<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) {
        int n = changed.size();
        vector<int> result;
        if (n%2!=0){
            return {};
        }
        unordered_map<int,int> freq;
        for (int i:changed){
            freq[i]++;
        }
        sort(changed.begin(), changed.end());
        for(int i:changed){
            if(freq[i]<=freq[i*2] && freq[i]!=0)
            {
                if(i==0)
                {
                    if(freq[i]%2!=0)
                        continue;
                    else{
                        for(int j=0;j<freq[i]/2;j++)
                        {
                            result.push_back(i);
                        }
                        freq[i]=0;
                    }
                }
                for(int j=0;j<freq[i];j++)
                {
                    result.push_back(i);
                }
                freq[i*2]-=freq[i];
                freq[i]=0; 
            }
        }
        if (result.size()!=n/2){
            return {};
        }
        return result;
    }
};
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