<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>

from typing import List

class Solution:
    def merge(self, nums, l, m, r):
        p1 = l
        p2 = m + 1
        temp = []

        # Merge the two halves
        while p1 <= m and p2 <= r:
            if nums[p1] <= nums[p2]:
                temp.append(nums[p1])
                p1 += 1
            else:
                temp.append(nums[p2])
                p2 += 1
    
        # Collect remaining elements from the left half
        while p1 <= m:
            temp.append(nums[p1])
            p1 += 1
        
        # Collect remaining elements from the right half
        while p2 <= r:
            temp.append(nums[p2])
            p2 += 1

        # Copy the sorted elements back into the original array
        for i in range(l, r + 1):
            nums[i] = temp[i - l]
   
    def sortArray(self, nums: List[int]) -> List[int]:
        # Recursive function for merge sort
        def mergesort(l, r):
            if l >= r:
                return
            
            mid = l + (r - l) // 2

            # Recursively sort both halves
            mergesort(l, mid)
            mergesort(mid + 1, r)

            # Merge the sorted halves
            self.merge(nums, l, mid, r)

        # Start the merge sort process
        mergesort(0, len(nums) - 1)
        return nums

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