<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:
    int partition(vector<int>& arr, int low, int high) {
    // Randomized pivot selection
    int randomPivotIndex = low + rand() % (high - low + 1);
    swap(arr[low], arr[randomPivotIndex]);  // Move the pivot to the beginning

    int pivot = arr[low];
    int i = low;  
    int j = high;

    while (i < j) {
        while (arr[i] <= pivot && i <= high - 1) {
            i++;
        }
        while (arr[j] > pivot && j >= low + 1) {
            j--;
        }
        if (i < j) {
            swap(arr[i], arr[j]);
        }
    }
    swap(arr[low], arr[j]);
    return j;
}

void qs(vector<int>& arr, int low, int high) {
    if (low < high) {
        int pIndex = partition(arr, low, high);
        qs(arr, low, pIndex - 1);
        qs(arr, pIndex + 1, high);
    }
}

vector<int> sortArray(vector<int>& nums) {
    if (nums.empty()) return nums;  // Handle empty input edge case
    qs(nums, 0, nums.size() - 1);
    return nums;
}
};
74041