<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:
    vector<int> sortArray(vector<int>& a) {
        quicksort(a, 0, a.size()-1);
        return a;
    }
    
private:
    int pickmid(vector<int>&a, const vector<int>& inds){
        int maxv = -1;
        int minv = 1e9;
        for(int id: inds){
            maxv = max(maxv, a[id]);
            minv = min(minv, a[id]);
        }
        for(int id: inds){
            if(a[id]>=minv && a[id] <= maxv){
                return id;
            }
        }
        return -1;
    }
    void quicksort(vector<int>&a, int l, int u){
        if(l>=u){
            return;
        }              
        bool sorted = true;
        for(int i=l+1; i<=u; ++i){
            if(a[i]<a[i-1]){
                sorted = false;
                break;
            }
        }
        if(sorted){
            return;
        }
        int randpick1 = l+rand()%(u-l+1);
        int randpick2 = l+rand()%(u-l+1);
        int randpick3 = l+rand()%(u-l+1);
      //  cout<<randpick1<<"..."<<randpick2<<"..."<<randpick3<<endl;
        int cand = pickmid(a, vector<int>{randpick1, randpick2 , randpick3});
        swap(a[u], a[cand]);
        int pivot = a[u];
        int pos = partition(a, l, u, pivot);  
     //   cout<<l<<" "<<pos<<" "<<u<<endl;
     //   cout<<a[l]<<"..."<<a[pos]<<"..."<<a[u]<<endl;
        quicksort(a, l, pos-1);
        quicksort(a, pos+1, u);
    }
    
    int partition(vector<int>&a, int l, int u, int t){        
        int j = l-1;      
        for(int i=l; i<=u; ++i){
            if(a[i]<=t){
                swap(a[i], a[++j]);
            }
        }        
        return j;
    }
};
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