<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:
    vector<int> sortArray(vector<int>& nums) {
        Sort(nums, 0, nums.size() - 1);
        return nums;
    }
private:
    void Sort(vector<int> &nums, int start, int end) {
        if (start >= end) {
            return;
        } else if (start == end - 1) {
            int smaller = std::min(nums[start], nums[end]);
            int larger = std::max(nums[start], nums[end]);
            nums[start] = smaller;
            nums[end] = larger;
        }

        int mid = start + (end - start) / 2;
        Sort(nums, start, mid);
        Sort(nums, mid + 1, end);

        vector<int> sorted;
        int i = start, j = mid + 1;
        for (int x = 0; x < end - start + 1; ++x) {
            if (i >= mid + 1 || (j <= end && nums[j] < nums[i])) {
                sorted.push_back(nums[j]);
                ++j;
            } else {
                sorted.push_back(nums[i]);
                ++i;
            }
        }

        for (int x = 0; x < end - start + 1; ++x) nums[start + x] = sorted[x];
    }
};
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