<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:
    void merge(vector<int>&elements,int l,int mid,int h)
    {
        int size1 = mid-l+1;
        int size2 = h-mid;
        vector<int> temp1(size1);
        vector<int> temp2(size2);
        for(int i=0; i<size1; i++)
            temp1[i] = elements[l + i];
        for(int j=0; j<size2; j++)
            temp2[j] = elements[mid + 1 + j];
        int i = 0, j = 0, k = l;
        while(i < size1 and j < size2)
        {
            if(temp1[i] <= temp2[j])
                elements[k++] = temp1[i++];
            else
                elements[k++] = temp2[j++];
        }
        while(i < size1)
            elements[k++] = temp1[i++];
        while(j < size2)
            elements[k++] = temp2[j++];

    }
    void mergeSort(vector<int>&elements, int l, int h)
    {
        if(l < h)
        {
            int mid = (l+h)/2;
            mergeSort(elements, l, mid);
            mergeSort(elements, mid+1, h);
            merge(elements, l, mid, h);
        }
    }
    void insertionSort(vector<int> &nums)
    {
        for(int i=1; i<nums.size(); i++)
        {
            int temp = nums[i];
            int j = i-1;
            while(j > -1 and nums[j] > temp)
            {
                nums[j+1] = nums[j];
                --j;
            }
            nums[j+1] = temp;
        }
    }
    
    int median(vector<int>& arr, int low, int high) {
        int mid = low + (high - low) / 2;
        if (arr[low] > arr[mid])
            swap(arr[low], arr[mid]);
        if (arr[low] > arr[high])
            swap(arr[low], arr[high]);
        if (arr[mid] > arr[high])
            swap(arr[mid], arr[high]);
        return arr[mid];
    }
    int partition(vector<int> &nums, int l, int h)
    {
        int pivot = median(nums,l,h);
        int i = l-1;
        for(int k=0; k<h; k++)
        {
            if(nums[k] < pivot)
            {
                ++i;
                std::swap(nums[i], nums[k]);
            }
        }
        std::swap(nums[i+1], nums[h]);
        return i+1;
    }
    void quickSort(vector<int> &nums, int l, int h)
    {
        if(l < h)
        {
            int pos = partition(nums, l, h);
            quickSort(nums,l,pos-1);
            quickSort(nums,pos+1,h);
        }
    }
public:
    vector<int> sortArray(vector<int>& nums) {
        if(nums.size() < 50)
            insertionSort(nums);
        else
            mergeSort(nums, 0, nums.size()-1);
        return nums;
    }
};
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