<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 merge_array(vector<int> &x, vector<int> &y, vector<int> &a, int s, int e)
    {
    int mid = s+(e-s)/2;
    int i=s;
    int j=s;
    int k=s;

    while(i<=mid && j<=e-mid-1)
    {
        if(x[i]<y[j])
        {
        a[k] = x[i];
        i++;
        k++;
        }
        else
        {
        a[k] = y[j];
        j++;
        k++;
        }
    }
    // Copy rest of the elements
    while(i<=mid)
    {
        a[k] = x[i];
        k++;
        i++;
    }
    // Copy rest of the elements
    while(j<=e-mid-1)
    {
        a[k] = y[j];
        k++;
        j++;
    }


    }
    void merge_sort(vector<int> &arr, int s, int e)
    {
    // Base Case
    if(s>=e) return;

    int mid = s+(e-s)/2;
    
    vector<int> x(s+e+1), y(s+e+1);

    // Copy elements
    for(int i=0;i<mid+1;i++)
        x[i] = arr[i];

    // Sort left side
    merge_sort(x,s,mid);
    
    // Copy elements
    for(int i=mid+1;i<=e;i++)
        y[i-mid-1] = arr[i];

    // Sort Right side
    merge_sort(y,s,e-mid-1);

    merge_array(x,y,arr,s,e);

    }

    vector<int> sortArray(vector<int>& nums) {
        int n = nums.size();
        merge_sort(nums,0,n-1);
        return nums;    
    }
};
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