<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>

// 912. Sort an Array
class Solution {
public:
    vector<int> sortArray(vector<int>& nums) {
        mergeSort(nums, 0, nums.size()-1);
        return nums;
    }

private:
    void mergeSort(vector<int>& nums, int l, int h) {
        if (l>=h) return;
        if (h-l==1 && nums[l]>nums[h]) {
            swap(nums[l], nums[h]);
            return;
        }
        int m = (h+l)/2;
        mergeSort(nums, l, m);
        mergeSort(nums, m+1, h);
        mergeArray(nums, l, m, h);
    }

    void mergeArray(vector<int>& nums, int lo, int mid, int hi) {
        vector<int> lhs(nums.begin()+lo, nums.begin()+mid+1);
        vector<int> rhs(nums.begin()+mid+1, nums.begin()+hi+1);        

        int l=0, r=0, p=lo;
        while (l<lhs.size() && r<rhs.size()) {
            if (lhs[l] < rhs[r]) nums[p] = lhs[l++];
            else nums[p] = rhs[r++];
            p++;
        }
        while (l<lhs.size()) nums[p++] = lhs[l++];
        while (r<rhs.size()) nums[p++] = rhs[r++];
    }
};
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