<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>

#include <vector>
using namespace std;

class Solution {
public:
    int reversePairs(vector<int>& nums) {
        if (nums.empty()) {
            return 0;
        }
        return reversePairsRecursive(nums, 0, nums.size() - 1);
    }

private:
    int reversePairsRecursive(vector<int>& nums, int left, int right) {
        if (left == right) {
            return 0;
        }

        int mid = left + (right - left) / 2;
        int n1 = reversePairsRecursive(nums, left, mid);
        int n2 = reversePairsRecursive(nums, mid + 1, right);
        int ret = n1 + n2;

        int i = left;
        int j = mid + 1;

        while (i <= mid) {
            while (j <= right && static_cast<long long>(nums[i]) > 2 * static_cast<long long>(nums[j])) {
                j++;
            }
            ret += j - mid - 1;
            i++;
        }

        // Merge the two sorted halves
        vector<int> sorted(right - left + 1);
        int p1 = left, p2 = mid + 1, p = 0;

        while (p1 <= mid && p2 <= right) {
            if (nums[p1] < nums[p2]) {
                sorted[p++] = nums[p1++];
            } else {
                sorted[p++] = nums[p2++];
            }
        }

        while (p1 <= mid) sorted[p++] = nums[p1++];
        while (p2 <= right) sorted[p++] = nums[p2++];

        // Copy back the sorted array into the original nums array
        for (int k = 0; k < sorted.size(); k++) {
            nums[left + k] = sorted[k];
        }

        return ret;
    }
};

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