<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>

struct DSU {
    vector<int> parent, size;

    DSU(int n) {
        parent.resize(n + 1);
        size.resize(n + 1, 1);
        for (int i = 0; i <= n; i++) {
            parent[i] = i;
        }
    }

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

    void unionBySize(int u, int v) {
        int pu = findParent(u);
        int pv = findParent(v);
        if (pu == pv) return;
        if (size[pu] > size[pv]) {
            parent[pv] = pu;
            size[pu] += size[pv];
        } else {
            parent[pu] = pv;
            size[pv] += size[pu];
        }
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        int maxNum = *max_element(nums.begin(), nums.end());
        DSU dsu(maxNum);
        
        unordered_map<int, int> primeToIndex;
        
        for (int num : nums) {
            int originalNum = num;
            for (int p = 2; p * p <= num; p++) {
                if (num % p == 0) {
                    if (!primeToIndex.count(p)) {
                        primeToIndex[p] = originalNum;
                    } else {
                        dsu.unionBySize(primeToIndex[p], originalNum);
                    }
                    while (num % p == 0) num /= p;
                }
            }
            if (num > 1) {
                if (!primeToIndex.count(num)) {
                    primeToIndex[num] = originalNum;
                } else {
                    dsu.unionBySize(primeToIndex[num], originalNum);
                }
            }
        }
        
        unordered_map<int, int> componentSize;
        int largestComponent = 0;
        
        for (int num : nums) {
            int parent = dsu.findParent(num);
            componentSize[parent]++;
            largestComponent = max(largestComponent, componentSize[parent]);
        }
        
        return largestComponent;
    }
};

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