mergesort

Merge Sort

• stable sort
• most common implementation does not sort in place
• external merge sort

void mergearray(vector<int> &a, int low, int mid, int high, vector<int> &tmp){
    // merge a[low,mid] and a[low+1,high]
    int i=low, j=mid+1;
    int k=0;
    while (i<=mid && j<=high){
        if (a[i]<a[j]) tmp[k++]=a[i++];
        else tmp[k++]=a[j++];
    }
    while (i<=mid) tmp[k++]=a[i++];
    while (j<=high) tmp[k++]=a[j++];
    // copy from tmp back to original array
    for (i=0;i<k;++i) a[low+i] = tmp[i];
}

void mergesort(vector<int> &a, int low, int high, vector<int> &tmp){
    if (low>=high) return;
    int mid=(low+high)/2;
    mergesort(a,low,mid,tmp);
    mergesort(a,mid+1,high,tmp);
    mergearray(a,low,mid,high,tmp);
}

int main() {
    vector<int> a={1,5,8,3,2};
    int n=a.size();
    vector<int> tmp(n);
    mergesort(a,0,n-1,tmp);
    for (auto x:a) cout<<x<<' ';
    return 0;
}

Time Complexity: O(nlogn)