<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>

#include <vector>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <cmath>

using namespace std;

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

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

    int find(int x) {
        if (parent[x] != x)
            parent[x] = find(parent[x]);
        return parent[x];
    }

    int unionSets(int x, int y) {
        int px = find(x);
        int py = find(y);

        if (px == py) return px;

        if (size[px] > size[py]) swap(px, py);

        parent[px] = py;
        size[py] += size[px];
        return py;
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& A) {
        int maxValue = *max_element(A.begin(), A.end());
        DisjointSetUnion dsu(maxValue);

        unordered_map<int, int> numFactorMap;

        for (int num : A) {
            vector<int> primeFactors = primeDecompose(num);
            numFactorMap[num] = primeFactors[0];
            for (size_t i = 0; i < primeFactors.size() - 1; ++i) {
                dsu.unionSets(primeFactors[i], primeFactors[i + 1]);
            }
        }

        int maxGroupSize = 0;
        unordered_map<int, int> groupCount;

        for (int num : A) {
            int groupId = dsu.find(numFactorMap[num]);
            groupCount[groupId]++;
            maxGroupSize = max(maxGroupSize, groupCount[groupId]);
        }

        return maxGroupSize;
    }

protected:
    vector<int> primeDecompose(int num) {
        vector<int> primeFactors;
        int factor = 2;
        while (num >= factor * factor) {
            if (num % factor == 0) {
                primeFactors.push_back(factor);
                num /= factor;
            } else {
                factor += 1;
            }
        }
        primeFactors.push_back(num);
        return primeFactors;
    }
};

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