<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 {
private:
    vector<int> find_pivot(int i, int j, vector<int> &nums) {
        int pivot = nums[i+(rand()%(j-i))];
        int low = i, high = j;
        for(int k=i; k<=j; ++k) {
            if(nums[k]<pivot) swap(nums[k], nums[low++]);
        }

        for(int k=j; k>=low; --k) {
            if(nums[k]>pivot) swap(nums[k], nums[high--]);
        }
        // int low = i, high = j+1, idx = i+1;
        // cout<<"In range ("<<i<<", "<<j<<"), pivot to be set : "<<pivot<<endl;
        // cout<<"Initially elements :";
        // for(int k=i; k<=j; ++k) cout<<nums[k]<<" ";
        // cout<<endl;
        // while(idx<high) {
        //     if(nums[idx]>pivot) {
        //         cout<<"Swapping "<<idx<<" with "<<(high-1)<<endl;
        //         swap(nums[idx], nums[--high]);
        //     } else {
        //         cout<<"Swapping "<<idx<<" with "<<low<<endl;
        //         swap(nums[idx++], nums[low++]);
        //         // idx++;
        //     }
        // }

        // nums[idx-1] = pivot;
        // cout<<"Returning pivot as "<<(idx-1)<<endl<<endl;
        // return idx-1;
        return {low-1, high+1};
    }
    void quick(int i, int j, vector<int> &nums) {
        if(i>=j) return;

        vector<int> pivot = find_pivot(i, j, nums);
        quick(i, pivot[0], nums);
        quick(pivot[1], j, nums);
    }
public:
    vector<int> sortArray(vector<int>& nums) {
        quick(0, nums.size()-1, nums);
        // sort(nums.begin(), nums.end());
        return nums;
    }
};
160853