merge函数

void merge(vector<int> &vec, int lo, int mid, int hi) {
    vector<int> save;
    //临时数组
    std::copy(vec.begin(), vec.end(), back_inserter(save));
    
    int i = lo, j = mid + 1;

    for (int k = lo; k <= hi; k++) {  //从lo向hi遍历
        if (i > mid) vec[k] = save[j++];      //(1)合并完之后，右半边部分还有剩余     
        else if (j > hi) vec[k] = save[i++];  //(2)合并完之后，左半部分还有剩余  
        
        //以下两部分均为合并完
        else if (save[i] > save[j]) vec[k] = save[j++]; //(3) 不能和（1）（2）同时进入，否则可能越界，因此需要使用else if
        else vec[k] = save[i++];
    }
}

递归方式

void merge_sort(vector<int> &vec, int lo, int hi) {
   if (lo < hi) {
			int mid = (lo + hi) / 2;
			merge_sort(vec, lo, mid);
			merge_sort(vec, mid + 1, hi);
			merge(vec, lo, mid, hi);
 	}
}

迭代方式

void merge_sort(vector<int> &vec, int lo, int hi) {
		for (int seg = 1; seg < vec.size(); seg += seg) //步长，亦或是子数组的size
			for （int i = lo; i < vec.size() - seg; i += seg + seg）{
				int lo = min(i, vec.size());
				int mid = min(i + seg - 1, vec.size());
				int hi = min(i + 2 * seg -1, vec.size() - 1);
				merge (vec, lo, mid, hi);
 		}
}