<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>

class Solution {
public:
    vector<int> findOriginalArray(vector<int>& changed) {
        map<int, int> freq;
        for (auto x : changed) {
            freq[x]++;
        }

        vector<int> ans;
        bool doubled = changed.size() % 2 == 0;
        for (auto& x : freq) {
            if (!x.second) continue;
            if (x.first == 0) {
                if (x.second % 2) {
                    doubled = false;
                    break;
                }
                
                if (doubled) {
                    for (int i = 0; i < x.second / 2; i++) {
                        ans.push_back(x.first);
                    }
                }
            } else {
                for (int i = 0; i < x.second; i++) {
                    ans.push_back(x.first);
                }

                freq[x.first * 2] -= x.second; 
                x.second = 0;
                if (freq[x.first * 2] < 0) {
                    doubled = false;
                    break;
                } 
            }
        } 
        
        if (doubled) {
            return ans;
        } else {
            return {};
        }
    }
};
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