<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 len = changed.size();
        if (len % 2 == 1) {
            return {};
        }

        sort(changed.begin(), changed.end());

        unordered_map<int, int> cnt;
        for (int i: changed) {
            cout << i << " ";
            cnt[i]++;
        }


        vector<int> original_array;
        for (int i : changed) {
            if (i == 0 and cnt[i] >= 2) {
                original_array.push_back(i);
                cnt[i] -= 2;
                continue;
            }
            cnt[i]--;
            if (i != 0 and cnt[i] >= 0 and cnt[2 * i] > 0) {
                original_array.push_back(i);
                cnt[2 * i]--;
            }
        }

        bool is_valid = original_array.size() == len / 2;

        return is_valid ? original_array : vector<int>();
    }
};

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