<p>Given an integer array of even length <code>arr</code>, return <code>true</code><em> if it is possible to reorder </em><code>arr</code><em> such that </em><code>arr[2 * i + 1] = 2 * arr[2 * i]</code><em> for every </em><code>0 &lt;= i &lt; len(arr) / 2</code><em>, or </em><code>false</code><em> otherwise</em>.</p>

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

<pre>
<strong>Input:</strong> arr = [3,1,3,6]
<strong>Output:</strong> false
</pre>

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

<pre>
<strong>Input:</strong> arr = [2,1,2,6]
<strong>Output:</strong> false
</pre>

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

<pre>
<strong>Input:</strong> arr = [4,-2,2,-4]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can take two groups, [-2,-4] and [2,4] to form [-2,-4,2,4] or [2,4,-2,-4].
</pre>

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

<ul>
	<li><code>2 &lt;= arr.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>arr.length</code> is even.</li>
	<li><code>-10<sup>5</sup> &lt;= arr[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    bool canReorderDoubled(vector<int>& arr) {
        int size = arr.size();

        sort(arr.begin(), arr.end(), [](int &a, int&b){
            return abs(a) < abs(b);
        });

        vector<bool> flag(size, false);

        int count = 0;
        int index = 0;

        while (count < size / 2)
        {
            while(flag[index])
                index++;

            flag[index] = true;
            int value = 2 * arr[index];
            
            if (abs(arr[size - 1]) < abs(value))
            {
                return false;
            }

            int start = index + 1;
            int end = size - 1;

            while (start < end)
            {
                int mid = (start + end) / 2;

                if (abs(arr[mid]) < abs(value))
                {
                    start = mid + 1;
                }
                else
                {
                    end = mid;
                }
            }

            while (end < size)
            {
                if ((arr[end] == value) && (flag[end] == false))
                {
                    flag[end] = true;
                    break;
                }
                else if (abs(arr[end]) == abs(value))
                {
                    end++;
                }
                else
                {
                    return false;
                }
            }

            if (end >= size)
            {
                return false;
            }

            count++;
        }

        return true;
    }
};
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