            }
        }
        for(int x : arr) {
            ret = max(ret, ++memo[findParent(x)]);
        }
        return ret;
    }
};

215306