<p>Given an array of integers <code>nums</code>, sort the array in ascending order and return it.</p>

<p>You must solve the problem <strong>without using any built-in</strong> functions in <code>O(nlog(n))</code> time complexity and with the smallest space complexity possible.</p>

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

<pre>
<strong>Input:</strong> nums = [5,2,3,1]
<strong>Output:</strong> [1,2,3,5]
<strong>Explanation:</strong> After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5).
</pre>

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

<pre>
<strong>Input:</strong> nums = [5,1,1,2,0,0]
<strong>Output:</strong> [0,0,1,1,2,5]
<strong>Explanation:</strong> Note that the values of nums are not necessairly unique.
</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>-5 * 10<sup>4</sup> &lt;= nums[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    template <typename RandomIt>
    void MergeSort(RandomIt range_begin, RandomIt range_end) {
        const int range_length = range_end - range_begin;
        
        if (range_length < 2) return;

        std::vector<typename RandomIt::value_type> elements(make_move_iterator(range_begin), make_move_iterator(range_end));

        auto one_third = begin(elements) + range_length / 3;
        auto two_third = begin(elements) + range_length * 2 / 3;

        MergeSort(begin(elements), one_third);
        MergeSort(one_third, two_third);
        MergeSort(two_third, end(elements));

        std::vector<typename RandomIt::value_type> interim_result;
        merge(make_move_iterator(begin(elements)), make_move_iterator(one_third), make_move_iterator(one_third), make_move_iterator(two_third), back_inserter(interim_result));

        merge(make_move_iterator(begin(interim_result)), make_move_iterator(end(interim_result)), make_move_iterator(two_third), make_move_iterator(end(elements)), range_begin);
    }

    std::vector<int> sortArray(std::vector<int>& nums) {
        MergeSort(nums.begin(), nums.end());
        return nums;
    }
};
202523