<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 {
    //Approach: implement merge sort with an iterative approach 
private:
    vector<int> merge(vector<int>& nums, int s1,int e1,int s2,int e2){
        int i,j;
        i=s1;
        j=s2;
        
        vector<int> result;
        while (i<=e1 && j<=e2){
            if (nums[i]<=nums[j]){
                result.push_back(nums[i++]);
            }   
            else{
                result.push_back(nums[j++]);
            }
        }
        while (i<=e1){
            result.push_back(nums[i++]);            
        }
        while (j<=e2){
            result.push_back(nums[j++]);            
        }
        return result;
    }
public:
    vector<int> sortArray(vector<int>& nums){

        int size=1;
        int n=nums.size();
        for (int size=1; size<n;size*=2){
            for (int i=0;i<n;i+=2*size){
                int s1=i;
                int e1=min(i+size-1,n-1);
                if (e1<n-1){
                    int s2=min(i+size,n-1); 
                    int e2=min(s2+size-1,n-1);
                    //cout <<"s1:"<<s1<<" e1:"<<e1<<" s2:"<<s2<<" e2:"<<e2<<endl;
                    vector<int> m=merge(nums,s1,e1,s2,e2);
                    copy(m.begin(), m.end(), nums.begin()+i);
                }          
            }            
        }
        return nums;
    }
};
192106