<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>a,visited(n,0);        
		// Sorting the array is important in this approach
        sort(changed.begin(), changed.end());
		
        int i=0,j=1;
        while((i<n && j < n)){
            if(visited[i] == 1){   // Keeping a track of all elements
                i++;              // make sure these elements are no picked up again
                if(i==j)          // jth index is for finding the double value of ith index element
                    j++;
                continue;
            }
            if(visited[j] == 1){        
                j++;
                continue;
            }
		    if(changed[j] == 2*changed[i]){ // If the doubled element is found then push back the element 
                a.push_back(changed[i]);
                visited[i]++;              // Mark the element in Visited array
                visited[j]++;
                i++;
                j++;
            }
            else{ // If element not found increment the jth index
                j++;
            }
        }
        
        if(2*a.size() == changed.size())  // array obtained should be of exactly half size that of Changed array
            return a;
        return {};
    }
};
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