<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</pre>

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

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

class Solution {
public:
    vector<int> countSmaller(std::span<const int> nums) {
        std::vector<int> res;
        res.resize(nums.size());
        std::vector<int> temp_nums;
        temp_nums.resize(nums.size());
        countSmallerImpl(nums, res, temp_nums);
        return res;
    }

    void countSmallerImpl(const std::span<const int> nums,
                     const std::span<int> res,
                     const std::span<int> temp_nums) {

        if (nums.size() <= 8) {
            for (size_t i = 0; i < nums.size(); ++i) {
                size_t num_smaller = 0;
                for (size_t j = i + 1; j < nums.size(); ++j)
                    if (nums[j] < nums[i])
                        ++num_smaller;
                res[i] = num_smaller;
            }
        } else {

            const auto middle = nums.size() / 2;
            const std::span<const int> left_nums = nums.subspan(0, middle);
            const std::span<const int> right_nums= nums.subspan(middle);

            countSmallerImpl(left_nums, res.subspan(0, middle), temp_nums.subspan(0, middle));
            countSmallerImpl(right_nums, res.subspan(middle), temp_nums.subspan(middle));

            // Modify left result.

            auto right_nums_sorted= temp_nums.subspan(middle);
            for(size_t i= 0; i < right_nums_sorted.size(); ++i)
                right_nums_sorted[i]= right_nums[i];

            std::sort(right_nums_sorted.begin(), right_nums_sorted.end());

            for (size_t i = 0; i < middle; ++i) {
                const auto it = std::lower_bound(
                    right_nums_sorted.begin(), right_nums_sorted.end(), left_nums[i]);
                res[i] += it - right_nums_sorted.begin();
            }
        }
    }
};
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