<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]:
        # [5,2,3,1]
        # to divide and conquer 
        # to divide the array until there are only 1 value 
        # return
        # the sorted array 
        # merge the sorted array to a temporary array
        # copy the temporary array to the nums
        def merge_sort(left, right):
            if left >= right: return
            # divide
            m = left + (right - left) // 2
            merge_sort(left, m)
            merge_sort(m+1, right)
            # merge
            l, r = left, m + 1
            tmp = []
            while l <= m and r <= right:
                if nums[l] < nums[r]:
                    tmp.append(nums[l])
                    l += 1
                else:
                    tmp.append(nums[r])
                    r += 1
            while l <= m:
                tmp.append(nums[l])
                l += 1
            while r <= right:
                tmp.append(nums[r])
                r += 1
            # copy
            for i in range(left, right+1):
                nums[i] = tmp[i - left]
        merge_sort(0, len(nums) - 1)
        return nums
        
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