Reverse Pairs
<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>
Binary Indexed Tree; Segment Tree; Array; Binary Search; Divide and Conquer; Ordered Set; Merge Sort
func reversePairs(nums []int) int {
	n := len(nums)
	t := make([]int, n)
	var mergeSort func(l, r int) int
	mergeSort = func(l, r int) int {
		if l >= r {
			return 0
		}
		mid := (l + r) >> 1
		ans := mergeSort(l, mid) + mergeSort(mid+1, r)
		i, j, k := l, mid+1, 0
		for i <= mid && j <= r {
			if nums[i] <= nums[j]*2 {
				i++
			} else {
				ans += mid - i + 1
				j++
			}
		}
		i, j = l, mid+1
		for i <= mid && j <= r {
			if nums[i] <= nums[j] {
				t[k] = nums[i]
				k, i = k+1, i+1
			} else {
				t[k] = nums[j]
				k, j = k+1, j+1
			}
		}
		for ; i <= mid; i, k = i+1, k+1 {
			t[k] = nums[i]
		}
		for ; j <= r; j, k = j+1, k+1 {
			t[k] = nums[j]
		}
		for i = l; i <= r; i++ {
			nums[i] = t[i-l]
		}
		return ans
	}
	return mergeSort(0, n-1)
}