<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 mergeSort2(self, nums, left, right):
        if right - left == 1:
            return
        mid = (left + right) // 2
        self.mergeSort2(nums, left, mid)
        self.mergeSort2(nums, mid, right)
        buf = []
        for i in range(left, mid):
            buf.append(nums[i])
        for i in range(right - 1, mid - 1, - 1):
            buf.append(nums[i])
        l_idx, r_idx = 0, len(buf) - 1
        for i in range(left, right):
            if buf[l_idx] < buf[r_idx]:
                nums[i] = buf[l_idx]
                l_idx += 1
            else:
                nums[i] = buf[r_idx]
                r_idx -= 1

    
    def quickSort(self, nums, left, right):
        if right - left <= 1:
            return

        # pivot_idx = (left + right) // 2
        # 乱択、成功テストが11 -> 17に
        pivot_idx = random.randrange(left, right)
        pivot = nums[pivot_idx]

        nums[pivot_idx], nums[right - 1] = nums[right - 1], nums[pivot_idx]

        i = left
        for j in range(left, right - 1):
            if nums[j] < pivot:
                nums[i], nums[j] = nums[j], nums[i]
                i += 1
        nums[i], nums[right - 1] = nums[right - 1], nums[i]

        self.quickSort(nums, left, i)
        self.quickSort(nums, i + 1, right)

             
    def mergeSort(self, nums, left, right):
        if right - left == 1:
            return

        # split
        mid = (left + right) // 2
        self.mergeSort(nums, mid, right)
        self.mergeSort(nums, left, mid)

        # merge
        buf = []
        for i in range(left, mid):
            buf.append(nums[i])
        for i in range(right - 1, mid - 1, - 1):
            buf.append(nums[i])
        
        l_idx, r_idx = 0, len(buf) - 1
        for i in range(left, right):
            if buf[l_idx] < buf[r_idx]:
                nums[i] = buf[l_idx]
                l_idx += 1
            else:
                nums[i] = buf[r_idx]
                r_idx -= 1

    def sortArray(self, nums: List[int]) -> List[int]:
        # merge sort
        self.mergeSort2(nums, 0, len(nums))

        # TLE
        # self.quickSort(nums, 0, len(nums))
        return nums

        
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