<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) {
        mergeSort(0, nums.size()-1, nums);
        return nums;
    }
    void mergeSort(int low, int high, vector<int>& nums){
        // base cases
        // cout << "(" << low << ", " << high << ")" << endl;
        if(low == high) return;
        else if((low+1) == high){
            cout << "hi" << endl;
            if(nums[low] > nums[high]){
                std::swap(nums[low], nums[high]);
            }
            return;
        }
        else{
            int mid = low + (high-low)/2;
            mergeSort(low, mid, nums);
            mergeSort(mid+1, high, nums);
            // merge
            int p1 = low;
            int p2 = mid+1;
            // cout << "p1: " << p1 << " p2: " << p2 << endl;
            vector<int> sorted(high-low+1);
            // cout << "inside" << endl;
            for(int i = 0; i < sorted.size(); i++){
                // cout << "p1: " << p1 << " p2: " << p2 << endl;
                if(p2 > high || (p1 <= mid && nums[p1] <= nums[p2])){
                    sorted[i] = nums[p1];
                    p1++;
                }
                else{
                    sorted[i] = nums[p2];
                    p2++;
                }
            }
            int sorted_index = 0;
            for(int i = low; i <= high; i++){
                nums[i] = sorted[sorted_index];
                sorted_index++;
            }
        }
    }
};
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