<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:
    def sortArray(self, nums: List[int]) -> List[int]:

        # merge sort 

        def merge_sort(nums):

            if len(nums) > 1:

                mid = len(nums)//2
                left = nums[0:mid]
                right = nums[mid:]

                # divide 
                merge_sort(left)
                merge_sort(right)

                # merge
                i, j, k = 0, 0, 0
                while i < len(left) and j < len(right):
                    if left[i] < right[j]:
                        nums[k] = left[i]
                        i += 1
                    else:
                        nums[k] = right[j]
                        j += 1
                    k += 1
                
                if len(left) > 0:
                    while i < len(left):
                        nums[k] = left[i]
                        i += 1
                        k += 1
                
                while j < len(right):
                    nums[k] = right[j]
                    j += 1
                    k += 1
        
        merge_sort(nums)
        return nums
        
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