<p>Given an integer array <code>nums</code>, return <em>the number of <strong>reverse pairs</strong> in the array</em>.</p>

<p>A <strong>reverse pair</strong> is a pair <code>(i, j)</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; j &lt; nums.length</code> and</li>
	<li><code>nums[i] &gt; 2 * nums[j]</code>.</li>
</ul>

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

<pre>
<strong>Input:</strong> nums = [1,3,2,3,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The reverse pairs are:
(1, 4) --&gt; nums[1] = 3, nums[4] = 1, 3 &gt; 2 * 1
(3, 4) --&gt; nums[3] = 3, nums[4] = 1, 3 &gt; 2 * 1
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,4,3,5,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The reverse pairs are:
(1, 4) --&gt; nums[1] = 4, nums[4] = 1, 4 &gt; 2 * 1
(2, 4) --&gt; nums[2] = 3, nums[4] = 1, 3 &gt; 2 * 1
(3, 4) --&gt; nums[3] = 5, nums[4] = 1, 5 &gt; 2 * 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    
    void merge(vector<int>& arr, int s, int e) {
        int mid = (s + e) / 2;
        int len1 = mid - s + 1;
        int len2 = e - mid;
        int *first = new int[len1];
        int *second = new int[len2];
        
        int mainArrayIndex = s;
        for (int i = 0; i < len1; i++) {
            first[i] = arr[mainArrayIndex++];
        }
        
        mainArrayIndex = mid + 1;
        for (int i = 0; i < len2; i++) {
            second[i] = arr[mainArrayIndex++];
        }
        
        int ind1 = 0, ind2 = 0;
        mainArrayIndex = s;
        while (ind1 < len1 && ind2 < len2) {
            if (first[ind1] < second[ind2]) {
                arr[mainArrayIndex++] = first[ind1++];
            } else {
                arr[mainArrayIndex++] = second[ind2++];
            }
        }
        
        while (ind1 < len1) {
            arr[mainArrayIndex++] = first[ind1++];
        }
        
        while (ind2 < len2) {
            arr[mainArrayIndex++] = second[ind2++];
        }
        
        delete[] first;
        delete[] second;
    }
    
    int countPairs(vector<int>& arr, int low, int mid, int high) {
        int right = mid + 1;
        int count = 0;
        for (int i = low; i <= mid; i++) {
            while (right <= high && static_cast<long long>(arr[i]) > 2LL * arr[right])
                right++;
            count += (right - (mid + 1));
        }
        return count;
    }
    
    int mergeSort(vector<int>& nums, int s, int e) {
        int count = 0;
        if (s >= e)
            return count;
        
        int mid = (s + e) / 2;
        count += mergeSort(nums, s, mid);
        count += mergeSort(nums, mid + 1, e);
        count += countPairs(nums, s, mid, e);
        merge(nums, s, e);
        return count;
    }

    int reversePairs(vector<int>& nums) {
        return mergeSort(nums, 0, nums.size() - 1);
    }
};
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