<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:
    static void sort4(const vector<int>::iterator begin,
                      const vector<int>::iterator& end) {
        assert(distance(begin, end) == 4);

        if (*(begin + 0) > *(begin + 2))
            swap(*(begin + 0), *(begin + 2));

        if (*(begin + 1) > *(begin + 3))
            swap(*(begin + 1), *(begin + 3));

        if (*(begin + 0) > *(begin + 1))
            swap(*(begin + 0), *(begin + 1));

        if (*(begin + 2) > *(begin + 3))
            swap(*(begin + 2), *(begin + 3));

        if (*(begin + 1) > *(begin + 2))
            swap(*(begin + 1), *(begin + 2));
    }
    static void sort3(const vector<int>::iterator begin,
                      const vector<int>::iterator& end) {
        assert(distance(begin, end) == 3);

        if (*(begin + 0) > *(begin + 2))
            swap(*(begin + 0), *(begin + 2));

        if (*(begin + 0) > *(begin + 1))
            swap(*(begin + 0), *(begin + 1));

        if (*(begin + 1) > *(begin + 2))
            swap(*(begin + 1), *(begin + 2));
    }
    void mergeSort(const vector<int>::iterator begin,
                   const vector<int>::iterator& end) {
        const int d = distance(begin, end);
        switch (d) {
        case 4:
            sort4(begin, end);
            return;
        case 3:
            sort3(begin, end);
            return;
        case 2:
            if (*begin > *(begin + 1))
                swap(*begin, *(begin + 1));

            return;
        case 1:
            return;
        case 0:
            return;
        default:
        }
        const auto mid = begin + (d / 2);
        mergeSort(begin, mid);
        mergeSort(mid, end);
        vector<int> result(d);
        auto i1 = begin;
        auto i2 = mid;
        auto o = result.begin();
        while ((i1 != mid) and (i2 != end)) {
            if (*i1 < *i2) {
                *(o++) = *(i1++);
            } else {
                *(o++) = *(i2++);
            }
        }
        while (i1 != mid)
            *(o++) = *(i1++);

        while (i2 != end)
            *(o++) = *(i2++);

        copy(result.begin(), result.end(), begin);
    }
    vector<int> sortArray(vector<int>& nums) {
        mergeSort(nums.begin(), nums.end());
        return move(nums);
    }
};
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