<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:
    void print_vec(vector<int>& a) {
        for(int x : a) cout << x << " ";
        cout << "\n";
    }

    vector<int> merge_sort(vector<int>& nums) {
        int n = nums.size();
        if(n == 1) return nums;
        if(n == 2) {
            if(nums[0] > nums[1]) swap(nums[0], nums[1]);
            return nums;
        }
        int sz_a = n / 2;
        int sz_b = n - sz_a;
        vector<int> a(sz_a), b(sz_b);
        for(int i = 0; i < n / 2; i++) a[i] = nums[i];
        for(int i = n / 2; i < n; i++) b[i - n / 2] = nums[i];

        vector<int> res1 = merge_sort(a);
        vector<int> res2 = merge_sort(b);

        //print_vec(res1);
        //print_vec(res2);
        for(int i = 0, j = 0, k = 0; k < n; k++) {
            if(i == sz_a) {
                nums[k] = b[j++];
                continue;
            }
            if(j == sz_b) {
                nums[k] = a[i++];
                continue;
            }
            //cout << i << " " << j << "\n";
            if(a[i] < b[j]) {
                nums[k] = a[i];
                i++;
            } else {
                nums[k] = b[j];
                j++;
            }
        }

        return nums;
    }

    vector<int> sortArray(vector<int>& nums) {
        return merge_sort(nums);
    }
};
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