<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 {
public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        unordered_map<int, int> primeToIndex;
        vector<int> parent(n);
        iota(parent.begin(), parent.end(), 0);

        // Lambda to find the root of the set
        function<int(int)> find = [&](int x) {
            if (parent[x] != x) {
                parent[x] = find(parent[x]); // Path compression
            }
            return parent[x];
        };

        // Lambda to union two sets
        auto unionSets = [&](int x, int y) {
            parent[find(x)] = find(y);
        };

        // Lambda to get all prime factors of a number
        auto getPrimes = [&](int x) {
            vector<int> primes;
            for (int i = 2; i * i <= x; ++i) {
                if (x % i == 0) {
                    primes.push_back(i);
                    while (x % i == 0) x /= i;
                }
            }
            if (x > 1) primes.push_back(x);
            return primes;
        };

        for (int i = 0; i < n; ++i) {
            vector<int> primes = getPrimes(nums[i]);
            for (int prime : primes) {
                if (primeToIndex.count(prime)) {
                    unionSets(i, primeToIndex[prime]);
                }
                primeToIndex[prime] = i;
            }
        }

        unordered_map<int, int> componentSize;
        int maxSize = 0;
        for (int i = 0; i < n; ++i) {
            int root = find(i);
            componentSize[root]++;
            maxSize = max(maxSize, componentSize[root]);
        }

        return maxSize;
    }
};

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