<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 Node{
    public:
    int l;
    int r;
    vector<int> arr;

    Node()
    {
        this->l = 0;
        this->r = 0;
        this->arr = vector<int>();
    }

    Node(int l, int r)
    {
        this->l = l;
        this->r = r;
        this->arr.assign(r-l+1, 0);
    }
};

class SegTree{
    public:
    vector<Node> t;

    SegTree(int n, vector<int>& nums)
    {
        t.assign(2*n, Node());

        build(0, 0, n-1, nums);
    }

    void build(int i, int l, int r, vector<int>& nums)
    {
        if(l > r)
        {
            return;
        }

        if(l == r)
        {
            t[i] = Node(l, r);
            t[i].arr[0] = nums[l];
            return;
        }

        t[i] = Node(l, r);
        int mid = l + (r-l)/2;
        build(i+1, l, mid, nums);
        build(i+2*(mid-l+1), mid+1, r, nums);
        merge(t[i], t[i+1], t[i+2*(mid-l+1)]);
    }

    void merge(Node& n1, Node& n2, Node& n3)
    {
        int i = 0;
        int j = 0;
        int k = 0;

        int n = n2.arr.size();
        int m = n3.arr.size();

        while(i < n && j < m)
        {
            if(n2.arr[i] <= n3.arr[j])
            {
                n1.arr[k] = n2.arr[i];
                i++;
                k++;
            }
            else
            {
                n1.arr[k] = n3.arr[j];
                j++;
                k++;
            }
        }

        while(i < n)
        {
            n1.arr[k] = n2.arr[i];
            i++;
            k++;
        }

        while(j < m)
        {
            n1.arr[k] = n3.arr[j];
            j++;
            k++;
        }
    }

    vector<int> ans()
    {
        return t[0].arr;
    }
};

class Solution {
public:
    vector<int> sortArray(vector<int>& nums) {
        int n = nums.size();
        SegTree st(n, nums);
        return st.ans();
    }
};
202523