<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> a;
    // I want to try to code merge sort as a divide and conquer approach
    // Just use indices and then pass the whole array
    // Interval from [i, j)

    void swap(int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    void merge(int i, int j) {
        if (j - i <= 2) {
            if (a[j - 1] < a[i]) {
                this->swap(i, j - 1);
            }
            return;
        }
        this->merge(i, (j + i) / 2);
        this->merge((j + i) / 2, j);
        int x = i;
        int y = (j + i) / 2;
        vector<int> b;
        for (int z = i; z < j; z++) {
            if (y >= j || x < (i + j) / 2 && a[x] < a[y]) {
                b.push_back(a[x]);
                x++;
            } else {
                b.push_back(a[y]);
                y++;
            }
        }
        for (int z = i; z < j; z++) {
            a[z] = b[z - i];
        }
    }


    vector<int> sortArray(vector<int>& nums) {
        int n = nums.size();
        a = nums;
        this->merge(0, n);
        return a;
    }
};
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