<p>An integer array <code>original</code> is transformed into a <strong>doubled</strong> array <code>changed</code> by appending <strong>twice the value</strong> of every element in <code>original</code>, and then randomly <strong>shuffling</strong> the resulting array.</p>

<p>Given an array <code>changed</code>, return <code>original</code><em> if </em><code>changed</code><em> is a <strong>doubled</strong> array. If </em><code>changed</code><em> is not a <strong>doubled</strong> array, return an empty array. The elements in</em> <code>original</code> <em>may be returned in <strong>any</strong> order</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> changed = [1,3,4,2,6,8]
<strong>Output:</strong> [1,3,4]
<strong>Explanation:</strong> One possible original array could be [1,3,4]:
- Twice the value of 1 is 1 * 2 = 2.
- Twice the value of 3 is 3 * 2 = 6.
- Twice the value of 4 is 4 * 2 = 8.
Other original arrays could be [4,3,1] or [3,1,4].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> changed = [6,3,0,1]
<strong>Output:</strong> []
<strong>Explanation:</strong> changed is not a doubled array.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> changed = [1]
<strong>Output:</strong> []
<strong>Explanation:</strong> changed is not a doubled array.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= changed.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= changed[i] &lt;= 10<sup>5</sup></code></li>
</ul>

#include <vector>
#include <set>
#include <algorithm>

class Solution {
public:
    #include <vector>
#include <unordered_map>
#include <algorithm>

std::vector<int> findOriginalArray(std::vector<int>& d) {
    std::unordered_map<int, int> count;
    std::vector<int> ans;

    // Count the frequency of each number
    for (int num : d) {
        count[num]++;
    }

    // Sort the array to handle the smallest numbers first
    std::sort(d.begin(), d.end());

    // Iterate through the sorted array
    for (int num : d) {
        if (count[num] == 0) {
            continue;
        }

        if (count[2 * num] == 0) {
            return {}; 
        }

        ans.push_back(num);
        count[num]--;
        count[2 * num]--;
    }

    return ans.size() * 2 == d.size() ? ans : std::vector<int>{};
}

};

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