<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 BinaryIndexedTree {
public:
    BinaryIndexedTree(int n) : m_size(n + 1) {
        m_data.resize(m_size);
    }

    void update(int x, int value) {
        for (int i = x; i < m_size; i += lsb(i)) {
            m_data[i] += value;
        }
    }

    int querySum(int x) {
        int sum = 0;
        for (int i = x; i > 0; i -= lsb(i)) {
            sum += m_data[i];
        }

        return sum;
    }

private:
    int m_size;
    std::vector<int> m_data;

    int lsb(int x) {
        return x & (-x);
    }
};

class Solution {
public:
    int reversePairs(vector<int>& nums) {
        int n = static_cast<int>(nums.size());
        if (n == 0) return 0;

        std::vector<long> doubleNums;
        for (const auto num : nums) {
            doubleNums.push_back(2L * (long)num);
        }

        std::set<long> sortedSet(nums.begin(), nums.end());
        sortedSet.insert(doubleNums.begin(), doubleNums.end());

        int index = 1;
        std::unordered_map<long, int> numAndCount;
        for (const auto &num : sortedSet) {
            numAndCount[num] = index++;
        }

        BinaryIndexedTree tree(index);
        int m = static_cast<int>(doubleNums.size());
        long result = 0;
        for (int i = m - 1; i >= 0; --i) {
            result += tree.querySum(numAndCount[doubleNums[i] / 2] - 1);
            tree.update(numAndCount[doubleNums[i]], 1);
        }

        return result;
    }
};
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